2604:
2257:
2232:
3207:
1931:
2895:
2599:{\displaystyle {\frac {\partial \langle {{\bf {x}}|{\hat {\rho }}_{t}|{\bf {y}}}\rangle }{\partial t}}=-{\frac {i}{\hbar }}\langle {{\bf {x}}|\left|{\bf {y}}}\rangle -\lambda {\frac {m^{2}}{m_{0}^{2}}}\left(1-e^{-{\tfrac {({\bf {x}}-{\bf {y}})^{2}}{4r_{C}^{2}}}}\right)\langle {{\bf {x}}|{\hat {\rho }}_{t}|{\bf {y}}}\rangle ,}
4569:
3748:
3563:. If a particle is electrically charged, the action of the coupling with the collapse noise will induce the emission of radiation. This result is in net contrast with the predictions of quantum mechanics, where no radiation is expected from a free particle. The predicted CSL-induced emission rate at frequency
2943:
Contrary to most other proposed solutions of the measurement problem, collapse models are experimentally testable. Experiments testing the CSL model can be divided in two classes: interferometric and non-interferometric experiments, which respectively probe direct and indirect effects of the collapse
2955:
experiments can detect the direct action of the collapse, which is to localize the wavefunction in space. They include all experiments where a superposition is generated and, after some time, its interference pattern is probed. The action of CSL is a reduction of the interference contrast, which is
3555:
Non-interferometric experiments consist in CSL tests, which are not based on the preparation of a superposition. They exploit an indirect effect of the collapse, which consists in a
Brownian motion induced by the interaction with the collapse noise. The effect of this noise amounts to an effective
2959:
4905:
4285:
2697:
1247:
6804:
Belli, Sebastiano; Bonsignori, Riccarda; D'Auria, Giuseppe; Fant, Lorenzo; Martini, Mirco; Peirone, Simone; Donadi, Sandro; Bassi, Angelo (2016-07-12). "Entangling macroscopic diamonds at room temperature: Bounds on the continuous-spontaneous-localization parameters".
7267:
Curceanu, C.; Bartalucci, S.; Bassi, A.; Bazzi, M.; Bertolucci, S.; Berucci, C.; Bragadireanu, A. M.; Cargnelli, M.; Clozza, A.; De Paolis, L.; Di Matteo, S. (2016-03-01). "Spontaneously
Emitted X-rays: An Experimental Signature of the Dynamical Reduction Models".
1046:
4375:
3609:
2227:{\displaystyle {\frac {\operatorname {d} \!{\hat {\rho }}_{t}}{\operatorname {d} \!t}}=-{\frac {i}{\hbar }}\left-{\frac {\lambda }{2m_{0}^{2}}}\int \operatorname {d} \!{\bf {x}}\int \operatorname {d} \!{\bf {y}}\,g({\bf {x}}-{\bf {y}})\left\right].}
3480:
Similarly, one can also quantify the minimum collapse strength to solve the measurement problem at the macroscopic level. Specifically, an estimate can be obtained by requiring that a superposition of a single-layered graphene disk of radius
8568:
Komori, Kentaro; Enomoto, Yutaro; Ooi, Ching Pin; Miyazaki, Yuki; Matsumoto, Nobuyuki; Sudhir, Vivishek; Michimura, Yuta; Ando, Masaki (2020-01-17). "Attonewton-meter torque sensing with a macroscopic optomechanical torsion pendulum".
741:
4756:
659:
4138:
3955:
1455:. The use of these operators satisfies the conservation of the symmetry properties of identical particles. Moreover, the mass proportionality implements automatically the amplification mechanism. The choice of the form of
490:
5877:
1093:
4954:. Although this increase is small, it is an unpleasant feature for a phenomenological model. The dissipative extension of the CSL model gives a remedy. One associates to the collapse noise a finite temperature
5964:
907:
8709:
Nobakht, J.; Carlesso, M.; Donadi, S.; Paternostro, M.; Bassi, A. (2018-10-08). "Unitary unraveling for the dissipative continuous spontaneous localization model: Application to optomechanical experiments".
3202:{\displaystyle \rho (x,x',t)={\frac {1}{2\pi \hbar }}\int _{-\infty }^{+\infty }\operatorname {d} \!k\int _{-\infty }^{+\infty }\operatorname {d} \!w\,e^{-ikw/\hbar }F_{CSL}(k,x-x',t)\rho ^{QM}(x+w,x'+w,t),}
865:
5338:
4350:
5810:
5110:
1307:
4934:
is the
Boltzmann constant. Several experiments can test such a spread. They range from cold atom free expansion, nano-cantilevers cooled to millikelvin temperatures, gravitational wave detectors,
7972:
Vinante, A.; Bahrami, M.; Bassi, A.; Usenko, O.; Wijts, G.; Oosterkamp, T. H. (2016-03-02). "Upper Bounds on
Spontaneous Wave-Function Collapse Models Using Millikelvin-Cooled Nanocantilevers".
5240:
2234:
Once the master equation is represented in the position basis, it becomes clear that its direct action is to diagonalize the density matrix in position. For a single point-like particle of mass
5181:
3475:
2890:{\displaystyle \lambda {\frac {m^{2}}{m_{0}^{2}}}\to \lambda {\frac {r_{C}^{3}}{\pi ^{3/2}m_{0}^{2}}}\int \operatorname {d} \!{\bf {k}}|{\tilde {\mu }}({\bf {k}})|^{2}e^{-k^{2}r_{C}^{2}},}
7208:
Morales, A.; Aalseth, C. E.; Avignone, F. T.; Brodzinski, R. L.; Cebrián, S.; Garcı́a, E.; Irastorza, I. G.; Kirpichnikov, I. V.; Klimenko, A. A.; Miley, H. S.; Morales, J. (2002-04-18).
1362:
4631:
2638:
1814:
1698:
6106:
1495:
1088:
6202:
Ghirardi, Gian Carlo; Pearle, Philip; Rimini, Alberto (1990-07-01). "Markov processes in
Hilbert space and continuous spontaneous localization of systems of identical particles".
4127:
m. Although small, such an energy increase can be tested by monitoring cold atoms. and bulk materials, as
Bravais lattices, low temperature experiments, neutron stars and planets
2672:
1582:
6994:
Bassi, Angelo; Ferialdi, Luca (2009-07-31). "Non-Markovian dynamics for a free quantum particle subject to spontaneous collapse in space: General solution and main properties".
2933:
1926:
4564:{\displaystyle \eta ={\frac {\lambda r_{C}^{3}}{2\pi ^{3/2}m_{0}^{2}}}\int \operatorname {d} \!{\bf {k}}\,e^{-{\bf {k}}^{2}r_{C}^{2}}k_{x}^{2}|{\tilde {\mu }}({\bf {k}})|^{2},}
4053:
3743:{\displaystyle {\frac {\operatorname {d} \!\Gamma (\omega )}{\operatorname {d} \!\omega }}={\frac {\hbar Q^{2}\lambda }{2\pi ^{2}\epsilon _{0}c^{3}m_{0}^{2}r_{C}^{2}\omega }},}
5461:
5379: K, although only experiments can indicate a definite value. Several interferometric and non-interferometric tests bound the CSL parameter space for different choices of
4135:. Another prediction of the CSL model is the increase of the spread in position of center-of-mass of a system. For a free particle, the position spread in one dimension reads
4664:
4017:
1887:
1771:
1655:
65:
The model does not significantly alter the dynamics of microscopic systems, while it becomes strong for macroscopic objects: the amplification mechanism ensures this scaling.
5548:
3545:
3512:
4125:
3775:
902:
6133:
6018:
5991:
4751:
519:
5377:
1426:
8515:
Vinante, A.; Pontin, A.; Rashid, M.; Toroš, M.; Barker, P. F.; Ulbricht, H. (2019-07-16). "Testing collapse models with levitated nanoparticles: Detection challenge".
6038:
2692:
1518:
89:
6741:
Lee, K. C.; Sprague, M. R.; Sussman, B. J.; Nunn, J.; Langford, N. K.; Jin, X.-M.; Champion, T.; Michelberger, P.; Reim, K. F.; England, D.; Jaksch, D. (2011-12-02).
5410:
4985:
4684:
3581:
3237:
3847:
130:
6065:
4932:
4370:
4082:
1843:
1727:
1611:
1545:
1453:
546:
116:
8462:
Pontin, A.; Bullier, N. P.; Toroš, M.; Barker, P. F. (2020). "An ultra-narrow line width levitated nano-oscillator for testing dissipative wavefunction collapse".
5494:
3984:
664:
8902:
8105:
Vinante, A.; Mezzena, R.; Falferi, P.; Carlesso, M.; Bassi, A. (2017-09-12). "Improved
Noninterferometric Test of Collapse Models Using Ultracold Cantilevers".
5009:
4724:
4704:
4589:
3842:
3822:
3795:
3601:
2252:
1402:
1382:
8408:
Zheng, Di; Leng, Yingchun; Kong, Xi; Li, Rui; Wang, Zizhe; Luo, Xiaohui; Zhao, Jie; Duan, Chang-Kui; Huang, Pu; Du, Jiangfeng; Carlesso, Matteo (2020-01-17).
8294:
Carlesso, Matteo; Bassi, Angelo; Falferi, Paolo; Vinante, Andrea (2016-12-23). "Experimental bounds on collapse models from gravitational wave detectors".
7784:
Bahrami, M.; Paternostro, M.; Bassi, A.; Ulbricht, H. (2014-05-29). "Proposal for a
Noninterferometric Test of Collapse Models in Optomechanical Systems".
551:
5340:. Assuming that the CSL noise has a cosmological origin (which is reasonable due to its supposed universality), a plausible value such a temperature is
746:
8835:
Bassi, A.; Deckert, D.-A.; Ferialdi, L. (2010-12-01). "Breaking quantum linearity: Constraints from human perception and cosmological implications".
7387:
Kovachy, Tim; Hogan, Jason M.; Sugarbaker, Alex; Dickerson, Susannah M.; Donnelly, Christine A.; Overstreet, Chris; Kasevich, Mark A. (2015-04-08).
55:
model, the CSL model describes the collapse of the wave function as occurring continuously in time, in contrast to the
Ghirardi-Rimini-Weber model.
4900:{\displaystyle \langle {{\hat {x}}^{2}}\rangle _{eq}={\frac {k_{B}T}{m\omega _{0}^{2}}}+{\frac {\hbar ^{2}\eta }{2m^{2}\omega _{0}^{2}\gamma }},}
5553:
5815:
52:
5014:
6686:
Fein, Yaakov Y.; Geyer, Philipp; Zwick, Patrick; Kiałka, Filip; Pedalino, Sebastian; Mayor, Marcel; Gerlich, Stefan; Arndt, Markus (2019).
7837:
Nimmrichter, Stefan; Hornberger, Klaus; Hammerer, Klemens (2014-07-10). "Optomechanical
Sensing of Spontaneous Wave-Function Collapse".
5882:
4280:{\displaystyle \langle {{\hat {x}}^{2}}\rangle _{t}=\langle {{\hat {x}}^{2}}\rangle _{t}^{(QM)}+{\frac {\hbar ^{2}\eta t^{3}}{3m^{2}}},}
5420:. If one attributes a physical origin to the CSL noise, then its spectrum cannot be white, but colored. In particular, in place of the
6625:
Toroš, Marko; Bassi, Angelo (2018-02-15). "Bounds on quantum collapse models from matter-wave interferometry: calculational details".
3986:
is the initial energy of the system. This increase is effectively small; for example, the temperature of a hydrogen atom increases by
3477:
Experiments testing such a reduction of the interference contrast are carried out with cold-atoms, molecules and entangled diamonds.
6490:
Kovachy, T.; Asenbaum, P.; Overstreet, C.; Donnelly, C. A.; Dickerson, S. M.; Sugarbaker, A.; Hogan, J. M.; Kasevich, M. A. (2015).
5245:
3797:
is the light speed. This prediction of CSL can be tested by analyzing the X-ray emission spectrum from a bulk Germanium test mass.
3242:
8229:
Vinante, A.; Carlesso, M.; Bassi, A.; Chiasera, A.; Varas, S.; Falferi, P.; Margesin, B.; Mezzena, R.; Ulbricht, H. (2020-09-03).
4290:
1242:{\displaystyle {\hat {M}}({\bf {x}})=\sum _{j}m_{j}\sum _{s}{\hat {a}}_{j}^{\dagger }({\bf {x}},s){\hat {a}}_{j}({\bf {x}},s),}
1252:
1041:{\displaystyle {\hat {N}}_{t}({\bf {x}})={\hat {M}}({\bf {x}})-\langle \psi _{t}|{\hat {M}}({\bf {x}})|\psi _{t}\rangle ,}
5186:
8907:
6868:
Carlesso, Matteo; Donadi, Sandro; Ferialdi, Luca; Paternostro, Mauro; Ulbricht, Hendrik; Bassi, Angelo (February 2022).
5115:
8176:
Carlesso, Matteo; Vinante, Andrea; Bassi, Angelo (2018-08-17). "Multilayer test masses to enhance the collapse noise".
6363:
Adler, Stephen L (2007-10-16). "Lower and upper bounds on CSL parameters from latent image formation and IGM~heating".
3556:
stochastic force acting on the system, and several experiments can be designed to quantify such a force. They include:
5879:. As an example, one can consider an exponentially decaying noise, whose time correlation function can be of the form
4947:
The CSL model consistently describes the collapse mechanism as a dynamical process. It has, however, two weak points.
7670:
Tilloy, Antoine; Stace, Thomas M. (2019-08-21). "Neutron Star Heating Constraints on Wave-Function Collapse Models".
1892:
From the dynamics of the wave function one can obtain the corresponding master equation for the statistical operator
7908:
Diósi, Lajos (2015-02-04). "Testing Spontaneous Wave-Function Collapse Models on Classical Mechanical Oscillators".
6156:
Pearle, Philip (1989-03-01). "Combining stochastic dynamical state-vector reduction with spontaneous localization".
7047:
Adler, Stephen L; Bassi, Angelo; Donadi, Sandro (2013-06-03). "On spontaneous photon emission in collapse models".
6933:
Adler, Stephen L; Ramazanoğlu, Fethi M (2007-10-16). "Photon-emission rate from atomic systems in the CSL model".
6320:
Ghirardi, G. C.; Rimini, A.; Weber, T. (1986-07-15). "Unified dynamics for microscopic and macroscopic systems".
1312:
48:
28:
4594:
6427:"Colored and dissipative continuous spontaneous localization model and bounds from matter-wave interferometry"
8048:"Non-interferometric test of the continuous spontaneous localization model based on rotational optomechanics"
2609:
1776:
1660:
7110:"Spontaneous photon emission from a non-relativistic free charged particle in collapse models: A case study"
4935:
8410:"Room temperature test of the continuous spontaneous localization model using a levitated micro-oscillator"
6070:
1458:
1051:
6555:"Matter–wave interference of particles selected from a molecular library with masses exceeding 10 000 amu"
2643:
1550:
2900:
1895:
7173:
Fu, Qijia (1997-09-01). "Spontaneous radiation of free electrons in a nonrelativistic collapse model".
4022:
8046:
Carlesso, Matteo; Paternostro, Mauro; Ulbricht, Hendrik; Vinante, Andrea; Bassi, Angelo (2018-08-17).
7563:
Adler, Stephen L.; Vinante, Andrea (2018-05-18). "Bulk heating effects as tests for collapse models".
5426:
8854:
8799:
8729:
8655:
8588:
8534:
8481:
8431:
8380:
8313:
8252:
8195:
8124:
8069:
7991:
7927:
7856:
7803:
7750:
7689:
7642:
7582:
7537:
7476:
7454:
7410:
7356:
7287:
7231:
7182:
7131:
7109:
7066:
7013:
6952:
6891:
6824:
6754:
6699:
6644:
6576:
6503:
6448:
6426:
6329:
6275:
6253:
6211:
6165:
4636:
3989:
3804:. A prediction of CSL is the increase of the total energy of a system. For example, the total energy
1848:
1732:
1616:
5499:
3517:
3484:
4087:
3753:
7731:
Romero-Isart, Oriol (2011-11-28). "Quantum superposition of massive objects and collapse models".
1364:
are, respectively, the second quantized creation and annihilation operators of a particle of type
870:
8878:
8844:
8789:
8755:
8719:
8645:
8614:
8578:
8550:
8524:
8497:
8471:
8421:
8370:
8339:
8303:
8276:
8242:
8211:
8185:
8158:
8114:
8059:
8025:
7981:
7951:
7917:
7890:
7846:
7819:
7793:
7766:
7740:
7713:
7679:
7632:
7598:
7572:
7527:
7500:
7466:
7400:
7346:
7311:
7277:
7221:
7155:
7121:
7090:
7056:
7029:
7003:
6976:
6942:
6915:
6881:
6850:
6814:
6786:
6723:
6668:
6634:
6566:
6535:
6472:
6438:
6398:
6372:
6299:
6265:
6111:
5996:
5969:
4729:
36:
6108:
Hz. As for the dissipative extension, experimental bounds were obtained for different values of
495:
7329:
Piscicchia, Kristian; Bassi, Angelo; Curceanu, Catalina; Grande, Raffaele Del; Donadi, Sandro;
5343:
1500:
The action of the CSL model is quantified by the values of the two phenomenological parameters
1407:
8870:
8817:
8691:
8673:
8268:
8150:
8087:
8017:
7943:
7882:
7705:
7492:
7428:
7303:
7249:
7147:
7082:
6968:
6907:
6778:
6770:
6715:
6660:
6602:
6594:
6553:
Eibenberger, Sandra; Gerlich, Stefan; Arndt, Markus; Mayor, Marcel; Tüxen, Jens (2013-08-14).
6527:
6519:
6464:
6390:
6345:
6291:
6227:
6181:
6023:
2677:
1503:
74:
32:
5382:
4957:
4669:
3566:
8862:
8807:
8745:
8737:
8681:
8663:
8604:
8596:
8542:
8489:
8439:
8388:
8329:
8321:
8260:
8203:
8140:
8132:
8077:
8007:
7999:
7935:
7872:
7864:
7811:
7758:
7697:
7650:
7590:
7545:
7484:
7418:
7364:
7330:
7295:
7239:
7190:
7139:
7074:
7021:
6960:
6899:
6840:
6832:
6762:
6707:
6652:
6584:
6511:
6456:
6382:
6337:
6283:
6219:
6173:
3212:
6043:
4910:
4355:
4058:
1819:
1703:
1587:
1523:
1431:
736:{\displaystyle w_{t}({\bf {x}})=\operatorname {d} \!W_{t}({\bf {x}})/\operatorname {d} \!t}
524:
94:
8230:
7877:
5470:
5464:
3960:
7078:
8858:
8803:
8733:
8659:
8592:
8538:
8485:
8435:
8384:
8317:
8256:
8199:
8128:
8073:
7995:
7931:
7860:
7807:
7754:
7693:
7646:
7586:
7541:
7480:
7414:
7360:
7291:
7235:
7186:
7135:
7070:
7017:
6956:
6895:
6828:
6758:
6703:
6648:
6580:
6507:
6452:
6333:
6279:
6215:
6169:
8686:
8633:
8231:"Narrowing the Parameter Space of Collapse Models with Ultracold Layered Force Sensors"
4994:
4988:
4709:
4689:
4574:
3827:
3807:
3780:
3586:
2952:
2237:
1387:
1367:
7244:
7209:
6964:
6870:"Present status and future challenges of non-interferometric tests of collapse models"
6742:
6386:
6287:
8896:
8882:
8618:
8501:
8493:
8444:
8409:
8357:
Helou, Bassam; Slagmolen, B. J. J.; McClelland, David E.; Chen, Yanbei (2017-04-28).
8280:
7770:
7717:
7159:
7094:
7033:
6919:
6869:
6854:
6790:
6727:
6672:
6539:
6476:
6402:
6303:
5467:
is considered, which is characterized by a non-trivial temporal correlation function
62:
The localization takes place in position, which is the preferred basis in this model.
8759:
8554:
8343:
8215:
8162:
8029:
7955:
7894:
7823:
7602:
7504:
7315:
6980:
6687:
654:{\displaystyle g({\bf {x}}-{\bf {y}})=e^{-{({\bf {x}}-{\bf {y}})^{2}}/{4r_{C}^{2}}}}
8866:
8264:
8136:
8003:
7939:
7868:
7815:
7701:
7423:
7388:
7143:
6460:
118:, which are respectively the collapse rate and the correlation length of the model.
7619:
Adler, Stephen L.; Bassi, Angelo; Carlesso, Matteo; Vinante, Andrea (2019-05-10).
5993:, whose inverse describes the time scale of the noise correlations. The parameter
8812:
8777:
2956:
quantified by the reduction of the off-diagonal terms of the statistical operator
8600:
8546:
7488:
7453:
Bilardello, Marco; Donadi, Sandro; Vinante, Andrea; Bassi, Angelo (2016-11-15).
7210:"Improved constraints on wimps from the international germanium experiment IGEX"
5421:
8741:
8393:
8358:
8325:
8207:
8082:
8047:
7762:
7655:
7620:
7594:
7549:
7025:
6903:
6836:
6656:
3950:{\displaystyle E(t)=E(0)+{\frac {3m\lambda \hbar ^{2}}{4m_{0}^{2}r_{C}^{2}}}t,}
485:{\displaystyle \operatorname {d} \!|\psi _{t}\rangle =\left|\psi _{t}\rangle .}
7299:
6711:
6491:
3239:
denotes the statistical operator described by quantum mechanics, and we define
127:
The CSL dynamical equation for the wave function is stochastic and non-linear:
8874:
8821:
8677:
8091:
7496:
7307:
7253:
7194:
7151:
7086:
6972:
6911:
6774:
6719:
6664:
6598:
6523:
6468:
6394:
6295:
6177:
6766:
6341:
8695:
8272:
8154:
8021:
7947:
7886:
7709:
7432:
6782:
6606:
6531:
6223:
2674:, are preserved. For a composite system, the single-particle collapse rate
6349:
6231:
6185:
8750:
8609:
8334:
8145:
6377:
6270:
6515:
6020:
works now as the third parameter of the colored CSL model together with
2640:, decay exponentially. Conversely, the diagonal terms, characterized by
7226:
6845:
6589:
6554:
5872:{\displaystyle {\bar {\tau }}=\int _{0}^{t}\operatorname {d} \!s\,f(s)}
8668:
8012:
7518:
Bahrami, M. (2018-05-18). "Testing collapse models by a thermometer".
7369:
7334:
4666:. In experiments, such an increase is limited by the dissipation rate
6067:. Assuming a cosmological origin of the noise, a reasonable guess is
8794:
8724:
8583:
8529:
8476:
8426:
8375:
8308:
8247:
8190:
8119:
8064:
7986:
7684:
7637:
7577:
7532:
7471:
7351:
7282:
6886:
6819:
6639:
6443:
8849:
8778:"Colored collapse models from the non-interferometric perspective"
8650:
7922:
7851:
7798:
7745:
7405:
7126:
7061:
7008:
6947:
6571:
5959:{\displaystyle f(t)={\tfrac {1}{2}}\Omega _{C}e^{-\Omega _{C}|t|}}
51:(also known as collapse) models is the CSL model. Building on the
7621:"Testing continuous spontaneous localization with Fermi liquids"
5463:, whose correlation is proportional to a Dirac delta in time, a
904:
denotes the stochastic average over the noise. Finally, we write
860:{\displaystyle \mathbb {E} =g({\bf {x}}-{\bf {y}})\delta (t-s),}
1889:
m. Eventually, these values have to be bounded by experiments.
521:
is the Hamiltonian describing the quantum mechanical dynamics,
8776:
Carlesso, Matteo; Ferialdi, Luca; Bassi, Angelo (2018-09-18).
5333:{\displaystyle \chi =\hbar ^{2}/(8m_{0}k_{B}T_{CSL}r_{C}^{2})}
8634:"Dissipative Continuous Spontaneous Localization (CSL) model"
6135:: they include interferometric and non-interferometric tests.
3844:
in three dimensions grows linearly in time according to
6425:
Toroš, Marko; Gasbarri, Giulio; Bassi, Angelo (2017-12-20).
2935:
is the Fourier transform of the mass density of the system.
68:
It preserves the symmetry properties of identical particles.
4686:. Assuming that the experiment is performed at temperature
4345:{\displaystyle \langle {{\hat {x}}^{2}}\rangle _{t}^{(QM)}}
297:
293:
35:, proposed in 1989 by Philip Pearle. and finalized in 1990
7335:"CSL Collapse Model Mapped with the Spontaneous Radiation"
5805:{\displaystyle F_{cCSL}(k,q,t)=F_{CSL}(k,q,t)\exp \left,}
5011:
in three dimensions, the energy evolution is described by
8359:"LISA pathfinder appreciably constrains collapse models"
4753:, at equilibrium reaches a spread in position given by
1547:. Originally, the Ghirardi-Rimini-Weber model proposed
7455:"Bounds on collapse models from cold-atom experiments"
5902:
5136:
5105:{\displaystyle E(t)=e^{-\beta t}(E(0)-E_{as})+E_{as},}
3215:
2478:
1302:{\displaystyle {\hat {a}}_{j}^{\dagger }({\bf {y}},s)}
548:
is a reference mass taken equal to that of a nucleon,
7459:
Physica A: Statistical Mechanics and Its Applications
6743:"Entangling Macroscopic Diamonds at Room Temperature"
6114:
6073:
6046:
6026:
5999:
5972:
5885:
5818:
5556:
5502:
5473:
5429:
5385:
5346:
5248:
5189:
5118:
5017:
4997:
4960:
4913:
4759:
4732:
4712:
4692:
4672:
4639:
4597:
4577:
4378:
4358:
4293:
4141:
4090:
4061:
4025:
3992:
3963:
3850:
3830:
3810:
3783:
3756:
3612:
3589:
3569:
3520:
3487:
3245:
2962:
2903:
2700:
2680:
2646:
2612:
2260:
2240:
1934:
1898:
1851:
1822:
1779:
1735:
1706:
1663:
1619:
1590:
1553:
1526:
1506:
1461:
1434:
1410:
1390:
1370:
1315:
1255:
1096:
1054:
910:
873:
749:
667:
554:
527:
498:
133:
97:
77:
4952:
CSL does not conserve the energy of isolated systems
2694:
should be replaced with that of the composite system
5966:. In such a way, one introduces a frequency cutoff
5235:{\displaystyle \beta =4\chi \lambda /(1+\chi )^{5}}
7049:Journal of Physics A: Mathematical and Theoretical
6935:Journal of Physics A: Mathematical and Theoretical
6688:"Quantum superposition of molecules beyond 25 kDa"
6627:Journal of Physics A: Mathematical and Theoretical
6365:Journal of Physics A: Mathematical and Theoretical
6127:
6100:
6059:
6032:
6012:
5985:
5958:
5871:
5804:
5542:
5488:
5455:
5404:
5371:
5332:
5234:
5176:{\displaystyle E_{as}={\tfrac {3}{2}}k_{B}T_{CSL}}
5175:
5104:
5003:
4979:
4926:
4899:
4745:
4718:
4698:
4678:
4658:
4625:
4583:
4563:
4364:
4344:
4279:
4119:
4076:
4047:
4011:
3978:
3949:
3836:
3816:
3789:
3769:
3742:
3595:
3575:
3539:
3506:
3469:
3231:
3201:
2927:
2889:
2686:
2666:
2632:
2598:
2246:
2226:
1920:
1881:
1837:
1808:
1765:
1721:
1692:
1649:
1605:
1576:
1539:
1512:
1489:
1447:
1420:
1396:
1376:
1356:
1301:
1241:
1082:
1040:
896:
859:
735:
653:
540:
513:
484:
110:
83:
6252:Bassi, Angelo; Ghirardi, GianCarlo (2003-06-01).
5852:
5496:. The effect can be quantified by a rescaling of
4453:
3637:
3619:
3459:
3376:
3294:
3065:
3037:
2799:
2085:
2071:
1966:
1941:
729:
697:
452:
350:
336:
268:
224:
192:
137:
16:Quantum mechanical theory of spontaneous collapse
7389:"Matter Wave Lensing to Picokelvin Temperatures"
6492:"Quantum superposition at the half-metre scale"
4991:. Thus, for a free point-like particle of mass
4571:where the motion is assumed to occur along the
1657:m, while later Adler considered larger values:
4633:is the Fourier transform of the mass density
3470:{\displaystyle F_{CSL}(k,q,t)=\exp {\bigg }.}
8:
8632:Smirne, Andrea; Bassi, Angelo (2015-08-05).
4785:
4760:
4319:
4294:
4204:
4179:
4167:
4142:
2590:
2542:
2420:
2345:
2315:
2267:
1497:ensures the collapse in the position basis.
1032:
974:
476:
153:
1357:{\displaystyle {\hat {a}}_{j}({\bf {y}},s)}
58:Some of the key features of the model are:
4626:{\displaystyle {\tilde {\mu }}({\bf {k}})}
4352:is the free quantum mechanical spread and
8848:
8811:
8793:
8749:
8723:
8685:
8667:
8649:
8608:
8582:
8528:
8475:
8443:
8425:
8392:
8374:
8333:
8307:
8246:
8189:
8144:
8118:
8081:
8063:
8011:
7985:
7921:
7876:
7850:
7797:
7744:
7683:
7654:
7636:
7576:
7531:
7470:
7422:
7404:
7368:
7350:
7281:
7243:
7225:
7125:
7060:
7007:
6946:
6885:
6844:
6818:
6638:
6588:
6570:
6442:
6376:
6269:
6119:
6113:
6097:
6091:
6078:
6072:
6051:
6045:
6025:
6004:
5998:
5977:
5971:
5949:
5941:
5935:
5927:
5917:
5901:
5884:
5856:
5843:
5838:
5820:
5819:
5817:
5781:
5776:
5764:
5758:
5750:
5735:
5730:
5718:
5712:
5700:
5681:
5655:
5654:
5648:
5604:
5561:
5555:
5507:
5501:
5472:
5444:
5443:
5434:
5428:
5390:
5384:
5351:
5345:
5321:
5316:
5300:
5290:
5280:
5265:
5259:
5247:
5226:
5205:
5188:
5161:
5151:
5135:
5123:
5117:
5090:
5071:
5037:
5016:
4996:
4965:
4959:
4918:
4912:
4882:
4877:
4867:
4849:
4842:
4830:
4825:
4807:
4800:
4788:
4777:
4766:
4765:
4763:
4758:
4737:
4731:
4711:
4691:
4671:
4647:
4646:
4638:
4614:
4613:
4599:
4598:
4596:
4576:
4552:
4547:
4537:
4536:
4522:
4521:
4516:
4510:
4505:
4493:
4488:
4478:
4472:
4471:
4466:
4461:
4455:
4454:
4438:
4433:
4419:
4415:
4400:
4395:
4385:
4377:
4372:is the CSL diffusion constant, defined as
4357:
4327:
4322:
4311:
4300:
4299:
4297:
4292:
4265:
4250:
4237:
4230:
4212:
4207:
4196:
4185:
4184:
4182:
4170:
4159:
4148:
4147:
4145:
4140:
4108:
4095:
4089:
4065:
4060:
4036:
4024:
4000:
3991:
3962:
3932:
3927:
3917:
3912:
3897:
3881:
3849:
3829:
3809:
3782:
3761:
3755:
3725:
3720:
3710:
3705:
3695:
3685:
3675:
3657:
3647:
3613:
3611:
3588:
3568:
3561:Radiation emission from charged particles
3528:
3519:
3495:
3486:
3458:
3457:
3443:
3438:
3430:
3425:
3418:
3399:
3389:
3385:
3380:
3367:
3362:
3348:
3326:
3321:
3311:
3305:
3293:
3292:
3250:
3244:
3220:
3214:
3149:
3101:
3087:
3074:
3069:
3053:
3045:
3025:
3017:
2995:
2961:
2905:
2904:
2902:
2876:
2871:
2861:
2853:
2843:
2838:
2828:
2827:
2813:
2812:
2807:
2801:
2800:
2784:
2779:
2765:
2761:
2750:
2745:
2739:
2725:
2720:
2710:
2704:
2699:
2679:
2658:
2657:
2648:
2647:
2645:
2624:
2623:
2614:
2613:
2611:
2606:where the off-diagonal terms, which have
2583:
2582:
2577:
2571:
2560:
2559:
2553:
2547:
2546:
2545:
2525:
2520:
2505:
2495:
2494:
2485:
2484:
2477:
2473:
2450:
2445:
2435:
2429:
2413:
2412:
2407:
2395:
2384:
2383:
2381:
2367:
2366:
2356:
2350:
2349:
2348:
2335:
2308:
2307:
2302:
2296:
2285:
2284:
2278:
2272:
2271:
2270:
2261:
2259:
2239:
2204:
2193:
2192:
2190:
2177:
2176:
2162:
2161:
2160:
2159:
2142:
2141:
2127:
2126:
2125:
2111:
2110:
2101:
2100:
2093:
2087:
2086:
2073:
2072:
2056:
2051:
2038:
2023:
2012:
2011:
2009:
1995:
1994:
1979:
1955:
1944:
1943:
1935:
1933:
1912:
1901:
1900:
1897:
1878:
1869:
1856:
1850:
1826:
1821:
1805:
1790:
1778:
1762:
1753:
1740:
1734:
1710:
1705:
1689:
1674:
1662:
1646:
1637:
1624:
1618:
1594:
1589:
1573:
1564:
1552:
1531:
1525:
1505:
1478:
1477:
1463:
1462:
1460:
1439:
1433:
1412:
1411:
1409:
1389:
1369:
1339:
1338:
1329:
1318:
1317:
1314:
1284:
1283:
1274:
1269:
1258:
1257:
1254:
1221:
1220:
1211:
1200:
1199:
1183:
1182:
1173:
1168:
1157:
1156:
1149:
1139:
1129:
1113:
1112:
1098:
1097:
1095:
1090:is the mass density operator, which reads
1071:
1070:
1056:
1055:
1053:
1026:
1017:
1008:
1007:
993:
992:
987:
981:
962:
961:
947:
946:
934:
933:
924:
913:
912:
909:
875:
874:
872:
827:
826:
817:
816:
795:
794:
785:
772:
771:
762:
751:
750:
748:
743:has zero average and correlation equal to
721:
712:
711:
702:
682:
681:
672:
666:
642:
637:
629:
624:
617:
607:
606:
597:
596:
592:
588:
572:
571:
562:
561:
553:
532:
526:
500:
499:
497:
470:
461:
440:
439:
430:
419:
418:
408:
407:
398:
387:
386:
376:
375:
366:
365:
358:
352:
351:
338:
337:
321:
316:
303:
283:
282:
273:
256:
255:
246:
235:
234:
232:
226:
225:
210:
199:
178:
177:
167:
147:
138:
132:
102:
96:
76:
4019: K per year considering the values
6145:
5256:
4846:
4234:
3894:
3650:
3092:
3007:
2633:{\displaystyle {\bf {x}}\neq {\bf {y}}}
2340:
1984:
1809:{\displaystyle \lambda =10^{-6\pm 2}\,}
1693:{\displaystyle \lambda =10^{-8\pm 2}\,}
172:
71:It is characterized by two parameters:
8771:
8769:
8457:
8455:
3777:is the vacuum dielectric constant and
8041:
8039:
7967:
7965:
7614:
7612:
7448:
7446:
7444:
7442:
7382:
7380:
6620:
6618:
6616:
6101:{\displaystyle \Omega _{C}=10^{12}\,}
1490:{\displaystyle {\hat {M}}({\bf {x}})}
1083:{\displaystyle {\hat {M}}({\bf {x}})}
7:
8903:Interpretations of quantum mechanics
7108:Bassi, A.; Donadi, S. (2014-02-14).
6420:
6418:
6416:
6414:
6412:
6315:
6313:
6247:
6245:
6243:
6241:
6197:
6195:
6151:
6149:
4726:, harmonically trapped at frequency
39:, Philip Pearle and Alberto Rimini.
6559:Physical Chemistry Chemical Physics
2667:{\displaystyle {\bf {x}}={\bf {y}}}
1577:{\displaystyle \lambda =10^{-17}\,}
21:continuous spontaneous localization
6116:
6075:
6001:
5974:
5932:
5914:
5849:
4943:Dissipative and colored extensions
4450:
3634:
3620:
3616:
3373:
3062:
3057:
3049:
3034:
3029:
3021:
2928:{\displaystyle {\tilde {\mu }}(k)}
2796:
2320:
2264:
2082:
2068:
1963:
1938:
1921:{\displaystyle {\hat {\rho }}_{t}}
726:
694:
449:
347:
333:
265:
221:
189:
134:
47:The most widely studied among the
14:
4048:{\displaystyle \lambda =10^{-16}}
8494:10.1103/PhysRevResearch.2.023349
8445:10.1103/PhysRevResearch.2.013057
5456:{\displaystyle w_{t}({\bf {x}})}
5445:
4648:
4615:
4538:
4473:
4456:
2829:
2802:
2659:
2649:
2625:
2615:
2584:
2548:
2496:
2486:
2414:
2351:
2309:
2273:
2178:
2143:
2112:
2102:
2088:
2074:
1479:
1413:
1340:
1285:
1222:
1184:
1114:
1072:
1009:
963:
935:
828:
818:
796:
773:
713:
683:
608:
598:
573:
563:
441:
409:
377:
367:
353:
339:
284:
257:
227:
8782:The European Physical Journal D
5418:The CSL noise spectrum is white
4987:at which the system eventually
4659:{\displaystyle \mu ({\bf {r}})}
4012:{\displaystyle \simeq 10^{-14}}
3551:Non-interferometric experiments
1882:{\displaystyle r_{C}=10^{-6}\,}
1766:{\displaystyle r_{C}=10^{-7}\,}
1650:{\displaystyle r_{C}=10^{-7}\,}
8265:10.1103/PhysRevLett.125.100404
8137:10.1103/PhysRevLett.119.110401
8004:10.1103/PhysRevLett.116.090402
7940:10.1103/PhysRevLett.114.050403
7878:11858/00-001M-0000-0024-7705-F
7869:10.1103/PhysRevLett.113.020405
7816:10.1103/PhysRevLett.112.210404
7702:10.1103/PhysRevLett.123.080402
7424:10.1103/PhysRevLett.114.143004
7144:10.1016/j.physleta.2014.01.002
7079:10.1088/1751-8113/46/24/245304
6461:10.1016/j.physleta.2017.10.002
5950:
5942:
5895:
5889:
5866:
5860:
5825:
5709:
5685:
5660:
5634:
5616:
5594:
5576:
5543:{\displaystyle F_{CSL}(k,q,t)}
5537:
5519:
5483:
5477:
5450:
5440:
5327:
5270:
5223:
5210:
5080:
5061:
5055:
5049:
5027:
5021:
4771:
4653:
4643:
4620:
4610:
4604:
4548:
4543:
4533:
4527:
4517:
4337:
4328:
4305:
4222:
4213:
4190:
4153:
3973:
3967:
3875:
3869:
3860:
3854:
3629:
3623:
3540:{\displaystyle \simeq 10^{-2}}
3507:{\displaystyle \simeq 10^{-5}}
3415:
3390:
3280:
3262:
3193:
3158:
3142:
3113:
2989:
2966:
2922:
2916:
2910:
2839:
2834:
2824:
2818:
2808:
2733:
2578:
2565:
2554:
2502:
2481:
2408:
2389:
2372:
2357:
2303:
2290:
2279:
2198:
2183:
2173:
2167:
2148:
2138:
2132:
2117:
2097:
2017:
2000:
1949:
1906:
1484:
1474:
1468:
1351:
1335:
1323:
1296:
1280:
1263:
1233:
1217:
1205:
1195:
1179:
1162:
1119:
1109:
1103:
1077:
1067:
1061:
1018:
1014:
1004:
998:
988:
968:
958:
952:
940:
930:
918:
891:
879:
851:
839:
833:
813:
804:
801:
791:
778:
768:
755:
718:
708:
688:
678:
614:
593:
578:
558:
505:
462:
446:
436:
424:
414:
404:
392:
382:
362:
289:
279:
262:
252:
240:
183:
139:
1:
7245:10.1016/S0370-2693(02)01545-9
6288:10.1016/S0370-1573(03)00103-0
4120:{\displaystyle r_{C}=10^{-7}}
3770:{\displaystyle \epsilon _{0}}
6254:"Dynamical reduction models"
897:{\displaystyle \mathbb {E} }
8601:10.1103/PhysRevA.101.011802
8547:10.1103/PhysRevA.100.012119
7489:10.1016/j.physa.2016.06.134
7333:; Pichler, Andreas (2017).
6965:10.1088/1751-8113/40/44/017
6387:10.1088/1751-8121/40/44/c01
6128:{\displaystyle \Omega _{C}}
6013:{\displaystyle \Omega _{C}}
5986:{\displaystyle \Omega _{C}}
4746:{\displaystyle \omega _{0}}
3824:of a free particle of mass
2948:Interferometric experiments
8924:
8867:10.1209/0295-5075/92/50006
8813:10.1140/epjd/e2018-90248-x
8742:10.1103/PhysRevA.98.042109
8394:10.1103/PhysRevD.95.084054
8326:10.1103/PhysRevD.94.124036
8208:10.1103/PhysRevA.98.022122
7763:10.1103/PhysRevA.84.052121
7656:10.1103/PhysRevD.99.103001
7595:10.1103/PhysRevA.97.052119
7550:10.1103/PhysRevA.97.052118
7026:10.1103/PhysRevA.80.012116
6904:10.1038/s41567-021-01489-5
6837:10.1103/PhysRevA.94.012108
514:{\displaystyle {\hat {H}}}
29:spontaneous collapse model
8837:EPL (Europhysics Letters)
7300:10.1007/s10701-015-9923-4
6712:10.1038/s41567-019-0663-9
5372:{\displaystyle T_{CSL}=1}
3802:Heating in bulk materials
3583:for a particle of charge
3514:m collapses in less than
1421:{\displaystyle {\bf {y}}}
8464:Physical Review Research
8414:Physical Review Research
8083:10.1088/1367-2630/aad863
7195:10.1103/PhysRevA.56.1806
6657:10.1088/1751-8121/aaabc6
6178:10.1103/PhysRevA.39.2277
6033:{\displaystyle \lambda }
2687:{\displaystyle \lambda }
1513:{\displaystyle \lambda }
84:{\displaystyle \lambda }
8235:Physical Review Letters
8107:Physical Review Letters
7974:Physical Review Letters
7910:Physical Review Letters
7839:Physical Review Letters
7786:Physical Review Letters
7672:Physical Review Letters
7393:Physical Review Letters
6767:10.1126/science.1211914
6342:10.1103/PhysRevD.34.470
5405:{\displaystyle T_{CSL}}
4980:{\displaystyle T_{CSL}}
4936:levitated optomechanics
4679:{\displaystyle \gamma }
3576:{\displaystyle \omega }
3232:{\textstyle \rho ^{QM}}
8052:New Journal of Physics
7270:Foundations of Physics
6224:10.1103/PhysRevA.42.78
6129:
6102:
6061:
6034:
6014:
5987:
5960:
5873:
5806:
5544:
5490:
5457:
5406:
5373:
5334:
5236:
5177:
5106:
5005:
4981:
4928:
4901:
4747:
4720:
4700:
4680:
4660:
4627:
4585:
4565:
4366:
4346:
4281:
4121:
4078:
4049:
4013:
3980:
3951:
3838:
3818:
3791:
3771:
3744:
3597:
3577:
3541:
3508:
3471:
3233:
3203:
2929:
2891:
2688:
2668:
2634:
2600:
2248:
2228:
1922:
1883:
1839:
1810:
1767:
1723:
1694:
1651:
1607:
1578:
1541:
1514:
1491:
1449:
1422:
1398:
1378:
1358:
1303:
1243:
1084:
1042:
898:
861:
737:
661:, and the noise field
655:
542:
515:
486:
112:
85:
6130:
6103:
6062:
6060:{\displaystyle r_{C}}
6035:
6015:
5988:
5961:
5874:
5807:
5545:
5491:
5458:
5407:
5374:
5335:
5237:
5178:
5107:
5006:
4982:
4929:
4927:{\displaystyle k_{B}}
4902:
4748:
4721:
4706:, a particle of mass
4701:
4681:
4661:
4628:
4586:
4566:
4367:
4365:{\displaystyle \eta }
4347:
4282:
4122:
4079:
4077:{\displaystyle ^{-1}}
4050:
4014:
3981:
3952:
3839:
3819:
3792:
3772:
3745:
3598:
3578:
3542:
3509:
3472:
3234:
3204:
2930:
2892:
2689:
2669:
2635:
2601:
2249:
2229:
1923:
1884:
1840:
1838:{\displaystyle ^{-1}}
1811:
1768:
1724:
1722:{\displaystyle ^{-1}}
1695:
1652:
1608:
1606:{\displaystyle ^{-1}}
1579:
1542:
1540:{\displaystyle r_{C}}
1515:
1492:
1450:
1448:{\displaystyle m_{j}}
1423:
1399:
1379:
1359:
1304:
1244:
1085:
1043:
899:
862:
738:
656:
543:
541:{\displaystyle m_{0}}
516:
487:
113:
111:{\displaystyle r_{C}}
86:
53:Ghirardi-Rimini-Weber
7331:Hiesmayr, Beatrix C.
6112:
6071:
6044:
6024:
5997:
5970:
5883:
5816:
5554:
5500:
5489:{\displaystyle f(t)}
5471:
5427:
5383:
5344:
5246:
5187:
5116:
5015:
4995:
4958:
4911:
4757:
4730:
4710:
4690:
4670:
4637:
4595:
4575:
4376:
4356:
4291:
4139:
4088:
4059:
4023:
3990:
3979:{\displaystyle E(0)}
3961:
3848:
3828:
3808:
3781:
3754:
3610:
3587:
3567:
3518:
3485:
3243:
3213:
2960:
2901:
2698:
2678:
2644:
2610:
2258:
2238:
1932:
1896:
1849:
1820:
1777:
1733:
1704:
1661:
1617:
1588:
1551:
1524:
1504:
1459:
1432:
1408:
1388:
1368:
1313:
1253:
1094:
1052:
908:
871:
747:
665:
552:
525:
496:
131:
95:
75:
8908:Quantum measurement
8859:2010EL.....9250006B
8804:2018EPJD...72..159C
8734:2018PhRvA..98d2109N
8660:2015NatSR...512518S
8593:2020PhRvA.101a1802K
8539:2019PhRvA.100a2119V
8486:2020PhRvR...2b3349P
8436:2020PhRvR...2a3057Z
8385:2017PhRvD..95h4054H
8318:2016PhRvD..94l4036C
8257:2020PhRvL.125j0404V
8200:2018PhRvA..98b2122C
8129:2017PhRvL.119k0401V
8074:2018NJPh...20h3022C
7996:2016PhRvL.116i0402V
7932:2015PhRvL.114e0403D
7861:2014PhRvL.113b0405N
7808:2014PhRvL.112u0404B
7755:2011PhRvA..84e2121R
7694:2019PhRvL.123h0402T
7647:2019PhRvD..99j3001A
7587:2018PhRvA..97e2119A
7542:2018PhRvA..97e2118B
7481:2016PhyA..462..764B
7415:2015PhRvL.114n3004K
7361:2017Entrp..19..319P
7292:2016FoPh...46..263C
7236:2002PhLB..532....8M
7187:1997PhRvA..56.1806F
7136:2014PhLA..378..761B
7071:2013JPhA...46x5304A
7018:2009PhRvA..80a2116B
6957:2007JPhA...4013395A
6941:(44): 13395–13406.
6896:2022NatPh..18..243C
6829:2016PhRvA..94a2108B
6759:2011Sci...334.1253L
6753:(6060): 1253–1256.
6704:2019NatPh..15.1242F
6649:2018JPhA...51k5302T
6581:2013PCCP...1514696E
6565:(35): 14696–14700.
6516:10.1038/nature16155
6508:2015Natur.528..530K
6453:2017PhLA..381.3921T
6334:1986PhRvD..34..470G
6280:2003PhR...379..257B
6216:1990PhRvA..42...78G
6170:1989PhRvA..39.2277P
5848:
5786:
5740:
5326:
4887:
4835:
4515:
4498:
4443:
4405:
4341:
4226:
3937:
3922:
3730:
3715:
3448:
3372:
3331:
3061:
3033:
2881:
2789:
2755:
2730:
2530:
2455:
2061:
1279:
1178:
647:
326:
49:dynamical reduction
37:Gian Carlo Ghirardi
8638:Scientific Reports
6590:10.1039/C3CP51500A
6125:
6098:
6057:
6030:
6010:
5983:
5956:
5911:
5869:
5834:
5802:
5772:
5726:
5540:
5486:
5453:
5402:
5369:
5330:
5312:
5232:
5173:
5145:
5102:
5001:
4977:
4938:, torsion pendula.
4924:
4897:
4873:
4821:
4743:
4716:
4696:
4676:
4656:
4623:
4581:
4561:
4501:
4484:
4429:
4391:
4362:
4342:
4318:
4277:
4203:
4117:
4074:
4045:
4009:
3976:
3947:
3923:
3908:
3834:
3814:
3787:
3767:
3740:
3716:
3701:
3593:
3573:
3537:
3504:
3467:
3434:
3358:
3317:
3229:
3199:
3041:
3013:
2939:Experimental tests
2925:
2887:
2867:
2775:
2741:
2716:
2684:
2664:
2630:
2596:
2533:
2516:
2441:
2244:
2224:
2047:
1918:
1879:
1835:
1806:
1763:
1719:
1690:
1647:
1603:
1574:
1537:
1510:
1487:
1445:
1418:
1394:
1374:
1354:
1299:
1256:
1239:
1155:
1154:
1134:
1080:
1038:
894:
857:
733:
651:
633:
538:
511:
482:
312:
123:Dynamical equation
108:
81:
8712:Physical Review A
8669:10.1038/srep12518
8571:Physical Review A
8517:Physical Review A
8363:Physical Review D
8296:Physical Review D
8178:Physical Review A
7733:Physical Review A
7625:Physical Review D
7565:Physical Review A
7520:Physical Review A
7370:10.3390/e19070319
7214:Physics Letters B
7175:Physical Review A
7114:Physics Letters A
6996:Physical Review A
6807:Physical Review A
6698:(12): 1242–1245.
6502:(7583): 530–533.
6437:(47): 3921–3927.
6431:Physics Letters A
6322:Physical Review D
6204:Physical Review A
6158:Physical Review A
5910:
5828:
5670:
5663:
5144:
5004:{\displaystyle m}
4892:
4837:
4774:
4719:{\displaystyle m}
4699:{\displaystyle T}
4607:
4584:{\displaystyle x}
4530:
4445:
4308:
4272:
4193:
4156:
4133:Diffusive effects
3939:
3837:{\displaystyle m}
3817:{\displaystyle E}
3790:{\displaystyle c}
3735:
3642:
3596:{\displaystyle Q}
3412:
3356:
3332:
3011:
2913:
2821:
2791:
2731:
2568:
2532:
2456:
2392:
2375:
2343:
2327:
2293:
2247:{\displaystyle m}
2201:
2170:
2135:
2063:
2020:
2003:
1987:
1971:
1952:
1909:
1471:
1397:{\displaystyle s}
1377:{\displaystyle j}
1326:
1266:
1208:
1165:
1145:
1125:
1106:
1064:
1001:
955:
921:
890:
884:
508:
427:
395:
328:
243:
216:
205:
186:
175:
33:quantum mechanics
8915:
8887:
8886:
8852:
8832:
8826:
8825:
8815:
8797:
8773:
8764:
8763:
8753:
8727:
8706:
8700:
8699:
8689:
8671:
8653:
8629:
8623:
8622:
8612:
8586:
8565:
8559:
8558:
8532:
8512:
8506:
8505:
8479:
8459:
8450:
8449:
8447:
8429:
8405:
8399:
8398:
8396:
8378:
8354:
8348:
8347:
8337:
8311:
8291:
8285:
8284:
8250:
8226:
8220:
8219:
8193:
8173:
8167:
8166:
8148:
8122:
8102:
8096:
8095:
8085:
8067:
8043:
8034:
8033:
8015:
7989:
7969:
7960:
7959:
7925:
7905:
7899:
7898:
7880:
7854:
7834:
7828:
7827:
7801:
7781:
7775:
7774:
7748:
7728:
7722:
7721:
7687:
7667:
7661:
7660:
7658:
7640:
7616:
7607:
7606:
7580:
7560:
7554:
7553:
7535:
7515:
7509:
7508:
7474:
7450:
7437:
7436:
7426:
7408:
7384:
7375:
7374:
7372:
7354:
7326:
7320:
7319:
7285:
7264:
7258:
7257:
7247:
7229:
7205:
7199:
7198:
7181:(3): 1806–1811.
7170:
7164:
7163:
7129:
7105:
7099:
7098:
7064:
7044:
7038:
7037:
7011:
6991:
6985:
6984:
6950:
6930:
6924:
6923:
6889:
6865:
6859:
6858:
6848:
6822:
6801:
6795:
6794:
6738:
6732:
6731:
6683:
6677:
6676:
6642:
6622:
6611:
6610:
6592:
6574:
6550:
6544:
6543:
6487:
6481:
6480:
6446:
6422:
6407:
6406:
6380:
6378:quant-ph/0605072
6360:
6354:
6353:
6317:
6308:
6307:
6273:
6271:quant-ph/0302164
6249:
6236:
6235:
6199:
6190:
6189:
6164:(5): 2277–2289.
6153:
6134:
6132:
6131:
6126:
6124:
6123:
6107:
6105:
6104:
6099:
6096:
6095:
6083:
6082:
6066:
6064:
6063:
6058:
6056:
6055:
6039:
6037:
6036:
6031:
6019:
6017:
6016:
6011:
6009:
6008:
5992:
5990:
5989:
5984:
5982:
5981:
5965:
5963:
5962:
5957:
5955:
5954:
5953:
5945:
5940:
5939:
5922:
5921:
5912:
5903:
5878:
5876:
5875:
5870:
5847:
5842:
5830:
5829:
5821:
5811:
5809:
5808:
5803:
5798:
5794:
5793:
5789:
5788:
5787:
5785:
5780:
5768:
5763:
5762:
5742:
5741:
5739:
5734:
5722:
5717:
5716:
5704:
5671:
5666:
5665:
5664:
5656:
5649:
5615:
5614:
5575:
5574:
5549:
5547:
5546:
5541:
5518:
5517:
5495:
5493:
5492:
5487:
5462:
5460:
5459:
5454:
5449:
5448:
5439:
5438:
5411:
5409:
5408:
5403:
5401:
5400:
5378:
5376:
5375:
5370:
5362:
5361:
5339:
5337:
5336:
5331:
5325:
5320:
5311:
5310:
5295:
5294:
5285:
5284:
5269:
5264:
5263:
5241:
5239:
5238:
5233:
5231:
5230:
5209:
5182:
5180:
5179:
5174:
5172:
5171:
5156:
5155:
5146:
5137:
5131:
5130:
5111:
5109:
5108:
5103:
5098:
5097:
5079:
5078:
5048:
5047:
5010:
5008:
5007:
5002:
4986:
4984:
4983:
4978:
4976:
4975:
4933:
4931:
4930:
4925:
4923:
4922:
4906:
4904:
4903:
4898:
4893:
4891:
4886:
4881:
4872:
4871:
4858:
4854:
4853:
4843:
4838:
4836:
4834:
4829:
4816:
4812:
4811:
4801:
4796:
4795:
4783:
4782:
4781:
4776:
4775:
4767:
4752:
4750:
4749:
4744:
4742:
4741:
4725:
4723:
4722:
4717:
4705:
4703:
4702:
4697:
4685:
4683:
4682:
4677:
4665:
4663:
4662:
4657:
4652:
4651:
4632:
4630:
4629:
4624:
4619:
4618:
4609:
4608:
4600:
4590:
4588:
4587:
4582:
4570:
4568:
4567:
4562:
4557:
4556:
4551:
4542:
4541:
4532:
4531:
4523:
4520:
4514:
4509:
4500:
4499:
4497:
4492:
4483:
4482:
4477:
4476:
4460:
4459:
4446:
4444:
4442:
4437:
4428:
4427:
4423:
4406:
4404:
4399:
4386:
4371:
4369:
4368:
4363:
4351:
4349:
4348:
4343:
4340:
4326:
4317:
4316:
4315:
4310:
4309:
4301:
4286:
4284:
4283:
4278:
4273:
4271:
4270:
4269:
4256:
4255:
4254:
4242:
4241:
4231:
4225:
4211:
4202:
4201:
4200:
4195:
4194:
4186:
4175:
4174:
4165:
4164:
4163:
4158:
4157:
4149:
4126:
4124:
4123:
4118:
4116:
4115:
4100:
4099:
4083:
4081:
4080:
4075:
4073:
4072:
4054:
4052:
4051:
4046:
4044:
4043:
4018:
4016:
4015:
4010:
4008:
4007:
3985:
3983:
3982:
3977:
3956:
3954:
3953:
3948:
3940:
3938:
3936:
3931:
3921:
3916:
3903:
3902:
3901:
3882:
3843:
3841:
3840:
3835:
3823:
3821:
3820:
3815:
3796:
3794:
3793:
3788:
3776:
3774:
3773:
3768:
3766:
3765:
3749:
3747:
3746:
3741:
3736:
3734:
3729:
3724:
3714:
3709:
3700:
3699:
3690:
3689:
3680:
3679:
3666:
3662:
3661:
3648:
3643:
3641:
3632:
3614:
3602:
3600:
3599:
3594:
3582:
3580:
3579:
3574:
3546:
3544:
3543:
3538:
3536:
3535:
3513:
3511:
3510:
3505:
3503:
3502:
3476:
3474:
3473:
3468:
3463:
3462:
3456:
3452:
3451:
3450:
3449:
3447:
3442:
3429:
3424:
3423:
3422:
3413:
3408:
3400:
3371:
3366:
3357:
3349:
3333:
3330:
3325:
3316:
3315:
3306:
3298:
3297:
3261:
3260:
3238:
3236:
3235:
3230:
3228:
3227:
3208:
3206:
3205:
3200:
3180:
3157:
3156:
3135:
3112:
3111:
3096:
3095:
3091:
3060:
3052:
3032:
3024:
3012:
3010:
2996:
2982:
2934:
2932:
2931:
2926:
2915:
2914:
2906:
2896:
2894:
2893:
2888:
2883:
2882:
2880:
2875:
2866:
2865:
2848:
2847:
2842:
2833:
2832:
2823:
2822:
2814:
2811:
2806:
2805:
2792:
2790:
2788:
2783:
2774:
2773:
2769:
2754:
2749:
2740:
2732:
2729:
2724:
2715:
2714:
2705:
2693:
2691:
2690:
2685:
2673:
2671:
2670:
2665:
2663:
2662:
2653:
2652:
2639:
2637:
2636:
2631:
2629:
2628:
2619:
2618:
2605:
2603:
2602:
2597:
2589:
2588:
2587:
2581:
2576:
2575:
2570:
2569:
2561:
2557:
2552:
2551:
2541:
2537:
2536:
2535:
2534:
2531:
2529:
2524:
2511:
2510:
2509:
2500:
2499:
2490:
2489:
2479:
2457:
2454:
2449:
2440:
2439:
2430:
2419:
2418:
2417:
2411:
2406:
2402:
2401:
2400:
2399:
2394:
2393:
2385:
2377:
2376:
2368:
2360:
2355:
2354:
2344:
2336:
2328:
2326:
2318:
2314:
2313:
2312:
2306:
2301:
2300:
2295:
2294:
2286:
2282:
2277:
2276:
2262:
2253:
2251:
2250:
2245:
2233:
2231:
2230:
2225:
2220:
2216:
2215:
2211:
2210:
2209:
2208:
2203:
2202:
2194:
2186:
2182:
2181:
2172:
2171:
2163:
2151:
2147:
2146:
2137:
2136:
2128:
2116:
2115:
2106:
2105:
2092:
2091:
2078:
2077:
2064:
2062:
2060:
2055:
2039:
2034:
2030:
2029:
2028:
2027:
2022:
2021:
2013:
2005:
2004:
1996:
1988:
1980:
1972:
1970:
1961:
1960:
1959:
1954:
1953:
1945:
1936:
1927:
1925:
1924:
1919:
1917:
1916:
1911:
1910:
1902:
1888:
1886:
1885:
1880:
1877:
1876:
1861:
1860:
1844:
1842:
1841:
1836:
1834:
1833:
1815:
1813:
1812:
1807:
1804:
1803:
1772:
1770:
1769:
1764:
1761:
1760:
1745:
1744:
1728:
1726:
1725:
1720:
1718:
1717:
1699:
1697:
1696:
1691:
1688:
1687:
1656:
1654:
1653:
1648:
1645:
1644:
1629:
1628:
1612:
1610:
1609:
1604:
1602:
1601:
1583:
1581:
1580:
1575:
1572:
1571:
1546:
1544:
1543:
1538:
1536:
1535:
1519:
1517:
1516:
1511:
1496:
1494:
1493:
1488:
1483:
1482:
1473:
1472:
1464:
1454:
1452:
1451:
1446:
1444:
1443:
1427:
1425:
1424:
1419:
1417:
1416:
1403:
1401:
1400:
1395:
1383:
1381:
1380:
1375:
1363:
1361:
1360:
1355:
1344:
1343:
1334:
1333:
1328:
1327:
1319:
1308:
1306:
1305:
1300:
1289:
1288:
1278:
1273:
1268:
1267:
1259:
1248:
1246:
1245:
1240:
1226:
1225:
1216:
1215:
1210:
1209:
1201:
1188:
1187:
1177:
1172:
1167:
1166:
1158:
1153:
1144:
1143:
1133:
1118:
1117:
1108:
1107:
1099:
1089:
1087:
1086:
1081:
1076:
1075:
1066:
1065:
1057:
1047:
1045:
1044:
1039:
1031:
1030:
1021:
1013:
1012:
1003:
1002:
994:
991:
986:
985:
967:
966:
957:
956:
948:
939:
938:
929:
928:
923:
922:
914:
903:
901:
900:
895:
888:
882:
878:
866:
864:
863:
858:
832:
831:
822:
821:
800:
799:
790:
789:
777:
776:
767:
766:
754:
742:
740:
739:
734:
725:
717:
716:
707:
706:
687:
686:
677:
676:
660:
658:
657:
652:
650:
649:
648:
646:
641:
628:
623:
622:
621:
612:
611:
602:
601:
577:
576:
567:
566:
547:
545:
544:
539:
537:
536:
520:
518:
517:
512:
510:
509:
501:
491:
489:
488:
483:
475:
474:
465:
460:
456:
445:
444:
435:
434:
429:
428:
420:
413:
412:
403:
402:
397:
396:
388:
381:
380:
371:
370:
357:
356:
343:
342:
329:
327:
325:
320:
304:
295:
292:
288:
287:
278:
277:
261:
260:
251:
250:
245:
244:
236:
231:
230:
217:
215:
214:
201:
200:
188:
187:
179:
176:
168:
152:
151:
142:
117:
115:
114:
109:
107:
106:
90:
88:
87:
82:
8923:
8922:
8918:
8917:
8916:
8914:
8913:
8912:
8893:
8892:
8891:
8890:
8834:
8833:
8829:
8775:
8774:
8767:
8708:
8707:
8703:
8631:
8630:
8626:
8567:
8566:
8562:
8514:
8513:
8509:
8461:
8460:
8453:
8407:
8406:
8402:
8356:
8355:
8351:
8293:
8292:
8288:
8228:
8227:
8223:
8175:
8174:
8170:
8104:
8103:
8099:
8045:
8044:
8037:
7971:
7970:
7963:
7907:
7906:
7902:
7836:
7835:
7831:
7783:
7782:
7778:
7730:
7729:
7725:
7669:
7668:
7664:
7618:
7617:
7610:
7562:
7561:
7557:
7517:
7516:
7512:
7452:
7451:
7440:
7386:
7385:
7378:
7328:
7327:
7323:
7266:
7265:
7261:
7207:
7206:
7202:
7172:
7171:
7167:
7120:(10): 761–765.
7107:
7106:
7102:
7046:
7045:
7041:
6993:
6992:
6988:
6932:
6931:
6927:
6867:
6866:
6862:
6803:
6802:
6798:
6740:
6739:
6735:
6685:
6684:
6680:
6624:
6623:
6614:
6552:
6551:
6547:
6489:
6488:
6484:
6424:
6423:
6410:
6362:
6361:
6357:
6319:
6318:
6311:
6258:Physics Reports
6251:
6250:
6239:
6201:
6200:
6193:
6155:
6154:
6147:
6142:
6115:
6110:
6109:
6087:
6074:
6069:
6068:
6047:
6042:
6041:
6022:
6021:
6000:
5995:
5994:
5973:
5968:
5967:
5931:
5923:
5913:
5881:
5880:
5814:
5813:
5754:
5746:
5708:
5677:
5676:
5672:
5650:
5647:
5643:
5600:
5557:
5552:
5551:
5550:, which becomes
5503:
5498:
5497:
5469:
5468:
5465:non-white noise
5430:
5425:
5424:
5386:
5381:
5380:
5347:
5342:
5341:
5296:
5286:
5276:
5255:
5244:
5243:
5222:
5185:
5184:
5157:
5147:
5119:
5114:
5113:
5086:
5067:
5033:
5013:
5012:
4993:
4992:
4961:
4956:
4955:
4945:
4914:
4909:
4908:
4863:
4859:
4845:
4844:
4817:
4803:
4802:
4784:
4764:
4755:
4754:
4733:
4728:
4727:
4708:
4707:
4688:
4687:
4668:
4667:
4635:
4634:
4593:
4592:
4573:
4572:
4546:
4470:
4462:
4411:
4407:
4387:
4374:
4373:
4354:
4353:
4298:
4289:
4288:
4261:
4257:
4246:
4233:
4232:
4183:
4166:
4146:
4137:
4136:
4104:
4091:
4086:
4085:
4062:
4057:
4056:
4032:
4021:
4020:
3996:
3988:
3987:
3959:
3958:
3904:
3893:
3883:
3846:
3845:
3826:
3825:
3806:
3805:
3779:
3778:
3757:
3752:
3751:
3691:
3681:
3671:
3667:
3653:
3649:
3633:
3615:
3608:
3607:
3585:
3584:
3565:
3564:
3553:
3524:
3516:
3515:
3491:
3483:
3482:
3414:
3401:
3381:
3341:
3337:
3307:
3246:
3241:
3240:
3216:
3211:
3210:
3173:
3145:
3128:
3097:
3070:
3000:
2975:
2958:
2957:
2953:Interferometric
2950:
2941:
2899:
2898:
2857:
2849:
2837:
2757:
2756:
2706:
2696:
2695:
2676:
2675:
2642:
2641:
2608:
2607:
2558:
2512:
2501:
2480:
2469:
2462:
2458:
2431:
2382:
2365:
2361:
2319:
2283:
2263:
2256:
2255:
2236:
2235:
2191:
2155:
2124:
2120:
2043:
2010:
1993:
1989:
1962:
1942:
1937:
1930:
1929:
1899:
1894:
1893:
1865:
1852:
1847:
1846:
1823:
1818:
1817:
1786:
1775:
1774:
1749:
1736:
1731:
1730:
1707:
1702:
1701:
1670:
1659:
1658:
1633:
1620:
1615:
1614:
1591:
1586:
1585:
1560:
1549:
1548:
1527:
1522:
1521:
1502:
1501:
1457:
1456:
1435:
1430:
1429:
1406:
1405:
1386:
1385:
1366:
1365:
1316:
1311:
1310:
1251:
1250:
1198:
1135:
1092:
1091:
1050:
1049:
1022:
977:
911:
906:
905:
869:
868:
781:
758:
745:
744:
698:
668:
663:
662:
613:
584:
550:
549:
528:
523:
522:
494:
493:
466:
417:
385:
308:
299:
296:
269:
233:
206:
163:
159:
143:
129:
128:
125:
98:
93:
92:
73:
72:
45:
17:
12:
11:
5:
8921:
8919:
8911:
8910:
8905:
8895:
8894:
8889:
8888:
8827:
8765:
8701:
8624:
8560:
8507:
8451:
8400:
8349:
8302:(12): 124036.
8286:
8241:(10): 100404.
8221:
8168:
8113:(11): 110401.
8097:
8035:
7961:
7900:
7829:
7792:(21): 210404.
7776:
7723:
7662:
7631:(10): 103001.
7608:
7555:
7510:
7438:
7399:(14): 143004.
7376:
7321:
7276:(3): 263–268.
7259:
7227:hep-ex/0110061
7200:
7165:
7100:
7055:(24): 245304.
7039:
6986:
6925:
6880:(3): 243–250.
6874:Nature Physics
6860:
6796:
6733:
6692:Nature Physics
6678:
6633:(11): 115302.
6612:
6545:
6482:
6408:
6355:
6328:(2): 470–491.
6309:
6264:(5): 257–426.
6237:
6191:
6144:
6143:
6141:
6138:
6137:
6136:
6122:
6118:
6094:
6090:
6086:
6081:
6077:
6054:
6050:
6029:
6007:
6003:
5980:
5976:
5952:
5948:
5944:
5938:
5934:
5930:
5926:
5920:
5916:
5909:
5906:
5900:
5897:
5894:
5891:
5888:
5868:
5865:
5862:
5859:
5855:
5851:
5846:
5841:
5837:
5833:
5827:
5824:
5801:
5797:
5792:
5784:
5779:
5775:
5771:
5767:
5761:
5757:
5753:
5749:
5745:
5738:
5733:
5729:
5725:
5721:
5715:
5711:
5707:
5703:
5699:
5696:
5693:
5690:
5687:
5684:
5680:
5675:
5669:
5662:
5659:
5653:
5646:
5642:
5639:
5636:
5633:
5630:
5627:
5624:
5621:
5618:
5613:
5610:
5607:
5603:
5599:
5596:
5593:
5590:
5587:
5584:
5581:
5578:
5573:
5570:
5567:
5564:
5560:
5539:
5536:
5533:
5530:
5527:
5524:
5521:
5516:
5513:
5510:
5506:
5485:
5482:
5479:
5476:
5452:
5447:
5442:
5437:
5433:
5414:
5413:
5399:
5396:
5393:
5389:
5368:
5365:
5360:
5357:
5354:
5350:
5329:
5324:
5319:
5315:
5309:
5306:
5303:
5299:
5293:
5289:
5283:
5279:
5275:
5272:
5268:
5262:
5258:
5254:
5251:
5229:
5225:
5221:
5218:
5215:
5212:
5208:
5204:
5201:
5198:
5195:
5192:
5170:
5167:
5164:
5160:
5154:
5150:
5143:
5140:
5134:
5129:
5126:
5122:
5101:
5096:
5093:
5089:
5085:
5082:
5077:
5074:
5070:
5066:
5063:
5060:
5057:
5054:
5051:
5046:
5043:
5040:
5036:
5032:
5029:
5026:
5023:
5020:
5000:
4974:
4971:
4968:
4964:
4944:
4941:
4940:
4939:
4921:
4917:
4896:
4890:
4885:
4880:
4876:
4870:
4866:
4862:
4857:
4852:
4848:
4841:
4833:
4828:
4824:
4820:
4815:
4810:
4806:
4799:
4794:
4791:
4787:
4780:
4773:
4770:
4762:
4740:
4736:
4715:
4695:
4675:
4655:
4650:
4645:
4642:
4622:
4617:
4612:
4606:
4603:
4580:
4560:
4555:
4550:
4545:
4540:
4535:
4529:
4526:
4519:
4513:
4508:
4504:
4496:
4491:
4487:
4481:
4475:
4469:
4465:
4458:
4452:
4449:
4441:
4436:
4432:
4426:
4422:
4418:
4414:
4410:
4403:
4398:
4394:
4390:
4384:
4381:
4361:
4339:
4336:
4333:
4330:
4325:
4321:
4314:
4307:
4304:
4296:
4276:
4268:
4264:
4260:
4253:
4249:
4245:
4240:
4236:
4229:
4224:
4221:
4218:
4215:
4210:
4206:
4199:
4192:
4189:
4181:
4178:
4173:
4169:
4162:
4155:
4152:
4144:
4129:
4128:
4114:
4111:
4107:
4103:
4098:
4094:
4071:
4068:
4064:
4042:
4039:
4035:
4031:
4028:
4006:
4003:
3999:
3995:
3975:
3972:
3969:
3966:
3946:
3943:
3935:
3930:
3926:
3920:
3915:
3911:
3907:
3900:
3896:
3892:
3889:
3886:
3880:
3877:
3874:
3871:
3868:
3865:
3862:
3859:
3856:
3853:
3833:
3813:
3786:
3764:
3760:
3739:
3733:
3728:
3723:
3719:
3713:
3708:
3704:
3698:
3694:
3688:
3684:
3678:
3674:
3670:
3665:
3660:
3656:
3652:
3646:
3640:
3636:
3631:
3628:
3625:
3622:
3618:
3605:
3604:
3592:
3572:
3552:
3549:
3534:
3531:
3527:
3523:
3501:
3498:
3494:
3490:
3466:
3461:
3455:
3446:
3441:
3437:
3433:
3428:
3421:
3417:
3411:
3407:
3404:
3398:
3395:
3392:
3388:
3384:
3379:
3375:
3370:
3365:
3361:
3355:
3352:
3347:
3344:
3340:
3336:
3329:
3324:
3320:
3314:
3310:
3304:
3301:
3296:
3291:
3288:
3285:
3282:
3279:
3276:
3273:
3270:
3267:
3264:
3259:
3256:
3253:
3249:
3226:
3223:
3219:
3198:
3195:
3192:
3189:
3186:
3183:
3179:
3176:
3172:
3169:
3166:
3163:
3160:
3155:
3152:
3148:
3144:
3141:
3138:
3134:
3131:
3127:
3124:
3121:
3118:
3115:
3110:
3107:
3104:
3100:
3094:
3090:
3086:
3083:
3080:
3077:
3073:
3068:
3064:
3059:
3056:
3051:
3048:
3044:
3040:
3036:
3031:
3028:
3023:
3020:
3016:
3009:
3006:
3003:
2999:
2994:
2991:
2988:
2985:
2981:
2978:
2974:
2971:
2968:
2965:
2949:
2946:
2940:
2937:
2924:
2921:
2918:
2912:
2909:
2886:
2879:
2874:
2870:
2864:
2860:
2856:
2852:
2846:
2841:
2836:
2831:
2826:
2820:
2817:
2810:
2804:
2798:
2795:
2787:
2782:
2778:
2772:
2768:
2764:
2760:
2753:
2748:
2744:
2738:
2735:
2728:
2723:
2719:
2713:
2709:
2703:
2683:
2661:
2656:
2651:
2627:
2622:
2617:
2595:
2592:
2586:
2580:
2574:
2567:
2564:
2556:
2550:
2544:
2540:
2528:
2523:
2519:
2515:
2508:
2504:
2498:
2493:
2488:
2483:
2476:
2472:
2468:
2465:
2461:
2453:
2448:
2444:
2438:
2434:
2428:
2425:
2422:
2416:
2410:
2405:
2398:
2391:
2388:
2380:
2374:
2371:
2364:
2359:
2353:
2347:
2342:
2339:
2334:
2331:
2325:
2322:
2317:
2311:
2305:
2299:
2292:
2289:
2281:
2275:
2269:
2266:
2243:
2223:
2219:
2214:
2207:
2200:
2197:
2189:
2185:
2180:
2175:
2169:
2166:
2158:
2154:
2150:
2145:
2140:
2134:
2131:
2123:
2119:
2114:
2109:
2104:
2099:
2096:
2090:
2084:
2081:
2076:
2070:
2067:
2059:
2054:
2050:
2046:
2042:
2037:
2033:
2026:
2019:
2016:
2008:
2002:
1999:
1992:
1986:
1983:
1978:
1975:
1969:
1965:
1958:
1951:
1948:
1940:
1915:
1908:
1905:
1875:
1872:
1868:
1864:
1859:
1855:
1832:
1829:
1825:
1802:
1799:
1796:
1793:
1789:
1785:
1782:
1759:
1756:
1752:
1748:
1743:
1739:
1716:
1713:
1709:
1686:
1683:
1680:
1677:
1673:
1669:
1666:
1643:
1640:
1636:
1632:
1627:
1623:
1600:
1597:
1593:
1570:
1567:
1563:
1559:
1556:
1534:
1530:
1509:
1486:
1481:
1476:
1470:
1467:
1442:
1438:
1415:
1393:
1373:
1353:
1350:
1347:
1342:
1337:
1332:
1325:
1322:
1298:
1295:
1292:
1287:
1282:
1277:
1272:
1265:
1262:
1238:
1235:
1232:
1229:
1224:
1219:
1214:
1207:
1204:
1197:
1194:
1191:
1186:
1181:
1176:
1171:
1164:
1161:
1152:
1148:
1142:
1138:
1132:
1128:
1124:
1121:
1116:
1111:
1105:
1102:
1079:
1074:
1069:
1063:
1060:
1037:
1034:
1029:
1025:
1020:
1016:
1011:
1006:
1000:
997:
990:
984:
980:
976:
973:
970:
965:
960:
954:
951:
945:
942:
937:
932:
927:
920:
917:
893:
887:
881:
877:
856:
853:
850:
847:
844:
841:
838:
835:
830:
825:
820:
815:
812:
809:
806:
803:
798:
793:
788:
784:
780:
775:
770:
765:
761:
757:
753:
732:
728:
724:
720:
715:
710:
705:
701:
696:
693:
690:
685:
680:
675:
671:
645:
640:
636:
632:
627:
620:
616:
610:
605:
600:
595:
591:
587:
583:
580:
575:
570:
565:
560:
557:
535:
531:
507:
504:
481:
478:
473:
469:
464:
459:
455:
451:
448:
443:
438:
433:
426:
423:
416:
411:
406:
401:
394:
391:
384:
379:
374:
369:
364:
361:
355:
349:
346:
341:
335:
332:
324:
319:
315:
311:
307:
302:
298:
294:
291:
286:
281:
276:
272:
267:
264:
259:
254:
249:
242:
239:
229:
223:
220:
213:
209:
204:
198:
195:
191:
185:
182:
174:
171:
166:
162:
158:
155:
150:
146:
141:
136:
124:
121:
120:
119:
105:
101:
80:
69:
66:
63:
44:
41:
15:
13:
10:
9:
6:
4:
3:
2:
8920:
8909:
8906:
8904:
8901:
8900:
8898:
8884:
8880:
8876:
8872:
8868:
8864:
8860:
8856:
8851:
8846:
8842:
8838:
8831:
8828:
8823:
8819:
8814:
8809:
8805:
8801:
8796:
8791:
8787:
8783:
8779:
8772:
8770:
8766:
8761:
8757:
8752:
8751:11368/2929989
8747:
8743:
8739:
8735:
8731:
8726:
8721:
8718:(4): 042109.
8717:
8713:
8705:
8702:
8697:
8693:
8688:
8683:
8679:
8675:
8670:
8665:
8661:
8657:
8652:
8647:
8643:
8639:
8635:
8628:
8625:
8620:
8616:
8611:
8610:1721.1/125376
8606:
8602:
8598:
8594:
8590:
8585:
8580:
8577:(1): 011802.
8576:
8572:
8564:
8561:
8556:
8552:
8548:
8544:
8540:
8536:
8531:
8526:
8523:(1): 012119.
8522:
8518:
8511:
8508:
8503:
8499:
8495:
8491:
8487:
8483:
8478:
8473:
8470:(2): 023349.
8469:
8465:
8458:
8456:
8452:
8446:
8441:
8437:
8433:
8428:
8423:
8420:(1): 013057.
8419:
8415:
8411:
8404:
8401:
8395:
8390:
8386:
8382:
8377:
8372:
8369:(8): 084054.
8368:
8364:
8360:
8353:
8350:
8345:
8341:
8336:
8335:11368/2889661
8331:
8327:
8323:
8319:
8315:
8310:
8305:
8301:
8297:
8290:
8287:
8282:
8278:
8274:
8270:
8266:
8262:
8258:
8254:
8249:
8244:
8240:
8236:
8232:
8225:
8222:
8217:
8213:
8209:
8205:
8201:
8197:
8192:
8187:
8184:(2): 022122.
8183:
8179:
8172:
8169:
8164:
8160:
8156:
8152:
8147:
8146:11368/2910142
8142:
8138:
8134:
8130:
8126:
8121:
8116:
8112:
8108:
8101:
8098:
8093:
8089:
8084:
8079:
8075:
8071:
8066:
8061:
8058:(8): 083022.
8057:
8053:
8049:
8042:
8040:
8036:
8031:
8027:
8023:
8019:
8014:
8009:
8005:
8001:
7997:
7993:
7988:
7983:
7980:(9): 090402.
7979:
7975:
7968:
7966:
7962:
7957:
7953:
7949:
7945:
7941:
7937:
7933:
7929:
7924:
7919:
7916:(5): 050403.
7915:
7911:
7904:
7901:
7896:
7892:
7888:
7884:
7879:
7874:
7870:
7866:
7862:
7858:
7853:
7848:
7845:(2): 020405.
7844:
7840:
7833:
7830:
7825:
7821:
7817:
7813:
7809:
7805:
7800:
7795:
7791:
7787:
7780:
7777:
7772:
7768:
7764:
7760:
7756:
7752:
7747:
7742:
7739:(5): 052121.
7738:
7734:
7727:
7724:
7719:
7715:
7711:
7707:
7703:
7699:
7695:
7691:
7686:
7681:
7678:(8): 080402.
7677:
7673:
7666:
7663:
7657:
7652:
7648:
7644:
7639:
7634:
7630:
7626:
7622:
7615:
7613:
7609:
7604:
7600:
7596:
7592:
7588:
7584:
7579:
7574:
7571:(5): 052119.
7570:
7566:
7559:
7556:
7551:
7547:
7543:
7539:
7534:
7529:
7526:(5): 052118.
7525:
7521:
7514:
7511:
7506:
7502:
7498:
7494:
7490:
7486:
7482:
7478:
7473:
7468:
7464:
7460:
7456:
7449:
7447:
7445:
7443:
7439:
7434:
7430:
7425:
7420:
7416:
7412:
7407:
7402:
7398:
7394:
7390:
7383:
7381:
7377:
7371:
7366:
7362:
7358:
7353:
7348:
7344:
7340:
7336:
7332:
7325:
7322:
7317:
7313:
7309:
7305:
7301:
7297:
7293:
7289:
7284:
7279:
7275:
7271:
7263:
7260:
7255:
7251:
7246:
7241:
7237:
7233:
7228:
7223:
7219:
7215:
7211:
7204:
7201:
7196:
7192:
7188:
7184:
7180:
7176:
7169:
7166:
7161:
7157:
7153:
7149:
7145:
7141:
7137:
7133:
7128:
7123:
7119:
7115:
7111:
7104:
7101:
7096:
7092:
7088:
7084:
7080:
7076:
7072:
7068:
7063:
7058:
7054:
7050:
7043:
7040:
7035:
7031:
7027:
7023:
7019:
7015:
7010:
7005:
7002:(1): 012116.
7001:
6997:
6990:
6987:
6982:
6978:
6974:
6970:
6966:
6962:
6958:
6954:
6949:
6944:
6940:
6936:
6929:
6926:
6921:
6917:
6913:
6909:
6905:
6901:
6897:
6893:
6888:
6883:
6879:
6875:
6871:
6864:
6861:
6856:
6852:
6847:
6842:
6838:
6834:
6830:
6826:
6821:
6816:
6813:(1): 012108.
6812:
6808:
6800:
6797:
6792:
6788:
6784:
6780:
6776:
6772:
6768:
6764:
6760:
6756:
6752:
6748:
6744:
6737:
6734:
6729:
6725:
6721:
6717:
6713:
6709:
6705:
6701:
6697:
6693:
6689:
6682:
6679:
6674:
6670:
6666:
6662:
6658:
6654:
6650:
6646:
6641:
6636:
6632:
6628:
6621:
6619:
6617:
6613:
6608:
6604:
6600:
6596:
6591:
6586:
6582:
6578:
6573:
6568:
6564:
6560:
6556:
6549:
6546:
6541:
6537:
6533:
6529:
6525:
6521:
6517:
6513:
6509:
6505:
6501:
6497:
6493:
6486:
6483:
6478:
6474:
6470:
6466:
6462:
6458:
6454:
6450:
6445:
6440:
6436:
6432:
6428:
6421:
6419:
6417:
6415:
6413:
6409:
6404:
6400:
6396:
6392:
6388:
6384:
6379:
6374:
6371:(44): 13501.
6370:
6366:
6359:
6356:
6351:
6347:
6343:
6339:
6335:
6331:
6327:
6323:
6316:
6314:
6310:
6305:
6301:
6297:
6293:
6289:
6285:
6281:
6277:
6272:
6267:
6263:
6259:
6255:
6248:
6246:
6244:
6242:
6238:
6233:
6229:
6225:
6221:
6217:
6213:
6209:
6205:
6198:
6196:
6192:
6187:
6183:
6179:
6175:
6171:
6167:
6163:
6159:
6152:
6150:
6146:
6139:
6120:
6092:
6088:
6084:
6079:
6052:
6048:
6027:
6005:
5978:
5946:
5936:
5928:
5924:
5918:
5907:
5904:
5898:
5892:
5886:
5863:
5857:
5853:
5844:
5839:
5835:
5831:
5822:
5799:
5795:
5790:
5782:
5777:
5773:
5769:
5765:
5759:
5755:
5751:
5747:
5743:
5736:
5731:
5727:
5723:
5719:
5713:
5705:
5701:
5697:
5694:
5691:
5688:
5682:
5678:
5673:
5667:
5657:
5651:
5644:
5640:
5637:
5631:
5628:
5625:
5622:
5619:
5611:
5608:
5605:
5601:
5597:
5591:
5588:
5585:
5582:
5579:
5571:
5568:
5565:
5562:
5558:
5534:
5531:
5528:
5525:
5522:
5514:
5511:
5508:
5504:
5480:
5474:
5466:
5435:
5431:
5423:
5419:
5416:
5415:
5397:
5394:
5391:
5387:
5366:
5363:
5358:
5355:
5352:
5348:
5322:
5317:
5313:
5307:
5304:
5301:
5297:
5291:
5287:
5281:
5277:
5273:
5266:
5260:
5252:
5249:
5227:
5219:
5216:
5213:
5206:
5202:
5199:
5196:
5193:
5190:
5168:
5165:
5162:
5158:
5152:
5148:
5141:
5138:
5132:
5127:
5124:
5120:
5099:
5094:
5091:
5087:
5083:
5075:
5072:
5068:
5064:
5058:
5052:
5044:
5041:
5038:
5034:
5030:
5024:
5018:
4998:
4990:
4972:
4969:
4966:
4962:
4953:
4950:
4949:
4948:
4942:
4937:
4919:
4915:
4894:
4888:
4883:
4878:
4874:
4868:
4864:
4860:
4855:
4850:
4839:
4831:
4826:
4822:
4818:
4813:
4808:
4804:
4797:
4792:
4789:
4778:
4768:
4738:
4734:
4713:
4693:
4673:
4640:
4601:
4578:
4558:
4553:
4524:
4511:
4506:
4502:
4494:
4489:
4485:
4479:
4467:
4463:
4447:
4439:
4434:
4430:
4424:
4420:
4416:
4412:
4408:
4401:
4396:
4392:
4388:
4382:
4379:
4359:
4334:
4331:
4323:
4312:
4302:
4274:
4266:
4262:
4258:
4251:
4247:
4243:
4238:
4227:
4219:
4216:
4208:
4197:
4187:
4176:
4171:
4160:
4150:
4134:
4131:
4130:
4112:
4109:
4105:
4101:
4096:
4092:
4069:
4066:
4063:
4040:
4037:
4033:
4029:
4026:
4004:
4001:
3997:
3993:
3970:
3964:
3944:
3941:
3933:
3928:
3924:
3918:
3913:
3909:
3905:
3898:
3890:
3887:
3884:
3878:
3872:
3866:
3863:
3857:
3851:
3831:
3811:
3803:
3800:
3799:
3798:
3784:
3762:
3758:
3737:
3731:
3726:
3721:
3717:
3711:
3706:
3702:
3696:
3692:
3686:
3682:
3676:
3672:
3668:
3663:
3658:
3654:
3644:
3638:
3626:
3590:
3570:
3562:
3559:
3558:
3557:
3550:
3548:
3532:
3529:
3525:
3521:
3499:
3496:
3492:
3488:
3478:
3464:
3453:
3444:
3439:
3435:
3431:
3426:
3419:
3409:
3405:
3402:
3396:
3393:
3386:
3382:
3377:
3368:
3363:
3359:
3353:
3350:
3345:
3342:
3338:
3334:
3327:
3322:
3318:
3312:
3308:
3302:
3299:
3289:
3286:
3283:
3277:
3274:
3271:
3268:
3265:
3257:
3254:
3251:
3247:
3224:
3221:
3217:
3196:
3190:
3187:
3184:
3181:
3177:
3174:
3170:
3167:
3164:
3161:
3153:
3150:
3146:
3139:
3136:
3132:
3129:
3125:
3122:
3119:
3116:
3108:
3105:
3102:
3098:
3088:
3084:
3081:
3078:
3075:
3071:
3066:
3054:
3046:
3042:
3038:
3026:
3018:
3014:
3004:
3001:
2997:
2992:
2986:
2983:
2979:
2976:
2972:
2969:
2963:
2954:
2947:
2945:
2938:
2936:
2919:
2907:
2884:
2877:
2872:
2868:
2862:
2858:
2854:
2850:
2844:
2815:
2793:
2785:
2780:
2776:
2770:
2766:
2762:
2758:
2751:
2746:
2742:
2736:
2726:
2721:
2717:
2711:
2707:
2701:
2681:
2654:
2620:
2593:
2572:
2562:
2538:
2526:
2521:
2517:
2513:
2506:
2491:
2474:
2470:
2466:
2463:
2459:
2451:
2446:
2442:
2436:
2432:
2426:
2423:
2403:
2396:
2386:
2378:
2369:
2362:
2337:
2332:
2329:
2323:
2297:
2287:
2241:
2221:
2217:
2212:
2205:
2195:
2187:
2164:
2156:
2152:
2129:
2121:
2107:
2094:
2079:
2065:
2057:
2052:
2048:
2044:
2040:
2035:
2031:
2024:
2014:
2006:
1997:
1990:
1981:
1976:
1973:
1967:
1956:
1946:
1913:
1903:
1890:
1873:
1870:
1866:
1862:
1857:
1853:
1830:
1827:
1824:
1800:
1797:
1794:
1791:
1787:
1783:
1780:
1757:
1754:
1750:
1746:
1741:
1737:
1714:
1711:
1708:
1684:
1681:
1678:
1675:
1671:
1667:
1664:
1641:
1638:
1634:
1630:
1625:
1621:
1598:
1595:
1592:
1568:
1565:
1561:
1557:
1554:
1532:
1528:
1507:
1498:
1465:
1440:
1436:
1404:at the point
1391:
1371:
1348:
1345:
1330:
1320:
1293:
1290:
1275:
1270:
1260:
1236:
1230:
1227:
1212:
1202:
1192:
1189:
1174:
1169:
1159:
1150:
1146:
1140:
1136:
1130:
1126:
1122:
1100:
1058:
1035:
1027:
1023:
995:
982:
978:
971:
949:
943:
925:
915:
885:
854:
848:
845:
842:
836:
823:
810:
807:
786:
782:
763:
759:
730:
722:
703:
699:
691:
673:
669:
643:
638:
634:
630:
625:
618:
603:
589:
585:
581:
568:
555:
533:
529:
502:
479:
471:
467:
457:
453:
431:
421:
399:
389:
372:
359:
344:
330:
322:
317:
313:
309:
305:
300:
274:
270:
247:
237:
218:
211:
207:
202:
196:
193:
180:
169:
164:
160:
156:
148:
144:
122:
103:
99:
78:
70:
67:
64:
61:
60:
59:
56:
54:
50:
42:
40:
38:
34:
30:
27:) model is a
26:
22:
8843:(5): 50006.
8840:
8836:
8830:
8785:
8781:
8715:
8711:
8704:
8644:(1): 12518.
8641:
8637:
8627:
8574:
8570:
8563:
8520:
8516:
8510:
8467:
8463:
8417:
8413:
8403:
8366:
8362:
8352:
8299:
8295:
8289:
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5228:5
5224:)
5217:+
5214:1
5211:(
5207:/
5197:4
5194:=
5169:L
5166:S
5163:C
5159:T
5153:B
5149:k
5142:2
5139:3
5133:=
5128:s
5125:a
5121:E
5100:,
5095:s
5092:a
5088:E
5084:+
5081:)
5076:s
5073:a
5069:E
5062:)
5059:0
5056:(
5053:E
5050:(
5045:t
5035:e
5031:=
5028:)
5025:t
5022:(
5019:E
4999:m
4973:L
4970:S
4967:C
4963:T
4920:B
4916:k
4895:,
4884:2
4879:0
4869:2
4865:m
4861:2
4851:2
4840:+
4832:2
4827:0
4819:m
4814:T
4809:B
4805:k
4798:=
4793:q
4790:e
4779:2
4769:x
4739:0
4714:m
4694:T
4654:)
4649:r
4644:(
4621:)
4616:k
4611:(
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4559:,
4554:2
4549:|
4544:)
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4512:2
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4480:2
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4464:e
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4451:d
4440:2
4435:0
4431:m
4425:2
4421:/
4417:3
4409:2
4402:3
4397:C
4393:r
4383:=
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4335:M
4332:Q
4329:(
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4313:2
4303:x
4275:,
4267:2
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4220:M
4217:Q
4214:(
4209:t
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4188:x
4177:=
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4161:2
4151:x
4113:7
4102:=
4097:C
4093:r
4070:1
4030:=
3974:)
3971:0
3968:(
3965:E
3945:,
3942:t
3934:2
3929:C
3925:r
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3914:0
3910:m
3906:4
3899:2
3888:m
3885:3
3879:+
3876:)
3873:0
3870:(
3867:E
3864:=
3861:)
3858:t
3855:(
3852:E
3832:m
3812:E
3785:c
3763:0
3738:,
3727:2
3722:C
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3707:0
3703:m
3697:3
3693:c
3687:0
3677:2
3669:2
3659:2
3655:Q
3645:=
3635:d
3630:)
3624:(
3617:d
3591:Q
3533:2
3500:5
3465:.
3460:]
3454:)
3445:2
3440:C
3436:r
3432:4
3427:/
3420:2
3416:)
3410:m
3403:k
3394:q
3391:(
3383:e
3374:d
3369:t
3364:0
3354:t
3351:1
3343:1
3339:(
3335:t
3328:2
3323:0
3319:m
3313:2
3309:m
3295:[
3284:=
3281:)
3278:t
3275:,
3272:q
3269:,
3266:k
3263:(
3258:L
3255:S
3252:C
3248:F
3225:M
3222:Q
3197:,
3194:)
3191:t
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3185:w
3182:+
3175:x
3171:,
3168:w
3165:+
3162:x
3159:(
3154:M
3151:Q
3143:)
3140:t
3137:,
3130:x
3123:x
3120:,
3117:k
3114:(
3109:L
3106:S
3103:C
3099:F
3089:/
3085:w
3082:k
3079:i
3072:e
3067:w
3063:d
3055:+
3039:k
3035:d
3027:+
3002:2
2998:1
2993:=
2990:)
2987:t
2984:,
2977:x
2973:,
2970:x
2967:(
2923:)
2920:k
2917:(
2885:,
2878:2
2873:C
2869:r
2863:2
2859:k
2851:e
2845:2
2840:|
2835:)
2830:k
2825:(
2809:|
2803:k
2797:d
2786:2
2781:0
2777:m
2771:2
2767:/
2763:3
2752:3
2747:C
2743:r
2727:2
2722:0
2718:m
2712:2
2708:m
2660:y
2655:=
2650:x
2626:y
2616:x
2594:,
2585:y
2579:|
2573:t
2555:|
2549:x
2539:)
2527:2
2522:C
2518:r
2514:4
2507:2
2503:)
2497:y
2487:x
2482:(
2471:e
2464:1
2460:(
2452:2
2447:0
2443:m
2437:2
2433:m
2415:y
2409:|
2404:]
2397:t
2379:,
2370:H
2363:[
2358:|
2352:x
2338:i
2330:=
2324:t
2310:y
2304:|
2298:t
2280:|
2274:x
2242:m
2222:.
2218:]
2213:]
2206:t
2188:,
2184:)
2179:y
2174:(
2165:M
2157:[
2153:,
2149:)
2144:x
2139:(
2130:M
2122:[
2118:)
2113:y
2103:x
2098:(
2095:g
2089:y
2083:d
2075:x
2069:d
2058:2
2053:0
2049:m
2045:2
2032:]
2025:t
2007:,
1998:H
1991:[
1982:i
1974:=
1968:t
1964:d
1957:t
1939:d
1928::
1914:t
1874:6
1863:=
1858:C
1854:r
1831:1
1816:s
1801:2
1795:6
1784:=
1758:7
1747:=
1742:C
1738:r
1715:1
1700:s
1685:2
1679:8
1668:=
1642:7
1631:=
1626:C
1622:r
1599:1
1584:s
1558:=
1533:C
1529:r
1485:)
1480:x
1475:(
1466:M
1441:j
1437:m
1414:y
1392:s
1372:j
1352:)
1349:s
1346:,
1341:y
1336:(
1331:j
1321:a
1297:)
1294:s
1291:,
1286:y
1281:(
1271:j
1261:a
1237:,
1234:)
1231:s
1228:,
1223:x
1218:(
1213:j
1203:a
1196:)
1193:s
1190:,
1185:x
1180:(
1170:j
1160:a
1151:s
1141:j
1137:m
1131:j
1123:=
1120:)
1115:x
1110:(
1101:M
1078:)
1073:x
1068:(
1059:M
1036:,
1028:t
1019:|
1015:)
1010:x
1005:(
996:M
989:|
983:t
969:)
964:x
959:(
950:M
944:=
941:)
936:x
931:(
926:t
916:N
892:]
880:[
876:E
855:,
852:)
849:s
843:t
840:(
834:)
829:y
819:x
814:(
811:g
808:=
805:]
802:)
797:y
792:(
787:s
783:w
779:)
774:x
769:(
764:t
760:w
756:[
752:E
731:t
727:d
723:/
719:)
714:x
709:(
704:t
700:W
695:d
692:=
689:)
684:x
679:(
674:t
670:w
644:2
639:C
635:r
631:4
626:/
619:2
615:)
609:y
599:x
594:(
586:e
582:=
579:)
574:y
564:x
559:(
556:g
534:0
530:m
503:H
480:.
472:t
463:|
458:]
454:t
450:d
447:)
442:y
437:(
432:t
422:N
415:)
410:x
405:(
400:t
390:N
383:)
378:y
368:x
363:(
360:g
354:y
348:d
340:x
334:d
323:2
318:0
314:m
310:2
290:)
285:x
280:(
275:t
271:W
266:d
263:)
258:x
253:(
248:t
238:N
228:x
222:d
212:0
208:m
197:+
194:t
190:d
181:H
170:i
161:[
157:=
149:t
140:|
135:d
104:C
100:r
23:(
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