Superconductivity of a Charged Ideal Bose Gas

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 ${T}_{c}$. Below ${T}_{c}$ 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 ${H}_{c}(T)$ is determined and found to be related to the penetration depth $d(T)$ by ${H}_{c}=\frac{\ensuremath{\hbar}c}{2e{d}^{2}}$ ($e$ being the boson charge).The $B(H)$ 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 ${T}_{c}$.

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