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 ${q}_{c}$ 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.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 ${q}_{c}$ 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.

Physical Review AMar 1, 198610 citations

Bose-Einstein condensation of nonrelativistic charged particles in a constant magnetic field

Guy B. Standen, David J. Toms

The statistical mechanics of a system of non-relativistic charged particles in a constant magnetic field is discussed. The spatial dimension $D$ is arbitrary with $D\geq 3$ assumed. Calculations are presented from first principles using the effective action method. For $D\geq 5$ the system has a phase transition with a Bose condensate. We show how the effective action method method deals with in a very natural way with the condensate and study it's rôle in the magnetization of the gas. For large values of the magnetic field we show how the magnetized gas in $D$ spatial dimensions behaves like the free Bose gas in $(D-2)$ spatial dimensions. Even though for D=3 the magnetized gas does not have a phase transition for any non-zero value of the magnetic field, we show how the specific heat starts to resemble the result for the free gas as the magnetic field is reduced. A number of analytical approximations for the magnetization and specific heat are given and compared with numerical results. In this way we are able to study in precise detail how the $B\to 0$ limit of the magnetized gas is achieved.The statistical mechanics of a system of non-relativistic charged particles in a constant magnetic field is discussed. The spatial dimension $D$ is arbitrary with $D\geq 3$ assumed. Calculations are presented from first principles using the effective action method. For $D\geq 5$ the system has a phase transition with a Bose condensate. We show how the effective action method method deals with in a very natural way with the condensate and study it's rôle in the magnetization of the gas. For large values of the magnetic field we show how the magnetized gas in $D$ spatial dimensions behaves like the free Bose gas in $(D-2)$ spatial dimensions. Even though for D=3 the magnetized gas does not have a phase transition for any non-zero value of the magnetic field, we show how the specific heat starts to resemble the result for the free gas as the magnetic field is reduced. A number of analytical approximations for the magnetization and specific heat are given and compared with numerical results. In this way we are able to study in precise detail how the $B\to 0$ limit of the magnetized gas is achieved.

arXiv:cond-mat/9712141Dec 12, 19971 citation

{q}_{c}

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.

The statistical mechanics of a system of non-relativistic charged particles in a constant magnetic field is discussed. The spatial dimension

D

is arbitrary with

D\geq 3

assumed. Calculations are presented from first principles using the effective action method. For

D\geq 5

the system has a phase transition with a Bose condensate. We show how the effective action method method deals with in a very natural way with the condensate and study it's rôle in the magnetization of the gas. For large values of the magnetic field we show how the magnetized gas in

D

spatial dimensions behaves like the free Bose gas in

(D-2)

spatial dimensions. Even though for D=3 the magnetized gas does not have a phase transition for any non-zero value of the magnetic field, we show how the specific heat starts to resemble the result for the free gas as the magnetic field is reduced. A number of analytical approximations for the magnetization and specific heat are given and compared with numerical results. In this way we are able to study in precise detail how the

B\to 0

limit of the magnetized gas is achieved.