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Journal articles on the topic 'Quantum degeneracy; Bose-Einstein condensation'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 February 2022

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1

Shlyapnikov, Gora V. "Quantum degeneracy and Bose–Einstein condensation in low-dimensional trapped gases." Comptes Rendus de l'Académie des Sciences - Series IV - Physics 2, no. 3 (2001): 407–17. http://dx.doi.org/10.1016/s1296-2147(01)01182-9.

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2

Wang, Jinhua, Pan Nie, Xiaokang Li, et al. "Critical point for Bose–Einstein condensation of excitons in graphite." Proceedings of the National Academy of Sciences 117, no. 48 (2020): 30215–19. http://dx.doi.org/10.1073/pnas.2012811117.

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An exciton is an electron–hole pair bound by attractive Coulomb interaction. Short-lived excitons have been detected by a variety of experimental probes in numerous contexts. An excitonic insulator, a collective state of such excitons, has been more elusive. Here, thanks to Nernst measurements in pulsed magnetic fields, we show that in graphite there is a critical temperature (T = 9.2 K) and a critical magnetic field (B = 47 T) for Bose–Einstein condensation of excitons. At this critical field, hole and electron Landau subbands simultaneously cross the Fermi level and allow exciton formation. By quantifying the effective mass and the spatial separation of the excitons in the basal plane, we show that the degeneracy temperature of the excitonic fluid corresponds to this critical temperature. This identification would explain why the field-induced transition observed in graphite is not a universal feature of three-dimensional electron systems pushed beyond the quantum limit.

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3

Deng, Shu-Jin, Peng-Peng Diao, Qian-Li Yu, and Hai-Bin Wu. "All-Optical Production of Quantum Degeneracy and Molecular Bose-Einstein Condensation of 6 Li." Chinese Physics Letters 32, no. 5 (2015): 053401. http://dx.doi.org/10.1088/0256-307x/32/5/053401.

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4

SHLYAPNIKOV, G. V. "SUPERFLUID REGIMES IN DEGENERATE ATOMIC FERMI GASES." International Journal of Modern Physics B 20, no. 19 (2006): 2739–54. http://dx.doi.org/10.1142/s0217979206035242.

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We give a brief overview of recent studies of quantum degenerate regimes in ultracold Fermi gases. The attention is focused on the regime of Bose-Einstein condensation of weakly bound molecules of fermionic atoms, formed at a large positive scattering length for the interspecies atom-atom interaction. We analyze remarkable collisional stability of these molecules and draw prospects for future studies.

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5

Öttl, Anton, Stephan Ritter, Michael Köhl, and Tilman Esslinger. "Hybrid apparatus for Bose-Einstein condensation and cavity quantum electrodynamics: Single atom detection in quantum degenerate gases." Review of Scientific Instruments 77, no. 6 (2006): 063118. http://dx.doi.org/10.1063/1.2216907.

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6

FUJITA, SHIGEJI, YOSHIYASU TAMURA, and AKIRA SUZUKI. "MICROSCOPIC THEORY OF THE QUANTUM HALL EFFECT." Modern Physics Letters B 15, no. 20 (2001): 817–25. http://dx.doi.org/10.1142/s0217984901002610.

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The phonon exchange between the electron and the elementary magnetic flux (fluxon) induces an attractive transition in the degenerate Landau states. This attraction bounds an electron–fluxon complex. The center-of-mass of the complex moves as a boson with a linear dispersion relation (∊ = cp). The 2D system of free massless bosons undergoes a Bose–Einstein condensation at k B T c = 1.954ℏcn1/2, where n is the boson density. For GaAs/AlGaAs, T c ~ 1 K at the principal Landau-level occupation ratio ν = 1, where the electron number equals the fluxon number. Below T c , there is an energy gap, which stabilizes the Hall resistivity plateau. The plateau value (j/N)(h/e2) at the fractional occupation ratio ν = N/j, for odd j, indicates that the composite boson containing an electron and j fluxons carries the fractional charge (magnitude) e/j due to the magnetic confinement.

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7

Zapf, Vivien, Marcelo Jaime, and C. D. Batista. "Bose-Einstein condensation in quantum magnets." Reviews of Modern Physics 86, no. 2 (2014): 563–614. http://dx.doi.org/10.1103/revmodphys.86.563.

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8

Aoki, Tosizumi. "Bose-Einstein Condensation in Quantum Lattice Model." Journal of the Physical Society of Japan 61, no. 2 (1992): 750–51. http://dx.doi.org/10.1143/jpsj.61.750.

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9

Ishikawa, Osamu. "Localized Bose–Einstein Condensation near Quantum Phase Transition." JPSJ News and Comments 5 (January 12, 2008): 01. http://dx.doi.org/10.7566/jpsjnc.5.01.

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10

Zapf, Vivien, Marcelo Jaime, and C. D. Batista. "ChemInform Abstract: Bose-Einstein Condensation in Quantum Magnets." ChemInform 46, no. 9 (2015): no. http://dx.doi.org/10.1002/chin.201509334.

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11

Haug, H. "Quantum Kinetics of the Exciton Bose-Einstein Condensation." Phase Transitions 75, no. 7-8 (2002): 941–51. http://dx.doi.org/10.1080/0141159021000008954.

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12

Bolte, Jens, and Joachim Kerner. "Many-particle quantum graphs and Bose-Einstein condensation." Journal of Mathematical Physics 55, no. 6 (2014): 061901. http://dx.doi.org/10.1063/1.4879497.

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13

Gagatsos, C. N., A. I. Karanikas, and G. Kordas. "Mutual Information and Bose-Einstein Condensation." Open Systems & Information Dynamics 20, no. 02 (2013): 1350008. http://dx.doi.org/10.1142/s123016121350008x.

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In this work we study an ideal bosonic quantum field system at finite temperature, and in a canonical and a grand canonical ensemble. For a simple spatial partition we derive the corresponding mutual information, a quantity that measures the total amount of information of one of the parts about the other. In order to find it, we first derive the von Neumann entropy that corresponds to the spatially separated subsystem (i.e. the geometric entropy) and then we subtract its extensive part which coincides with the thermal entropy of the subsystem. In the framework of the grand canonical description, we examine the influence of the underlying Bose-Einstein condensation on the behaviour of the mutual information, and we find that its derivative with respect to the temperature possesses a finite discontinuity at exactly the critical temperature.

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14

van Wijngaarden, W. A. "A second century of Einstein?BoseEinstein condensation and quantum information." Canadian Journal of Physics 83, no. 7 (2005): 671–85. http://dx.doi.org/10.1139/p05-042.

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A century ago Albert Einstein transformed classical physics with his seminal papers on Brownian motion, the Photoelectric effect, and, of course, special and later general relativity. Lesser well-known are his contributions to BoseEinstein Condensation and the EinsteinPodolskyRosen paradox, the latter being a criticism of Quantum Mechanics. These later works were regarded even by physicists for decades as mere Gedanken or thought experiments. In recent years, not only have they been verified experimentally but revolutionary technological applications are emerging including quantum cryptography and possibly quantum computing. PACS Nos.: 03.65, 03.67, 03.75, 05.30.Jp

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15

Hashimoto, Takahiro, Yuichi Ota, Akihiro Tsuzuki, et al. "Bose-Einstein condensation superconductivity induced by disappearance of the nematic state." Science Advances 6, no. 45 (2020): eabb9052. http://dx.doi.org/10.1126/sciadv.abb9052.

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The crossover from the superconductivity of the Bardeen-Cooper-Schrieffer (BCS) regime to the Bose-Einstein condensation (BEC) regime holds a key to understanding the nature of pairing and condensation of fermions. It has been mainly studied in ultracold atoms, but in solid systems, fundamentally previously unknown insights may be obtained because multiple energy bands and coexisting electronic orders strongly affect spin and orbital degrees of freedom. Here, we provide evidence for the BCS-BEC crossover in iron-based superconductors FeSe1 − xSx from laser-excited angle-resolved photoemission spectroscopy. The system enters the BEC regime with x = 0.21, where the nematic state that breaks the orbital degeneracy is fully suppressed. The substitution dependence is opposite to the expectation for single-band superconductors, which calls for a new mechanism of BCS-BEC crossover in this system.

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16

Timofeev, V. B., and A. V. Gorbunov. "Bose-Einstein condensation of dipolar excitons in quantum wells." Journal of Physics: Conference Series 148 (February 1, 2009): 012049. http://dx.doi.org/10.1088/1742-6596/148/1/012049.

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17

Li, Zhang, Wang Cheng, Li Yan-Min, and Wang Jin-Fang. "Dynamic Analysis for Bose–Einstein Condensation in Quantum Cavity." Communications in Theoretical Physics 43, no. 5 (2005): 900–904. http://dx.doi.org/10.1088/0253-6102/43/5/028.

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18

Ubriaco, Marcelo R. "Bose-Einstein condensation of a quantum group boson gas." Physical Review E 57, no. 1 (1998): 179–83. http://dx.doi.org/10.1103/physreve.57.179.

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19

Succi, Sauro. "Lattice Quantum Mechanics: An Application to Bose–Einstein Condensation." International Journal of Modern Physics C 09, no. 08 (1998): 1577–85. http://dx.doi.org/10.1142/s0129183198001424.

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A lattice formulation of nonrelativistic quantum mechanics is presented, based on a formal analogy with discrete kinetic theory. The method is applied to the Gross–Pitaevski equation, a specific form of self-interacting nonlinear Schrödinger equation relevant to the study of Bose–Einstein condensation.

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20

Lee, Y. C., and W. Zhu. "Quantum saturation of ortho-excitons near Bose-Einstein condensation." Journal of Physics: Condensed Matter 12, no. 4 (1999): L49—L51. http://dx.doi.org/10.1088/0953-8984/12/4/102.

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21

Maćkowiak, J. "On the Bose-Einstein condensation of a quantum liquid." Reports on Mathematical Physics 27, no. 1 (1989): 11–18. http://dx.doi.org/10.1016/0034-4877(89)90033-5.

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22

Lee, Y. C., and S. W. Nam. "Degree of Indistinguishability, Quantum Coherence, and Bose-Einstein Condensation." Journal of Low Temperature Physics 171, no. 1-2 (2012): 55–61. http://dx.doi.org/10.1007/s10909-012-0808-z.

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23

Das, Saurya. "Bose–Einstein condensation as an alternative to inflation." International Journal of Modern Physics D 24, no. 12 (2015): 1544001. http://dx.doi.org/10.1142/s0218271815440010.

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It was recently shown that gravitons with a very small mass should have formed a Bose–Einstein condensate (BEC) in the very early universe, whose density and quantum potential can account for the dark matter (DM) and dark energy (DE) in the universe respectively. Here, we show that the condensation can also naturally explain the observed large scale homogeneity and isotropy of the universe. Furthermore, gravitons continue to fall into their ground state within the condensate at every epoch, accounting for the observed flatness of space at cosmological distance scales. Finally, we argue that the density perturbations due to quantum fluctuations within the condensate give rise to a scale invariant spectrum. This therefore provides a viable alternative to inflation, which is not associated with the well-known problems associated with the latter.

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24

SILVERMAN, M. P. "FERMION CONDENSATION IN A RELATIVISTIC DEGENERATE STAR: ARRESTED COLLAPSE AND MACROSCOPIC EQUILIBRIUM." International Journal of Modern Physics D 15, no. 12 (2006): 2257–65. http://dx.doi.org/10.1142/s0218271806009522.

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Fermionic Cooper pairing leading to the BCS-type hadronic superfluidity is believed to account for periodic variations ("glitches") and subsequent slow relaxation in spin rates of neutron stars. Under appropriate conditions, however, fermions can also form a Bose–Einstein condensate of composite bosons. Both types of behavior have recently been observed in tabletop experiments with ultra-cold fermionic atomic gases. Since the behavior is universal (i.e., independent of atomic potential) when the modulus of the scattering length greatly exceeds the separation between particles, one can expect analogous processes to occur within the supradense matter of neutron stars. In this paper, I show how neutron condensation to a Bose–Einstein condensate, in conjunction with relativistically exact expressions for fermion energy and degeneracy pressure and the relations for thermodynamic equilibrium in a spherically symmetric space–time with Schwarzschild metric, leads to stable macroscopic equilibrium states of stars of finite density, irrespective of mass.

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25

Snoke, D. W. "Coherence and Optical Emission from Bilayer Exciton Condensates." Advances in Condensed Matter Physics 2011 (2011): 1–7. http://dx.doi.org/10.1155/2011/938609.

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Experiments aimed at demonstrating Bose-Einstein condensation of excitons in two types of experiments with bilayer structures (coupled quantum wells) are reviewed, with an emphasis on the basic effects. Bose-Einstein condensation implies the existence of a macroscopic coherence, also known as off-diagonal long-range order, and proposed tests and past claims for coherence in these excitonic systems are discussed.

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26

Koinov, Z. G. "Bose - Einstein condensation of excitons in a semiconductor quantum well." Journal of Physics: Condensed Matter 11, no. 14 (1999): L127—L131. http://dx.doi.org/10.1088/0953-8984/11/14/002.

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27

Perrin, H. "Ultra cold atoms and Bose-Einstein condensation for quantum metrology." European Physical Journal Special Topics 172, no. 1 (2009): 37–55. http://dx.doi.org/10.1140/epjst/e2009-01040-8.

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28

Lee, Su-Yong, Jayne Thompson, Sadegh Raeisi, Paweł Kurzyński, and Dagomir Kaszlikowski. "Quantum information approach to Bose–Einstein condensation of composite bosons." New Journal of Physics 17, no. 11 (2015): 113015. http://dx.doi.org/10.1088/1367-2630/17/11/113015.

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29

Koinov, Z. G. "Bose-Einstein condensation of excitons in a single quantum well." Physical Review B 61, no. 12 (2000): 8411–19. http://dx.doi.org/10.1103/physrevb.61.8411.

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30

Piper, I. M., P. R. Eastham, M. Ediger, et al. "Microcavity quantum-dot systems for non-equilibrium Bose-Einstein condensation." Journal of Physics: Conference Series 245 (September 1, 2010): 012059. http://dx.doi.org/10.1088/1742-6596/245/1/012059.

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31

Barbarani, Vito. "New Quantum Statistics and the Theory of Bose–Einstein Condensation." International Journal of Theoretical Physics 46, no. 10 (2007): 2401–28. http://dx.doi.org/10.1007/s10773-007-9358-6.

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32

SCHELLE, ALEXEJ. "QUANTUM FLUCTUATION DYNAMICS DURING THE TRANSITION OF A MESOSCOPIC BOSONIC GAS INTO A BOSE–EINSTEIN CONDENSATE." Fluctuation and Noise Letters 11, no. 04 (2012): 1250027. http://dx.doi.org/10.1142/s0219477512500277.

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The condensate number distribution during the transition of a dilute, weakly interacting gas of N = 200 bosonic atoms into a Bose–Einstein condensate is modeled within number conserving master equation theory of Bose–Einstein condensation. Initial strong quantum fluctuations occuring during the exponential cycle of condensate growth reduce in a subsequent saturation stage, before the Bose gas finally relaxes towards the Gibbs–Boltzmann equilibrium.

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33

GIUSIANO, GIOVANNI, FRANCESCO P. MANCINI, PASQUALE SODANO, and ANDREA TROMBETTONI. "TOPOLOGY INDUCED MACROSCOPIC QUANTUM COHERENCE IN JOSEPHSON JUNCTION NETWORKS." International Journal of Modern Physics B 18, no. 04n05 (2004): 691–704. http://dx.doi.org/10.1142/s0217979204024318.

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We argue that Josephson junction networks may be engineered to allow for the emergence of new and robust quantum coherent states. We provide a rather intuitive argument showing how the change in topology may affect the quantum properties of a bosonic particle hopping on a network. As a paradigmatic example, we analyze in detail the quantum and thermodynamical properties of non-interacting bosons hopping on a comb graph. We show how to explicitly compute the inhomogeneities in the distribution of bosons along the comb's fingers, evidencing the effects of the topology induced spatial Bose–Einstein condensation characteristic of the system. We propose an experiment enabling to detect the spatial Bose–Einstein condensation for Josephson networks built on comb graphs.

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34

BANNUR, VISHNU M., and K. M. UDAYANANDAN. "STATISTICAL MECHANICS OF CONFINED QUANTUM PARTICLES." Modern Physics Letters A 22, no. 30 (2007): 2297–305. http://dx.doi.org/10.1142/s0217732307022499.

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We develop statistical mechanics and thermodynamics of Bose and Fermi systems in relativistic harmonic oscillator (RHO) confining potential, which is applicable in quark gluon plasma (QGP), astrophysics, Bose–Einstein condensation (BEC) etc. Detailed study of QGP system is carried out and compared with lattice results. Furthermore, as an application, our equation of state (EoS) of QGP is used to study compact stars like quark star.

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35

Johnson, P. R., E. Della Torre, L. H. Bennett, and R. E. Watson. "Nonequilibrium quantum dynamics in ferromagnetic nanoparticles: Conditions for Bose–Einstein condensation." Journal of Applied Physics 105, no. 7 (2009): 07E115. http://dx.doi.org/10.1063/1.3067857.

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36

Boţan, V., and M. A. Liberman. "Bose–Einstein condensation of indirect magnetoexcitons in a double quantum well." Solid State Communications 134, no. 1-2 (2005): 69–72. http://dx.doi.org/10.1016/j.ssc.2004.06.042.

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37

Schmitt, O. M., D. B. Tran Thoai, L. Bányai, P. Gartner, and H. Haug. "Bose-Einstein Condensation Quantum Kinetics for a Gas of Interacting Excitons." Physical Review Letters 86, no. 17 (2001): 3839–42. http://dx.doi.org/10.1103/physrevlett.86.3839.

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38

Pearson, Sean, Tao Pang, and Changfeng Chen. "Bose-Einstein condensation in two dimensions: A quantum Monte Carlo study." Physical Review A 58, no. 6 (1998): 4811–15. http://dx.doi.org/10.1103/physreva.58.4811.

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39

Demokritov, S. O., V. E. Demidov, O. Dzyapko, G. A. Melkov, and A. N. Slavin. "Quantum coherence due to Bose–Einstein condensation of parametrically driven magnons." New Journal of Physics 10, no. 4 (2008): 045029. http://dx.doi.org/10.1088/1367-2630/10/4/045029.

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40

Li, Yan Min, Li Zhang, and Chen Di Li. "The Dynamics in the Bose-Einstein Condensation Process with Interaction between Three Energy-Level Bose Atoms." Advanced Materials Research 403-408 (November 2011): 2152–55. http://dx.doi.org/10.4028/www.scientific.net/amr.403-408.2152.

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The dynamics in the Bose-Einstein Condensation (BEC) process with interaction between three energy-level Bose atoms and Single-Mode active cavity field and between three Energy-Level Bose atoms in the quantum cavity is analyzed using the ordinary method for solving the wave function in the Schrödinger idea from the Heisenberg idea. A wave function has been established for the atoms under the BEC conditions in the quantum cavity, and the factors having effect on the BEC stability in the quantum cavity and the rules for selecting quantum leaps are analyzed.

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41

Accardi, Luigi, and Carlo Pandiscia. "Mathematical aspects of Bose–Einstein condensation in equilibrium and local equilibrium conditions." Infinite Dimensional Analysis, Quantum Probability and Related Topics 20, no. 04 (2017): 1750024. http://dx.doi.org/10.1142/s0219025717500242.

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In the paper4 the notion of local KMS condition, introduced in Ref. 3 and extended in Ref. 2, was shown to open new possibilities in the study of the problem of Bose–Einstein Condensation (BEC). In this paper we analyze the general structure of states on the CCR algebra over a pre-Hilbert space that satisfies the local KMS condition with respect to a free Hamiltonian [Formula: see text] and to a given inverse temperature function [Formula: see text]. The replacement of Hilbert space by a pre-Hilbert space allows one to deal with test functions more singular than those usually considered in the theory of distributions (thus allowing e.g., fractal critical surfaces) and is equivalent (in the language of Weyl algebras) to consider a degenerate symplectic form. It is precisely this degeneracy that allows one to introduce in an intrinsic way the notions of [Formula: see text]-critical subspace (resp. [Formula: see text]-critical surface) and of states exhibiting BEC, independently of infinite volume limits and of boundary conditions. We prove that the covariance of any local KMS state is uniquely determined by the pair [Formula: see text], through a nonlinear extension of the Planck factor. For a large class of such states (including all known examples) the covariance splits into a sum of two mutually singular terms: one corresponding to a regular state, the other one with support on a critical surface (or more generally a critical subspace) uniquely determined by [Formula: see text] and [Formula: see text]. In particular we prove that, if such a state is gauge invariant Gaussian (quasi-free), then the [Formula: see text]-equilibrium condition uniquely determines the regular part of the state, while the singular part is arbitrary.

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42

Bugaev, К. А., O. I. Ivanytskyi, B. E. Grinyuk, and I. P. Yakimenko. "Bose–Einstein Condensation as a Deposition Phase Transition of Quantum Hard Spheres and New Relations between Bosonic and Fermionic Pressures." Ukrainian Journal of Physics 65, no. 11 (2020): 963. http://dx.doi.org/10.15407/ujpe65.11.963.

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We investigate the phase transition of Bose–Einstein particles with the hard-core repulsion in the grand canonical ensemble within the Van der Waals approximation. It is shown that the pressure of non-relativistic Bose–Einstein particles is mathematically equivalent to the pressure of simplified version of the statistical multifragmentation model of nuclei with the vanishing surface tension coefficient and the Fisher exponent тF = 5/2 , which for such parameters has the 1-st order phase transition. The found similarity of these equations of state allows us to show that within the present approach the high density phase of Bose-Einstein particles is a classical macro-cluster with vanishing entropy at any temperature which, similarly to the system of classical hard spheres, is a kind of solid state. To show this we establish new relations which allow us to identically represent the pressure of Fermi–Dirac particles in terms of pressures of Bose–Einstein particles of two sorts.

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43

VÖRÖS, ZOLTÁN, and DAVID W. SNOKE. "QUANTUM WELL EXCITONS AT LOW DENSITY." Modern Physics Letters B 22, no. 10 (2008): 701–25. http://dx.doi.org/10.1142/s0217984908015292.

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In this paper, we give an overview of our recent work in the quest for Bose–Einstein condensation of spatially indirect excitons. After discussing the benefits of using such particles as the participants of this intriguing quantum phase transition, we turn to the experimental difficulties and obstacles in the way to a successful realization of excitonic BEC.

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44

Vasudev, Pranai, Jian-Hua Jiang, and Sajeev John. "Light-trapping for room temperature Bose-Einstein condensation in InGaAs quantum wells." Optics Express 24, no. 13 (2016): 14010. http://dx.doi.org/10.1364/oe.24.014010.

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45

Kitada, Atsushi, Zenji Hiroi, Yoshihiro Tsujimoto, et al. "Bose–Einstein Condensation of Quasi-Two-Dimensional Frustrated Quantum Magnet (CuCl)LaNb2O7." Journal of the Physical Society of Japan 76, no. 9 (2007): 093706. http://dx.doi.org/10.1143/jpsj.76.093706.

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46

Chiocchetta, A., P. É. Larré, and I. Carusotto. "Thermalization and Bose-Einstein condensation of quantum light in bulk nonlinear media." EPL (Europhysics Letters) 115, no. 2 (2016): 24002. http://dx.doi.org/10.1209/0295-5075/115/24002.

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47

Algin, A., and B. Deviren. "Bose–Einstein condensation of a two-parameter deformed quantum group boson gas." Journal of Physics A: Mathematical and General 38, no. 26 (2005): 5945–56. http://dx.doi.org/10.1088/0305-4470/38/26/008.

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48

Timofeev, V. B., and A. V. Gorbunov. "Bose-Einstein condensation of dipolar excitons in double and single quantum wells." physica status solidi (c) 5, no. 7 (2008): 2379–86. http://dx.doi.org/10.1002/pssc.200777602.

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49

Dzyapko, O., V. E. Demidov, G. A. Melkov, and S. O. Demokritov. "Bose–Einstein condensation of spin wave quanta at room temperature." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1951 (2011): 3575–87. http://dx.doi.org/10.1098/rsta.2011.0128.

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Spin waves are delocalized excitations of magnetic media that mainly determine their magnetic dynamics and thermodynamics at temperatures far below the critical one. The quantum-mechanical counterparts of spin waves are magnons, which can be considered as a gas of weakly interacting bosonic quasi-particles. Here, we discuss the room-temperature kinetics and thermodynamics of the magnon gas in yttrium iron garnet films driven by parametric microwave pumping. We show that for high enough pumping powers, the thermalization of the driven gas results in a quasi-equilibrium state described by Bose–Einstein statistics with a non-zero chemical potential. Further increases of the pumping power cause a Bose–Einstein condensation documented by an observation of the magnon accumulation at the lowest energy level. Using the sensitivity of the Brillouin light scattering spectroscopy to the degree of coherence of the scattering magnons, we confirm the spontaneous emergence of coherence of the magnons accumulated at the bottom of the spectrum, occurring if their density exceeds a critical value.

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50

CHEN, LIWEI, GUOZHEN SU, and JINCAN CHEN. "THE EFFECTS OF A FINITE NUMBER OF PARTICLES ON TWO TRAPPED QUANTUM GASES." International Journal of Modern Physics B 25, no. 32 (2011): 4435–42. http://dx.doi.org/10.1142/s0217979211059243.

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The effects of a finite number of particles on the thermodynamic properties of ideal Bose and Fermi gases trapped in any-dimensional harmonic potential are investigated. The orders of relative corrections to the thermodynamic quantities due to the finite number of particles are estimated in different situations. The results obtained for the two trapped quantum gases are compared, and consequently, it is shown that the finite-particle-number effects for the condensed Bose gas (a Bose gas with Bose–Einstein Condensation (BEC) occurring in the system) are much more significant than those for the Fermi gas and normal Bose gas (a Bose gas without BEC).

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