Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Thermodynamics of trapped quantum gases on weighted structures

Pinchen Xie, Bingjia Yang, Zhongzhi Zhang

Published May 22, 2017• 0 citations
OpenAlex

Abstract

We studied the thermodynamic behaviors of non-interacting bosons and fermions trapped by a scale-invariant branching structure of adjustable degree of heterogeneity. The full energy spectrum in tight-binding approximation was analytically solved . We found that the log-periodic oscillation of the specific heat for Fermi gas depended on the heterogeneity of hopping. Also, low dimensional Bose-Einstein condensation occurred only for non-homogeneous setup.

Related papers

Bose-Einstein condensation in anisotropic harmonic traps

Tor Haugset, Hårek Haugerud, Jens O. Andersen

We study the thermodynamic behavior of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic-oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin approximation. For a finite number of particles there is no phase transition, but there is a well-defined temperature at which the condensation starts. We also consider condensation in lower dimensions, and, for one-dimensional systems, we discuss the dependence of the condensate fraction and heat capacity on the ensemble used.

arXiv:cond-mat/9611061•Physical Review A•Apr 1, 1997•61 citations

Thermodynamics of inhomogeneous imperfect quantum gases in harmonic traps

Krzysztof Myśliwy, Marek Napiórkowski

Abstract We discuss thermodynamic properties of harmonically trapped imperfect quantum gases. The spatial inhomogeneity of these systems imposes a redefinition of the mean-field interparticle potential energy as compared to the homogeneous case. In our approach, it takes the form , where N is the number of particles, —the harmonic trap frequency, d —system’s dimensionality, and a is a parameter characterizing the interparticle interaction. We provide arguments that this model corresponds to the limiting case of a long-ranged interparticle potential of vanishingly small amplitude. This conclusion is drawn from a computation similar to the well-known Kac scaling procedure, which is presented here in a form adapted to the case of an isotropic harmonic trap. We show that within the model, the imperfect gas of trapped repulsive bosons undergoes the Bose–Einstein condensation provided d > 1. The main result of our analysis is that in d = 1 the gas of attractive imperfect fermions with is thermodynamically equivalent to the gas of repulsive bosons with provided the parameters and fulfill the relation . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional (2D) uniform imperfect repulsive Bose and attractive Fermi gases.

arXiv:1810.02209•Journal of Statistical Mechanics Theory and Experiment•Jun 1, 2019•6 citations

Universal thermodynamics of a strongly interacting Fermi gas: theory versus experiment

Hui Hu, Xia-Ji Liu, P. D. Drummond

Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.

arXiv:1001.2085•New Journal of Physics•Jun 30, 2010•72 citations

Bose-Einstein condensation temperature of a trapped interacting Bose-Fermi gas mixture

Yong-li Ma, S. T. Chui

We calculate the critical temperature of a trapped interacting Bose-Fermi gas mixture by means of a first-order perturbation method in a local-density approximation. An explicit analytical expression is derived for the dependence of the critical temperature on the numbers of bosons and fermions, the strengths of boson-boson and boson-fermion interactions, and the trapping frequencies.

Physical Review A•Nov 13, 2002•11 citations

Modified semiclassical approximation for trapped Bose gases

Vyacheslav I. Yukalov

A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.

arXiv:cond-mat/0510265•Physical Review A•Sep 12, 2005•60 citations

Bose-Einstein condensation in a two-dimensional, trapped, interacting gas

Mehmet Bayındır, B. Tanatar

We study the Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to a harmonic-oscillator-type confining potential. The interaction among the 2D bosons is described by a \ensuremath{\delta} function in configuration space. Solving the Gross-Pitaevskii equation within the two-fluid model we calculate the condensate fraction, ground-state energy, and specific heat of the system. Our results indicate that interacting bosons have similar behavior to those of an ideal system for weak interactions.

arXiv:cond-mat/9807377•Physical Review A•Oct 1, 1998•32 citations
We studied the thermodynamic behaviors of non-interacting bosons and fermions trapped by a scale-invariant branching structure of adjustable degree of heterogeneity. The full energy spectrum in tight-binding approximation was analytically solved . We found that the log-periodic oscillation of the specific heat for Fermi gas depended on the heterogeneity of hopping. Also, low dimensional Bose-Einstein condensation occurred only for non-homogeneous setup.
We study the thermodynamic behavior of an ideal gas of bosons trapped in a three-dimensional anisotropic harmonic-oscillator potential. The condensate fraction as well as the specific heat is calculated using the Euler-Maclaurin approximation. For a finite number of particles there is no phase transition, but there is a well-defined temperature at which the condensation starts. We also consider condensation in lower dimensions, and, for one-dimensional systems, we discuss the dependence of the condensate fraction and heat capacity on the ensemble used.
Abstract We discuss thermodynamic properties of harmonically trapped imperfect quantum gases. The spatial inhomogeneity of these systems imposes a redefinition of the mean-field interparticle potential energy as compared to the homogeneous case. In our approach, it takes the form , where N is the number of particles, —the harmonic trap frequency, d —system’s dimensionality, and a is a parameter characterizing the interparticle interaction. We provide arguments that this model corresponds to the limiting case of a long-ranged interparticle potential of vanishingly small amplitude. This conclusion is drawn from a computation similar to the well-known Kac scaling procedure, which is presented here in a form adapted to the case of an isotropic harmonic trap. We show that within the model, the imperfect gas of trapped repulsive bosons undergoes the Bose–Einstein condensation provided d > 1. The main result of our analysis is that in d = 1 the gas of attractive imperfect fermions with is thermodynamically equivalent to the gas of repulsive bosons with provided the parameters and fulfill the relation . This result supplements similar recent conclusion about thermodynamic equivalence of two-dimensional (2D) uniform imperfect repulsive Bose and attractive Fermi gases.
Strongly interacting, dilute Fermi gases exhibit a scale-invariant, universal thermodynamic behavior. This is notoriously difficult to understand theoretically because of the absence of a small interaction parameter. Here, we present a systematic comparison of theoretical predictions from different quantum many-body theories with recent experimental data of Nascimbne et al (2010 Nature 463 1057). Our comparisons have no adjustable parameters, either theoretically or experimentally. All the model approximations seem to fluctuate rather than converge on the experimental data. It turns out that a simple Gaussian pair fluctuation theory gives the best quantitative agreement, except at the critical superfluid transition region. In the normal state, we also calculate the equation of state by using a quantum cluster expansion theory and explore in detail its applicability to low temperatures. Using the accurate experimental result for the thermodynamic function S ( T ), we determine the temperature T of a trapped Fermi gas at unitarity as a function of a non-interacting temperature T i , which can be obtained by an adiabatic sweep to the free gas limit. By analyzing the recent experimental data, we find a characteristic temperature ( T / T F ) 0 =0.19±0.02 or ( T i / T F ) 0 =0.16±0.02 in a harmonic trap, below which there are deviations from normal Fermi-liquid-like behavior that may be attributed to pairing effects. Here, T F is the Fermi temperature for a trapped ideal, non-interacting Fermi gas. Our thorough comparison may shed light on the further theoretical development of strongly interacting fermions.
A generalization of the semiclassical approximation is suggested allowing for an essential extension of its region of applicability. In particular, it becomes possible to describe Bose-Einstein condensation of a trapped gas in low-dimensional traps and in traps of low confining dimensions, for which the standard semiclassical approximation is not applicable. The result of the modified approach is shown to coincide with purely quantum-mechanical calculations for harmonic traps, including the one-dimensional harmonic trap. The advantage of the semiclassical approximation is in its simplicity and generality. Power-law potentials of arbitrary powers are considered. The effective thermodynamic limit is defined for any confining dimension. The behavior of the specific heat, isothermal compressibility, and density fluctuations is analyzed, with an emphasis on low confining dimensions, where the usual semiclassical method fails. The peculiarities of the thermodynamic characteristics in the effective thermodynamic limit are discussed.
We study the Bose-Einstein condensation phenomenon in a two-dimensional (2D) system of bosons subjected to a harmonic-oscillator-type confining potential. The interaction among the 2D bosons is described by a \ensuremath{\delta} function in configuration space. Solving the Gross-Pitaevskii equation within the two-fluid model we calculate the condensate fraction, ground-state energy, and specific heat of the system. Our results indicate that interacting bosons have similar behavior to those of an ideal system for weak interactions.