Statistical mechanics of an ideal Bose gas in a confined geometry

A model of the non-ideal Bose gas is considered. We prove the existence of condensate in the model at sufficiently low temperature. The method of majorizing estimates for the Duhamel Two Point Functions is used. The equation for the critical temperature and the upper bound for the one-particle excitations energy are obtained.

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The condensation of ideal Bose gas in a gravitational field

Physica B Condensed Matter ◽

10.1016/j.physb.2012.07.037 ◽

2012 ◽

Vol 407 (21) ◽

pp. 4375-4378 ◽

Cited By ~ 3

Author(s):

Cong-Fei Du ◽

Hong Li ◽

Zhen-Quan Lin ◽

Xiang-Mu Kong

Keyword(s):

Gravitational Field ◽

Bose Gas ◽

Ideal Bose Gas

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Logarithmic Sobolev Inequalities for an Ideal Bose Gas

Advances in Quantum Mechanics - Springer INdAM Series ◽

10.1007/978-3-319-58904-6_7 ◽

2017 ◽

pp. 121-133

Author(s):

Fabio Cipriani

Keyword(s):

Bose Gas ◽

Sobolev Inequalities ◽

Logarithmic Sobolev Inequalities ◽

Ideal Bose Gas

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ON THE LOW-TEMPERATURE BEHAVIOR OF THE INFINITE-VOLUME IDEAL BOSE GAS

Infinite Dimensional Analysis Quantum Probability and Related Topics ◽

10.1142/s0219025710003997 ◽

2010 ◽

Vol 13 (01) ◽

pp. 39-63

Author(s):

KARL-HEINZ FICHTNER ◽

KEI INOUE ◽

MASANORI OHYA

Keyword(s):

Low Temperature ◽

Numerical Simulations ◽

Bose Gas ◽

Temperature Behavior ◽

Infinite Volume ◽

Position Distribution ◽

Bounded Volume ◽

Ideal Bose Gas ◽

The Ideal

In Ref. 11 clustering representations of the position distribution of the ideal Bose gas were considered. In principle that gives rise to possibilities concerning simulations of the system of positions of the particles. But one has to take into account that in case of low temperature the clusters are very large and their origins are far from a fixed bounded volume. For that reason we will consider some estimations of the influence of these clusters on the behavior of the subsystem of particles located in a fixed bounded volume. All points in the fixed bounded volume come from a bigger volume which the estimation (5.2) in Theorem 5.2 gives on average. Several numerical simulations in dimension two are shown in Sec. 5.

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