Quantum statistics of ideal gases in confined space

Dai, Wu-Sheng; Xie, Mi

doi:10.1016/s0375-9601(03)00510-3

Cited by 75 publications

(67 citation statements)

References 7 publications

(10 reference statements)

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“…Strictly speaking, however, when the fugacity z > 1, such as in Fermi-Dirac statistics, the grand potential ln Ξ can not be expanded in such a way. In the preceding paper [4] we perform the summation of the expansion of the grand potential without proving the convergence of the series, but, instead, we analyze the validity of the result by comparing it with the grand potential of an ideal quantum gas in free space and show that the grand potential in free space, whose validity is fully accepted, is just the zeroth-order approximation of our result. With the help of the exact solutions obtained above, we can make further improvement on the analysis of the validity of this treatment.…”

Section: The Validity Of the Approximate Methods For Calculating Geomementioning

confidence: 99%

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Geometry effects in confined space

Dai

Xie

2004

Phys. Rev. E

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In this paper we calculate some exact solutions of the grand partition functions for quantum gases in confined space, such as ideal gases in two-and three-dimensional boxes, in tubes, in annular containers, on the lateral surface of cylinders, and photon gases in three-dimensional boxes. Based on these exact solutions, which, of course, contain the complete information about the system, we discuss the geometry effect which is neglected in the calculation with the thermodynamic limit V → ∞, and analyze the validity of the quantum statistical method which can be used to calculate the geometry effect on ideal quantum gases confined in two-dimensional irregular containers. We also calculate the grand partition function for phonon gases in confined space. Finally, we discuss the geometry effects in realistic systems.

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Section: The Validity Of the Approximate Methods For Calculating Geomementioning

confidence: 99%

“…Furthermore, the validity of the method presented in Ref. [4] can be further justified by comparing it with these exact solutions.…”

Section: Introductionmentioning

confidence: 99%

Geometry effects in confined space

Dai

Xie

2004

Phys. Rev. E

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“…While for a degenerate quantum gas system in micro-/nanoscale, the quantum boundary effects may be more significant. The problem can be analyzed in more detail from the quantum statistics theory [19,20]. …”

Section: Resultsmentioning

confidence: 99%

Micro-/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristics

Nie

Liao

Zhang

et al. 2010

Energy

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“…[1][2][3][4][5][6][7][8][9][10] For example, based on Maxwell-Boltzmann statistics, Sisman and Muller 6,7 researched the boundary effect of the ideal classical gas confined in a rectangular box or spherical and cylindrical geometries and derived some significant results, and discussed the Casimir-like size effect of the gas in a confined space; based on quantum statistics, Dai et al [8][9][10] studied the properties of ideal quantum gases in a confined space and revealed some statistic characteristics of the systems. When the gas system is enclosed in a finite volume, the structure of the phase space will be changed and the energy spectrum of single-particle states will depend on the shape of the boundary.…”

Section: Introductionmentioning

confidence: 99%

Statistic Characteristics of Quantum Gases in a Confined Space

Lin

et al. 2011

Int. J. Mod. Phys. B

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With the help of the Euler-MacLaurin formula, the statistic characteristics of quantum gases confined in a rectangular box are investigated by using a unified way. Three components of the pressure tensor and the internal energy of the system are analytically derived. The important relation between the pressure tensor and the internal energy is strictly proved. It is pointed out that these results are different from those obtained in literature and textbooks under the thermodynamic limit condition. Moreover, the pressure of the system is rationally introduced with the help of the property of the diagonal tensor, so that some thermodynamic functions of the system may be conveniently obtained. The statistic characteristics of quantum and classical gases confined in some different containers are discussed, the influence of the size effect of the containers on the properties of gases is analyzed and some new significant results are obtained.

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Quantum statistics of ideal gases in confined space

Abstract: In this paper, the effects of boundary and connectivity on ideal gases in two-dimensional confined space and three-dimensional tubes are discussed in detail based on the analytical result. The implication of such effects on the mesoscopic system is also revealed.

Cited by 75 publications

References 7 publications

Geometry effects in confined space

Geometry effects in confined space

Micro-/nanoscaled irreversible Otto engine cycle with friction loss and boundary effects and its performance characteristics

Statistic Characteristics of Quantum Gases in a Confined Space

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