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arXiv:cond-mat/0305669 · Physical review. B, Condensed matter

Meissner effect in a charged Bose gas with short-range repulsion

Shun-ichiro Koh

Published Oct 2, 2003• 9 citations
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Abstract

The question of whether the Bose-Einstein condensate (BEC) is a necessary condition of the Meissner effect is examined. The electromagnetic susceptibility of a charged Bose gas with short-range repulsion is studied using the perturbation theory with respect to the repulsive force. With decreasing temperature, the Bose-statistical coherence grows, and prior to the BEC phase the susceptibility shows a singularity implying the Meissner effect. This means that the BEC is a sufficient, but not a necessary, condition of the Meissner effect in the charged Bose gas with short-range repulsion.

DOI
10.1103/physrevb.68.144502

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The question of whether the Bose-Einstein condensate (BEC) is a necessary condition of the Meissner effect is examined. The electromagnetic susceptibility of a charged Bose gas with short-range repulsion is studied using the perturbation theory with respect to the repulsive force. With decreasing temperature, the Bose-statistical coherence grows, and prior to the BEC phase the susceptibility shows a singularity implying the Meissner effect. This means that the BEC is a sufficient, but not a necessary, condition of the Meissner effect in the charged Bose gas with short-range repulsion.
It is shown that an ideal gas of charged bosons exhibits the essential equilibrium features of a superconductor. The onset of Bose-Einstein condensation marks the transition temperature Tc{T}_{c}Tc​. Below Tc{T}_{c}Tc​ a Meissner-Ochsenfeld effect is exhibited which is described in a very good approximation by London's equation.The singular nature of the condensed ideal Bose gas exhibits itself in a space dependence of the London constant $\ensuremath{\lambda}$, determined by the boundary conditions on the wave function. It is shown that the electrostatic repulsion between the bosons compensates this effect and leads to a spatially constant $\ensuremath{\lambda}$, independently of the boundary conditions.The critical field Hc(T){H}_{c}(T)Hc​(T) is determined and found to be related to the penetration depth d(T)d(T)d(T) by ${H}_{c}=\frac{\ensuremath{\hbar}c}{2e{d}^{2}}$ (eee being the boson charge).The B(H)B(H)B(H) law is different from the one usually assumed for actual superconductors. Corresponding changes occur in the thermodynamical relation.A comparison with superconducting metals is made. The main conclusion is that if superconductivity in metals is due to the concurrence of bosons, then the number of these bosons must be strongly temperaturedependent below Tc{T}_{c}Tc​.
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
We determine the behaviour of entanglement between regions of space in a Bose gas of fixed particle number around the critical temperature condensation. Long-range correlations develop in the Bose-Einstein condensate (BEC) phase transition and the aim here is to find out whether spatial coherence alone implies entanglement. We use a purity measure of entanglement to derive an entanglement witness that detects entanglement between two regions of space in the BEC. It is shown that spatial coherence between the two regions is necessary for entanglement with coherence and entanglement becoming equivalent only when the regions occupy the entire confining volume of the gas. The probabilities for Bosons to occupy the regions is the only other parameter that influences the amount of entanglement. We calculate explicitly the amount of entanglement between two regions for a cigar-shaped harmonic potential and find that it increases with decreasing temperature. A second entanglement witness is derived for entanglement between three regions of space, where again spatial coherence between each pair of regions is precursor to entanglement. It is shown that the state with the maximum amount of entanglement occurs when the probabilities for the Bosons to occupy the three regions are equal.
We examine the occurrence of Bose-Einstein condensation in both nonrelativistic and relativistic systems with no self-interactions in a general setting. A simple condition for the occurrence of Bose-Einstein condensation is given. We show that condensation can occur only if q> 3q>~3q> 3, where qqq is the dimension associated with the continuous part of the eigenvalue spectrum of the Hamiltonian for nonrelativistic systems or the spatial part of the Klein-Gordon operator for relativistic systems. Furthermore we show that the criterion for the appearance of the Meissner-Ochsenfeld effect is closely connected with that for the appearance of Bose-Einstein condensation.
We study analytically the ground-state stability of a Bose–Einstein condensate (BEC) confined in an harmonic trap with repulsive or attractive zero-range interaction by minimizing the energy functional of the system. In the case of repulsive interaction the BEC mean radius grows by increasing the number of bosons, instead in the case of attractive interaction the BEC mean radius decreases by increasing the number of bosons: to zero if the system is one-dimensional and to a constant minimum radius, with a maximum number of bosons, if the system is three-dimensional.