Bose-Einstein condensation under external conditions
Klaus Kirsten, David J. Toms
TL;DR
This paper explores Bose-Einstein condensation under various external conditions by linking thermodynamic properties to heat-kernel coefficients, applicable to arbitrary potentials and geometries.
Contribution
It introduces a general method connecting partition sums and the heat-equation to analyze Bose-Einstein condensation in complex external environments.
Findings
Critical temperature expressed via heat-kernel coefficients
Applicable to arbitrary confining potentials
Provides a unified approach for different geometries
Abstract
We discuss the phenomenon of Bose-Einstein condensation under general external conditions using connections between partition sums and the heat-equation. Thermodynamical quantities like the critical temperature are given in terms of the heat-kernel coefficients of the associated Schr\"odinger equation. The general approach is applied to situations where the gas is confined by arbitrary potentials or by boxes of arbitrary shape.
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