We have studied the effects of the externally applied electric and magnetic fields on Bose-Einstein condensation of the charged Bose gas. We have used a model density of states which takes the finite sample size into account to calculate the thermodynamic quantities. We have obtained condensate fraction, chemical potential, total energy and specific heat of the system using the semi classical density of states. We have studied the possibility for achieving Bose-Einstein condensation in three dimensional non interacting charged Bose gas under the cross electric and magnetic fields. The external fields made the system inhomogeneous and altered the Bose-Einstein condensation characteristics compared to the homogeneous case. We have found that the non interacting system of charged boson undergo Bose- Einstein condensation when external electric and magnetic fields were applied. The discontinuity in the specific heat was found as a function of external potentials. The obtained results were found in good agreement with previously obtained results.
We have studied the effects of the externally applied electric and magnetic fields on Bose-Einstein condensation of the charged Bose gas. We have used a model density of states which takes the finite sample size into account to calculate the thermodynamic quantities. We have obtained condensate fraction, chemical potential, total energy and specific heat of the system using the semi classical density of states. We have studied the possibility for achieving Bose-Einstein condensation in three dimensional non interacting charged Bose gas under the cross electric and magnetic fields. The external fields made the system inhomogeneous and altered the Bose-Einstein condensation characteristics compared to the homogeneous case. We have found that the non interacting system of charged boson undergo Bose- Einstein condensation when external electric and magnetic fields were applied. The discontinuity in the specific heat was found as a function of external potentials. The obtained results were found in good agreement with previously obtained results.
We discuss the occurrence of Bose-Einstein condensation in systems of noninteracting charged particles in three and one dimensions and in presence of an external magnetic field. In the one dimensional, as well as in the magnetic field cases, although not a critical temperature, a characteristic temperature can be found, corresponding to the case in which the ground state density becomes a macroscopic fraction of the total density. The case of relativistic charged scalar and vector particles is studied. The results give support to the existence of superconductivity in extremely strong magnetic fields, and lead to the prediction of superconductive-ferromagnetic behavior in the vector field case, which might be of interest in condensed matter as well as in cosmology. Some features of the magnetization in the early universe are conjectured.
We discuss the occurrence of Bose-Einstein condensation in systems of noninteracting charged particles in three in one dimensions and in presence of an external magnetic field. In the one dimensional, as well as in the magnetic field cases, although not a critical temperature, a characteristic temperature can be found, corresponding to the case in which the ground state density becomes a macroscopic fraction of the total density. The case of relativistic charged scalar and vector particles is studied. The results obtainedgive support to the existence of superconductivity in extremely strong magnetic fields, and leads to the prediction of superconductive-ferromagnetic behavior in the vector field case, which might be of interest in condensed matter as well as in cosmology. Some features of the magnetization in the early universe are conjectured.
Since the experimental realization of Bose–Einstein condensation of ultra cold atoms, extensive studies have been conducted on boson systems. One of recent epochmaking technologies is the synthesis of a fictitious gauge field acting on neutral atoms, which opened another wide field of studies on bosons and/or fermions in a synthetic magnetic field. Charged bosons were studied more than half a century ago by Schafroth. Charged bosons in a magnetic field were then studied in some respects and a rigorous proof was given by Angelescu and Corviovei, who showed absence of Bose– Einstein condensation of free charged bosons in a uniform magnetic field. This is due to the divergence of the density of states at the lowest band energy, i.e., the lowest Landau level. However the situation changes in the presence of a periodic potential. Namely some external periodic potentials are able to restore the Bose–Einstein condensation of the free charge bosons in a magnetic field in threedimensions (3D), although there has been no actual calculation of the condensation temperature of bosons in a typical lattice structure under a magnetic field. According to these previous studies, it is expected that free cold bosonic atoms under a synthetic magnetic field, if realized experimentally, would not condensate in a continuum space but would have a finite Bose–Einstein condensation temperature in the presence of an optical lattice potential. The aim of this short note is to demonstrate the restoration of the Bose–Einstein condensation under a magnetic field by the introduction of a periodic potential, taking typical lattice structures as examples and calculating the condensation temperature analytically. In what follows, with focus on bosons in a 3D lattice under a uniform magnetic field, we calculate the condensation temperature for different lattices and different magnitude of the magnetic field. In particular we consider a layered structure of two dimensional lattices such as square, triangular and honeycomb ones, with a magnetic field applied in the direction normal to the two-dimensional (2D) lattices. The energy spectrum of a particle on a two dimensional lattice, which we assume to be a square lattice for a moment, under a uniform magnetic field shows a characteristic pattern, so-called Hofstadter’s diagram. The one-particle energy of this system is described by the following Hamiltonian in the tight-binding approximation.
The thermodynamic properties of a Bose gas of particles with nonzero spin and magnetic moment in states with and without a Bose-Einstein condensate are studied as a function of the external magnetic field. It is shown that there exists a temperature interval where a transition into a state with a Bose-Einstein condensate occurs in a Bose gas with constant temperature and particle number density when the magnetic field is increasing and reaches a critical magnitude. The temperature and magnetic field derivatives of the specific heat at constant volume and the magnetic susceptibility undergo a jump at such a transition.
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≥3 assumed. Calculations are presented from first principles using the effective action method. For D≥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→0 limit of the magnetized gas is achieved.
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.