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Journal of Experimental and Theoretical Physics

Theory of a weakly nonideal Bose gas in a magnetic field

Alexander I. Akhiezer, S. V. Peletminskiǐ, Yu. V. Slyusarenko

Published Mar 1, 1998• 17 citations
Publisher

Abstract

This paper investigates Bose-Einstein condensation of an ideal gas of finite-spin bosons in an external magnetic field. We generalize Bogolyubov’s theory of a weakly nonideal Bose gas to the case where the gas of finite-spin bosons is located in an external magnetic field. We find the corresponding quasiparticle spectrum and formulate the superfluidity criterion for the boson gas. The magnetization of the weakly nonideal Bose gas is also determined. Finally, we specify a method of studying kinetic processes that take place in a weakly nonideal Bose gas.

DOI
10.1134/1.558495

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This paper investigates Bose-Einstein condensation of an ideal gas of finite-spin bosons in an external magnetic field. We generalize Bogolyubov’s theory of a weakly nonideal Bose gas to the case where the gas of finite-spin bosons is located in an external magnetic field. We find the corresponding quasiparticle spectrum and formulate the superfluidity criterion for the boson gas. The magnetization of the weakly nonideal Bose gas is also determined. Finally, we specify a method of studying kinetic processes that take place in a weakly nonideal Bose gas.
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.
It is shown that a system of excitons in a high magnetic field is similar to a weakly nonideal Bose gas and is capable of forming the Bose-Einstein condensate as well as a superfluid state even at a relatively high temperature. The stability of the Bose condensate due to an essential decrease of the interaction between excitons and an increase of their binding energy in a high magnetic field is established. The possible observable effects of the Bose condensate and the interaction of light with the Bose-Einstein condensate of excitons is studied. The appearance of the Bose condensate in a broad range of the densities significantly changes the spectrum of the coupled excitons and photons. The dielectric theory of polaritons which accounts for the new excitation spectrum predicts a number of interesting phenomena.
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.
We have developed a microscopic theory of superfluidity in a two-dimensional, slightly nonideal Bose gas. The theory is rooted in the fact that a number of bosons are concentrated in the small momentum region at low temperatures when the interaction is weak, in spite of the fact that there is no Bose condensate in the two-dimensional case when T≠0. This fact lets us reduce the description of the system from one employing creation ak+ and annihilation ak operators for bosons to one based on combinations of these operators ρk and φk(ρk = S−1Σqaq+aq+k, φk· = −(i/ns) Σ(kq/k2 + l)aq+aq+k, where n is the boson density, and S is the area of the system). The description in terms of ρk and φk is simple because the hamiltonian is quadratic with respect to ρk and φk. The operators ρk and φk can also be used to express the occupation number Nk = ak+ak and current operators. We find the elementary excitation spectrum (which is identical to the Bogolyubov spectrum) and the momentum distribution of the bosons. We calculate the normal density due to thermal oscillations in the Bose gas and to interactions with impurity centers in the substrate.