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

Physical Review A

Density of states of particles in a generic power-law potential in any dimensional space

Mingzhe Li, Lixuan Chen, Chuanhong Chen

Published Apr 1, 1999• 30 citations
Publisher

Abstract

An ideal gas trapped in a generic power-law potential in any dimensional space is studied. The density of states of this system is derived. Both Fermi and Bose gases are discussed, and their properties are derived straightforwardly from the density of states.
DOI
10.1103/physreva.59.3109

Related papers

Density of states and thermodynamic properties of an ideal system trapped in any dimension

Zijun Yan, Mingzhe Li, Lixuan Chen +2 more

The density of states and thermodynamic properties of an ideal gas system trapped in a generic power-law potential in an n -dimensional space are studied. A unified description for the Bose, Fermi and classical gases is given by using the grand potential of the system. Consequently, not only the results in current textbooks of statistical mechanics but also some new general important conclusions, such as the conditions for the occurence of Bose-Eisntein condensation in a trapped Bose system in any dimensional space, can be derived directly using the results of this paper.

Journal of Physics A Mathematical and General•Jan 1, 1999•30 citations

Thermodynamic Properties of an Ideal Fermi Gas Trapped in a Two-Dimensional Space

Liu Jing-yi

Thermodynamic properties of an ideal Fermi gas in a two-dimensional space trapped in a generic power-law potential are studied, based on the local density approximation.The total energy E,Fermi energy ,chemical potential μ and heat capacity C in the high-and low-temperature approximations are derived.How these physical quantities depend on the external potential are discussed.

Journal of Zhangzhou Normal University•Jan 1, 2001•0 citations

Ideal quantum gases in D-dimensional space and power-law potentials

Luca Salasnich

We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. From such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose–Einstein condensation can set up in a confining power-law potential if and only if D/2+D/n>1, where D is the space dimension and n is the power-law exponent.

arXiv:math-ph/0008030•Journal of Mathematical Physics•Dec 1, 2000•69 citations

Thermodynamics of Ideal Bose Gas Under Generic Power Law Potential in ddd-dimensions

Mir Mehedi Faruk

Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.

arXiv:1502.07054•Acta Physica Polonica B•Jan 1, 2015•2 citations

Thermodynamics of Ideal Fermi Gas Under Generic Power Law Potential in ddd-dimensions

Mir Mehedi Faruk, G.M. Bhuiyan

Thermodynamics of ideal Fermi gas trapped in an external generic power law potential $U=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}$ are investigated systematically from the grand thermodynamic potential in $d$ dimensional space. These properties are explored deeply in the degenerate limit ($μ>> K_BT$), where the thermodynamic properties are greatly dominated by Pauli exclusion principle. Pressure and energy along with the isothermal compressibilty is non zero at $T=0K$, denoting trapped Fermi system is quite live even at absolute zero temperature. The nonzero value of compressibilty denotes zero point pressure is not just a constant but depends on volume.

arXiv:1504.06050•Acta Physica Polonica B•Jan 1, 2015•3 citations

Pseudovolume and equation of state for an ideal trapped Bose gas in n dimensions

Zijun Yan

The equation of state of a trapped atomic gas, which is an important and fundamental property for a thermodynamic system, has been elusive to date. We address here this long-standing problem by introducing the concept of pseudovolume which can play an important role as the volume. The equation of state of an ideal Bose gas trapped in an n-dimensional generic power-law potential is derived. It is not only a long-sought equation of state for the trapped Bose gas but also including that of a free Bose gas. Moreover, we find that the thermal wavelength for the particles in n-dimensional space with any kinematic characteristic must be redefined.

Physical Review A•May 16, 2000•22 citations
The density of states and thermodynamic properties of an ideal gas system trapped in a generic power-law potential in an n -dimensional space are studied. A unified description for the Bose, Fermi and classical gases is given by using the grand potential of the system. Consequently, not only the results in current textbooks of statistical mechanics but also some new general important conclusions, such as the conditions for the occurence of Bose-Eisntein condensation in a trapped Bose system in any dimensional space, can be derived directly using the results of this paper.
We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. From such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose–Einstein condensation can set up in a confining power-law potential if and only if D/2+D/n>1, where D is the space dimension and n is the power-law exponent.
Thermodynamic properties of ideal Bose gas trapped in an external generic power law potential are investigated systematically from the grand thermodynamic potential in ddd dimensional space. The most general conditions for Bose-Einstein condensate and the discontinuous conditions of heat capacity at the critical temperature in presence of generic power law potential are presented in this manuscript. The dependence of the physical quantities on external potential, particle characteristics and space dimensionality are discussed. The more general results obtained in this paper presents an unified illustration of Bose-Einstein condensation of ideal Bose systems as they reduces to the expressions and conclusions available in the literature with appropiate choice of power law exponent.
Thermodynamics of ideal Fermi gas trapped in an external generic power law potential U=∑i=1dci∣xiai∣niU=\sum_{i=1} ^d c_i |\frac{x_i}{a_i}|^{n_i}U=∑i=1d​ci​∣ai​xi​​∣ni​ are investigated systematically from the grand thermodynamic potential in ddd dimensional space. These properties are explored deeply in the degenerate limit (μ>>KBTμ>> K_BTμ>>KB​T), where the thermodynamic properties are greatly dominated by Pauli exclusion principle. Pressure and energy along with the isothermal compressibilty is non zero at T=0KT=0KT=0K, denoting trapped Fermi system is quite live even at absolute zero temperature. The nonzero value of compressibilty denotes zero point pressure is not just a constant but depends on volume.
The equation of state of a trapped atomic gas, which is an important and fundamental property for a thermodynamic system, has been elusive to date. We address here this long-standing problem by introducing the concept of pseudovolume which can play an important role as the volume. The equation of state of an ideal Bose gas trapped in an n-dimensional generic power-law potential is derived. It is not only a long-sought equation of state for the trapped Bose gas but also including that of a free Bose gas. Moreover, we find that the thermal wavelength for the particles in n-dimensional space with any kinematic characteristic must be redefined.