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Ideal quantum gases in \(D\)-dimensional space and power-law potentials. (English) Zbl 1062.82500

Summary: The authors 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 ffermions 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.

MSC:

82B10 Quantum equilibrium statistical mechanics (general)
82B26 Phase transitions (general) in equilibrium statistical mechanics
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