68:
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The Efimov states are independent of the underlying physical interaction and can in principle be observed in all quantum mechanical systems (i.e. molecular, atomic, and nuclear). The states are very special because of their "non-classical" nature: The size of each three-particle Efimov state is much
682:
atoms. In 2006, they published their findings in the scientific journal Nature. Further experimental support for the existence of the Efimov state has been given recently by independent groups. Almost 40 years after Efimov's purely theoretical prediction, the characteristic periodic behavior of the
615:
1498:
Kunitski, Maksim; Zeller, Stefan; Voigtsberger, Jörg; Kalinin, Anton; Schmidt, Lothar Ph. H.; Schöffler, Markus; Czasch, Achim; Schöllkopf, Wieland; Grisenti, Robert E.; Jahnke, Till; Blume, Dörte; Dörner, Reinhard (May 2015). "Observation of the Efimov state of the helium trimer".
305:
512:
1110:
Pollack, S. E.; Dries, D.; Hulet, R. G.; Danzl, J. G.; Chin, C.; Engeser, B.; Lange, A. D.; Pilch, K.; Jaakkola, A.; Naegerl, H. -C.; Grimm, R. (2009). "Universality in Three- and Four-Body Bound States of
Ultracold Atoms".
370:
55:) of three bosons even if the two-particle attraction is too weak to allow two bosons to form a pair. A (three-particle) Efimov state, where the (two-body) sub-systems are unbound, is often depicted symbolically by the
942:
T. Kraemer; M. Mark; P. Waldburger; J. G. Danzl; C. Chin; B. Engeser; A. D. Lange; K. Pilch; A. Jaakkola; H.-C. Nägerl; R. Grimm (2006). "Evidence for Efimov quantum states in an ultracold gas of caesium atoms".
50:
interact, with the prediction of an infinite series of excited three-body energy levels when a two-body state is exactly at the dissociation threshold. One corollary is that there exist bound states (called
723:
Interest in the "universal phenomena" of cold atomic gases is still growing. The discipline of universality in cold atomic gases near the Efimov states is sometimes referred to as "Efimov physics".
206:
201:
1057:
Zaccanti, M.; Deissler, B.; D’Errico, C.; Fattori, M.; Jona-Lasinio, M.; Müller, S.; Roati, G.; Inguscio, M.; Modugno, G. (2009). "Observation of an Efimov spectrum in an atomic system".
485:
1004:
Knoop, S.; Ferlaino, F.; Mark, M.; Berninger, M.; Schöbel, H.; Nägerl, H. -C.; Grimm, R. (2009). "Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering".
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137:
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larger than the force-range between the individual particle pairs. This means that the state is purely quantum mechanical. Similar phenomena are observed in two-neutron
928:
1437:
R. Pires; J. Ulmanis; S. Häfner; M. Repp; A. Arias; E. D. Kuhnle; M. Weidemüller (2014). "Observation of Efimov
Resonances in a Mixture with Extreme Mass Imbalance".
660:
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The most accurate experimental value of the scaling factor of the states has been determined by the experimental group of Rudolf Grimm at
Innsbruck University as
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164:
314:
505:
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that describes the radial dependence of the wavefunction. By virtue of the resonance-determined boundary conditions, this is the unique positive value of
1376:
Shih-Kuang Tung; Karina Jiménez-García; Jacob
Johansen; Colin V. Parker; Cheng Chin (2014). "Geometric Scaling of Efimov States in a Li6−Cs133 Mixture".
376:
59:. This means that if one of the particles is removed, the remaining two fall apart. In this case, the Efimov state is also called a Borromean state.
1172:
Huang, Bo; Sidorenkov, Leonid A.; Grimm, Rudolf; Hutson, Jeremy M. (2014). "Observation of the Second
Triatomic Resonance in Efimov's Scenario".
610:{\displaystyle -s\cosh \left.{\tfrac {\mathrm {\pi } s}{2}}\right.+{\tfrac {8}{\sqrt {3}}}\sinh \left.{\tfrac {\mathrm {\pi } s}{6}}\right.=0.}
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Overwhelming proof for Efimov State that's become a hotbed for research some 40 years after it first appeared (2009.12.14)
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67:
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300:{\displaystyle {\begin{aligned}a_{N}&=a_{0}\lambda ^{N}\\E_{N}&=E_{0}\lambda ^{-2N}\end{aligned}}}
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869:"DLMF: §10.45 Functions of Imaginary Order ‣ Modified Bessel Functions ‣ Chapter 10 Bessel Functions"
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The geometric progression of the energy levels of Efimov states is an example of a emergent discrete
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Braaten, E.; Hammer, H. (2006). "Universality in few-body systems with large scattering length".
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experimentally confirmed the existence of such a state for the first time in an ultracold gas of
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770:. (Halo nuclei could be seen as special Efimov states, depending on the subtle definitions.)
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the Efimov effect gives rise to a broad class of phenomena that have been referred to as
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S. M. Dawid, R. Gonsior, J. Kwapisz, K. Serafin, M. Tobolski, and S. D. Glazek (2018).
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831:(1970). "Energy levels arising from resonant two-body forces in a three-body system".
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43:
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Thøgersen, Martin (2009). "Universality in Ultra-Cold Few- and Many-Boson
Systems".
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of the state becomes infinite. In this limit, Efimov predicted that the three-body
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A computer depiction of the quantum effect predicted by Efimov, said to resemble
427:
is the order of the imaginary-order modified Bessel function of the second kind
1573:
Observation of the Second
Triatomic Resonance in Efimov’s Scenario (2014.05.15)
1339:
763:
365:{\displaystyle \lambda =\mathrm {e} ^{\mathrm {\pi } /s_{0}}=22.69438\ldots }
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and Hanns-Christoph Nägerl at the
Institute for Experimental Physics at the
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17:
1538:
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805:[Weakly Bound States of Three Resonantly Interacting Particles].
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of some two-body bound state approaches zero, or equivalently, the s-wave
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atoms, extending Efimov's original picture of three identical bosons.
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1451:
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Naidon, Pascal; Endo, Shimpei (2017). "Efimov
Physics: a review".
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66:
47:
803:Слабосвязанные состояния трех резонансно взаимодействующих частиц
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limit cycle, is closely related to the scale invariance of the
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Press release about the experimental confirmation (2006.03.16)
1364:. ... is however not clearly defined and somewhat subjective.
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Pair interactions among three identical bosons will approach
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form of the quantum mechanical potential of the system.
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have observed Efimov states in an ultracold mixture of
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899:"Renormalization group procedure for potential −g/r2"
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745:An Efimov state existing as an excited state of a
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46:in 1970. Efimov's effect is where three identical
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927:: CS1 maint: multiple names: authors list (
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480:{\displaystyle {\tilde {K}}_{s_{0}}(r/a)}
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749:was observed in an experiment in 2015.
507:satisfying the transcendental equation
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418:{\displaystyle s_{0}=1.0062378\ldots }
7:
713:{\displaystyle \lambda =21.0\pm 1.3}
326:
25:
730:and Matthias Weidemüller of the
623:. This phenomenon, exhibiting a
879:from the original on 2018-03-04
670:In 2005, the research group of
132:{\displaystyle N=0,1,2,\ldots }
1469:10.1103/PhysRevLett.112.250404
1408:10.1103/PhysRevLett.113.240402
1310:Reports on Progress in Physics
1204:10.1103/PhysRevLett.112.190401
915:10.1016/j.physletb.2017.12.028
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441:
374:is a universal constant (OEIS
81:"Resonance (particle physics)"
1:
1265:10.1016/j.physrep.2006.03.001
855:10.1016/0370-2693(70)90349-7
683:states has been confirmed.
1604:
139:whose scattering lengths
39:predicted by the Russian
1340:10.1088/1361-6633/aa50e8
806:
802:
732:University of Heidelberg
1531:10.1126/science.aaa5601
1439:Physical Review Letters
1378:Physical Review Letters
1174:Physical Review Letters
1143:10.1126/science.1182840
801:Ефимов, В. И. (1970).
676:University of Innsbruck
655:{\displaystyle 1/r^{2}}
309:where the common ratio
73:"Russian nesting dolls"
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728:University of Chicago
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625:renormalization group
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195:geometric progression
188:
186:{\displaystyle E_{N}}
166:and binding energies
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159:{\displaystyle a_{N}}
134:
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41:theoretical physicist
813:] (in Russian).
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666:Experimental results
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31:is an effect in the
1523:2015Sci...348..551K
1461:2014PhRvL.112y0404P
1400:2014PhRvL.113x0402T
1332:2017RPPh...80e6001N
1257:2006PhR...428..259B
1196:2014PhRvL.112s0401H
1135:2009Sci...326.1683P
1119:(5960): 1683–1685.
1081:2009NatPh...5..586Z
1028:2009NatPh...5..227K
975:10.1038/nature04626
967:2006Natur.440..315K
847:1970PhLB...33..563E
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1588:Quantum mechanics
1507:(6234): 551–555.
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951:(7082): 315–318.
903:Physics Letters B
834:Physics Letters B
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33:quantum mechanics
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1358:. pp. 3–4:
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44:V. N. Efimov
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18:Efimov State
909:: 260–264.
760:halo-nuclei
1514:1512.02036
1323:1610.09805
1065:(8): 586.
1012:(3): 227.
883:2018-02-16
829:Efimov, V.
786:References
764:lithium-11
762:, such as
1547:206635093
1452:1403.7246
1391:1402.5943
1356:206095127
1293:0908.0852
1187:1402.6161
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