Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Dimensionality effects in the ideal Bose and Fermi gases

Marian Apostol

Published Oct 1, 1997• 14 citations

Abstract

A recently established equivalence between the ideal Bose and Fermi gases [M. H. Lee, Phys. Rev. E 55, 1518 (1997)] is further analyzed with emphasis on the dimensionality effects. The equivalence is shown to be a peculiarity of the bosonlike correlations in two dimensions.

DOI: 10.1103/physreve.56.4854

Related papers

Similarities and differences between Bose and Fermi gases

Raj K. Pathria

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMar 1, 199825 citations

Thermodynamic equivalence of certain ideal Bose and Fermi gases

Kelly R. Patton, Michael R. Geller, M. P. Blencowe

arXiv:cond-mat/0406285Physica A Statistical Mechanics and its ApplicationsMay 18, 20055 citations

Quantum Statistics of Ideal Gases in Two Dimensions

Robert Mccredie May

Physical ReviewSep 14, 196496 citations

Virial Coefficients from Unified Statistical Thermodynamics of Quantum Gases Trapped under Generic Power Law Potential in d Dimension and Equivalence of Quantum Gases

Shah Mohammad Bahauddin, Mir Mehedi Faruk

Communications in Theoretical PhysicsSep 1, 20162 citations

Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in $d$ dimension and the equivalence of trapped quantum gases

Mir Mehedi Faruk, Shah Mohammad Bahauddin

arXiv:1601.07946Jan 28, 20160 citations

Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions

裕太関野, Yuta Sekino, 祐介西田 +1 more

Jan 1, 20180 citations

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics

Dimensionality effects in the ideal Bose and Fermi gases

Marian Apostol

Published Oct 1, 1997• 14 citations

Publisher

Abstract

DOI: 10.1103/physreve.56.4854

Related papers

Similarities and differences between Bose and Fermi gases

Raj K. Pathria

The purported ``equivalence'' between noninteracting Bose and Fermi gases in two dimensions is critically examined. Staying away from the thermodynamic limit, an exact calculation reveals some subtle, but significant, differences between the properties of the two systems that arise characteristically from the statistics obeyed by them. At the same time, certain physical quantities show differences that are not so subtle, in that they remain present even when the thermodynamic limit is taken. The role played by the spatial dimensionality $d$ is also elucidated and it turns out that there is nothing fundamentally special about dimensionality 2; if the single-particle energy spectrum operating in the systems is of the form $\ensuremath{\varepsilon}\ensuremath{\propto}{p}^{s},$ then the equivalence in question arises when and only when $d=s.$ The purported ``equivalence'' between noninteracting Bose and Fermi gases in two dimensions is critically examined. Staying away from the thermodynamic limit, an exact calculation reveals some subtle, but significant, differences between the properties of the two systems that arise characteristically from the statistics obeyed by them. At the same time, certain physical quantities show differences that are not so subtle, in that they remain present even when the thermodynamic limit is taken. The role played by the spatial dimensionality $d$ is also elucidated and it turns out that there is nothing fundamentally special about dimensionality 2; if the single-particle energy spectrum operating in the systems is of the form $\ensuremath{\varepsilon}\ensuremath{\propto}{p}^{s},$ then the equivalence in question arises when and only when $d=s.$

Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topicsMar 1, 199825 citations

Thermodynamic equivalence of certain ideal Bose and Fermi gases

Kelly R. Patton, Michael R. Geller, M. P. Blencowe

arXiv:cond-mat/0406285Physica A Statistical Mechanics and its ApplicationsMay 18, 20055 citations

Quantum Statistics of Ideal Gases in Two Dimensions

Robert Mccredie May

It is shown that in two dimensions the specific heat ${C}_{V}(T, N)$ for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all $T$ and $N$ . This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: $n=2$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1$ .It is shown that in two dimensions the specific heat ${C}_{V}(T, N)$ for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all $T$ and $N$. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable: $n=2$ is seen to be a special case. In the extreme relativistic region, the analogous special case is $n=1$.

Physical ReviewSep 14, 196496 citations

Virial Coefficients from Unified Statistical Thermodynamics of Quantum Gases Trapped under Generic Power Law Potential in d Dimension and Equivalence of Quantum Gases

Shah Mohammad Bahauddin, Mir Mehedi Faruk

Abstract From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.Abstract From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases, trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in d = 3 and d = 2. But more importantly we found that, the virial coefficients of Bose and Fermi gases become identical (except the second virial coefficient, where the sign is different) when the gases are trapped under harmonic potential in d = 1. This result suggests the equivalence between Bose and Fermi gases established in d = 1 (J. Stat. Phys. DOI 10.1007/s10955-015-1344-4). Also, it is found that the virial coefficients of two-dimensional free Bose (Fermi) gas are equal to the virial coefficients of one-dimensional harmonically trapped Bose (Fermi) gas.

Communications in Theoretical PhysicsSep 1, 20162 citations

Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in $d$ dimension and the equivalence of trapped quantum gasesVirial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in $d$ dimension and the equivalence of trapped quantum gases

Mir Mehedi Faruk, Shah Mohammad Bahauddin

From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in $d=3$ and $d=2$ . But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap the gases under harmonic potential in $d=1$ . This result suggests the equivalence between Bose and Fermi gases which is already established for $d=1$ by M M Faruk (J Stat Phys, DOI 10.1007/s10955-015-1344-4). Surprisingly our investigation also shows that the virial coefficients of two dimensional free quantum gases are identical to the virial coefficients of one dimensional harmonically trapped quantum gases.From the unified statistical thermodynamics of quantum gases, the virial coefficients of ideal Bose and Fermi gases which are trapped under generic power law potential are derived systematically. From the general result of virial coefficients, one can produce the known results in $d=3$ and $d=2$. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap the gases under harmonic potential in $d=1$. This result suggests the equivalence between Bose and Fermi gases which is already established for $d=1$ by M M Faruk (J Stat Phys, DOI 10.1007/s10955-015-1344-4). Surprisingly our investigation also shows that the virial coefficients of two dimensional free quantum gases are identical to the virial coefficients of one dimensional harmonically trapped quantum gases.

arXiv:1601.07946Jan 28, 20160 citations

Comparative study of one-dimensional Bose and Fermi gases with contact interactions from the viewpoint of universal relations for correlation functions

裕太関野, Yuta Sekino, 祐介西田 +1 more

Jan 1, 20180 citations

d

is also elucidated and it turns out that there is nothing fundamentally special about dimensionality 2; if the single-particle energy spectrum operating in the systems is of the form $\ensuremath{\varepsilon}\ensuremath{\propto}{p}^{s},$ then the equivalence in question arises when and only when

d=s.

It is shown that in two dimensions the specific heat

{C}_{V}(T, N)

for an ideal gas of Fermi particles is identical with that for an ideal Bose gas for all

T

and

N

. This is true despite the great difference in the distribution functions of the two systems at low temperatures. To shed further light on this identity, the quantum statistics of ideal gases are investigated treating the number of dimensions as a continuous variable:

n=2

is seen to be a special case. In the extreme relativistic region, the analogous special case is

n=1

Virial coefficients from unified statistical thermodynamics of quantum gases trapped under generic power law potential in

d

dimension and the equivalence of trapped quantum gases

d=3

and

d=2

. But more importantly we found that, the virial coefficients of bosons and fermions become equal (except the the second virial coefficient, where the sign is different) when we trap the gases under harmonic potential in

d=1

. This result suggests the equivalence between Bose and Fermi gases which is already established for

d=1

by M M Faruk (J Stat Phys, DOI 10.1007/s10955-015-1344-4). Surprisingly our investigation also shows that the virial coefficients of two dimensional free quantum gases are identical to the virial coefficients of one dimensional harmonically trapped quantum gases.