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Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Superconductivity of the Bose gas

John Daicic, Norman E. Frankel

Published May 15, 1996• 13 citations
Publisher

Abstract

We investigate the magnetic properties of the ideal Bose gas in both the relativistic and nonrelativistic regimes, and demonstrate its remarkable behavior as a superconductor, where it expels totally an external homogeneous field, and also a new phenomenon, which we call superdiamagnetism, where the gas very nearly does so. These two phenomena are shown to exist in two distinct temperature regimes for both the nonrelativistic and relativistic gases, and are revealed by a careful consideration of the analytic structure of the thermodynamic potential of the system, accessible by the powerful method of the Mellin integral transform. We also comment on other approaches to this problem which have recently appeared.

DOI
10.1103/physrevd.53.5745

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A comment on the ideal relativistic Bose gas

Jeremy Dunning-Davies

Rigorous results are proved which are directly applicable to the problem of writing the thermodynamic properties of an ideal relativistic Bose gas in terms of modified Bessel functions of the second kind. The results are particularly important when the Bose gas is at, or below, its condensation temperature.

Journal of Physics A Mathematical and General•Nov 1, 1981•3 citations
We investigate the magnetic properties of the ideal Bose gas in both the relativistic and nonrelativistic regimes, and demonstrate its remarkable behavior as a superconductor, where it expels totally an external homogeneous field, and also a new phenomenon, which we call superdiamagnetism, where the gas very nearly does so. These two phenomena are shown to exist in two distinct temperature regimes for both the nonrelativistic and relativistic gases, and are revealed by a careful consideration of the analytic structure of the thermodynamic potential of the system, accessible by the powerful method of the Mellin integral transform. We also comment on other approaches to this problem which have recently appeared.
We consider the mathematical model of an ideal gas of charged bosons or fermions in an n-dimensional space, treating n as a continuous variable. The investigation shows the extent to which the magnetic behavior depends on the dimensionality of the system. In particular, the charged Bose gas in a homogeneous magnetic field does not condense unless n > 4, in contrast to the field-free gas which condenses for n > 2: however so long as n > 2 and T < Tc this system completely expels homogeneous magnetic fields weaker than a certain critical field, Hc. (Tc is the field free transition temperature.) This field expulsion comes explicitly from the condensed ground-state bosons for n > 4; but it is still present, and Hc has the same form, for 4 > n > 2 where there is no condensation.
The relationship between the two different ordering procedures taking place in an ideal charged relativistic Bose gas in the presence of a uniform external magnetic field B is investigated in an arbitrary number of spatial dimensions d. In particular the analytical form of the charge-density condensate qc{q}_{c}qc​ and the magnetization density \ensuremath{\rho} are calculated as a function of B and the inverse temperature \ensuremath{\beta} for relativistic bosons without spin. In the small-field limit (B\ensuremath{\rightarrow}0) this system exhibits the complete restoration of the symmetry of the ideal relativistic Bose gas for all d at any finite temperature.
Bose-Einstein condensation of charged scalar and vector particles may actually occur in presence of a constant homogeneous magnetic field, but there is no critical temperature at which condensation starts. The condensate is described by the statistical distribution. The Meissner effect is possible in the scalar, but not in the vector field case, which exhibits a ferromagnetic behavior. Permanent address: Grupo de Fisica Teórica, ICIMAF, Academia de Ciencias de Cuba, Calle E No. 309,Vedado, La Habana 4, Cuba. It was pointed out long ago by Schafroth [1] that for a non-relativistic boson gas, Bose-Einstein condensation (BEC) does not take place in the presence of a constant magnetic field. The problem was studied afterwards by May [2], who investigated the condensation in the non-relativistic case for an arbitrary dimension d and showed that it occurs for d ≥ 5, and later by Daicic et al [3], [4], who extended the considerations made by [2] to the relativistic high temperature case and found new magnetization properties. More recently Toms [5] has proved that BEC in presence of a constant magnetic field does not occur in any number of spatial dimensions, and Elmfors et al [6] consider that a in the 3d