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arXiv:cond-mat/0111490 · Physical Review A

Bose-Einstein condensation in the presence of a uniform field and a pointlike impurity

R. M. Cavalcanti, Paola Giacconi A, Guido Pupillo, Roberto Soldati

Published Apr 23, 2002• 13 citations
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Abstract

The behavior of an ideal D-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrary to a long-standing belief, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at $T\ensuremath{\ne}0$ for $D=1,2,3$ if there is a pointlike impurity at the bottom of the vessel containing the gas.

DOI
10.1103/physreva.65.053606

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Physical Review A•Feb 1, 1973•25 citations
The behavior of an ideal D-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrary to a long-standing belief, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at T\ensuremath≠0T\ensuremath{\ne}0T\ensuremath=0 for D=1,2,3D=1,2,3D=1,2,3 if there is a pointlike impurity at the bottom of the vessel containing the gas.
\n\nIn this paper, we consider the effect of a uniform gravitational field on a spin-orbit coupled Bose gas. In a semiclassical approximation, we find that the gravitational field triggers Bose-Einstein condensation at finite temperature. For weak gravitational field, the critical temperature increases as the gravitational field goes more intense. And it first increases and then decreases along with increasing spin-orbit coupling strength. The heat capacity of the Bose gas varies continuously with the temperature around the critical one, which is different from the one in cases without a spin-orbit coupling.\n
The properties of a trapped ideal Bose gas in n -dimensional space are studied. General analytic expressions of the critical temperature of Bose-Einstein condensation, the jump of heat capacity at and the fraction of condensation at temperatures below have been derived. How these physical quantities depend on the external potential, particle characteristics and space dimensionality are discussed. We find that when a proper external potential is taken, Bose-Einstein condensation may occur in any dimensional space.
We study the thermodynamics of a one-dimensional system of noninteracting bosons in the presence of random fixed finite-range repulsive potentials. It is shown that a Bose---Einstein condensation into the lowest state occurs. The critical temperature increases with the number of impurities. The specific heat exhibits a discontinuity and is infinitely differentiable from both sides of the critical point. For a suitably defined pressure the isothermals exhibit a flat portion below the "transition length."