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Modern Physics Letters B

MAGNETIC SUSCEPTIBILITY OF THE RELATIVISTIC BOSON GAS

Laurean Homorodean

Published Oct 30, 2001• 4 citations
Publisher

Abstract

We present the temperature dependences of the magnetic susceptibilities for degenerate (below the Bose–Einstein-condensation temperature) and nondegenerate ideal gases of relativistic charged spinless bosons. The nonrelativistic limits of these laws are also discussed. A comparison with the relativistic electron gas is made.
DOI
10.1142/s021798490100283x

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The magnetic susceptibilities of the degenerate (below the Bose–Einstein condensation temperature) and nondegenerate ideal gases of nonrelativistic charged spinless bosons are presented. In both cases, the boson gas is diamagnetic. The magnetic susceptibility of the degenerate boson gas below the Bose–Einstein condensation temperature increases in modulus as the temperature increases. As expected, the magnetic susceptibility of the nondegenerate boson gas decreases in modulus with increasing temperature according to the Curie law in low magnetic fields.
Abstract We study the effects of a uniform and constant magnetic field on the Bose–Einstein condensation (BEC) of relativistic charged scalar bosons. The condensation of magnetized charged bosons is usually discussed in the weak or strong field regimes separately, and in each case, the properties predicted for the condensate are different. Here, we develop a low‐temperature analysis suitable for any field that allows us to observe how the gas behaves for intermediate values of the magnetic field. We find that BEC may occur at finite magnetic fields, despite the gas becoming effectively one‐dimensional due to Landau quantization of the momentum perpendicular to the magnetic axis.
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.
The magnetic properties of charged vector boson gas are studied in the very weak, and very strong (near critical value) external magnetic field limits. When the density of the vector boson gas is low, or when the external field is strong, no true Bose–Einstein condensation occurs, though significant amount of bosons will accumulate in the ground state. The gas is ferromagnetic in nature at low temperature. However, Bose–Einstein condensation of vector bosons (scalar bosons as well) is likely to occur in the presence of a uniform weak magnetic field when the gas density is sufficiently high. A transitional density depending on the magnetic field seems to exist below which the vector boson gas changes its property with respect to the Bose–Einstein condensation in a uniform magnetic field.
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.