The Meissner effect in the ground state of free charged Bosons in a constant magnetic field

The model of free charged Bosons in an external constant magnetic field inside a cylinder, one of the few locally gauge covariant systems amenable to analytic treatment, is rigorously investigated in the semiclassical approximation. The model was first studied by Schafroth and is suitable for the description of quasi-bound electron pairs localized in physical space, so-called Schafroth pairs, which occur in certain compounds. Under the assumption of existence of a solution of the semiclassical problem for which the ground state (g.s.) expectation value of the current $<\vec{j}(\vec{x})>$ is of the London form, i.e., $<\vec{j}(\vec{x})> = -c |\phi_{0}(\vec{x})|^{2} \vec{A}(\vec{x})$,wherecisapositiveconstant,$\vec{A}$ the vector potential and ${\varphi }_0$ the one-particle g.s. wave-function. as well as some regularity assumptions, the magnetic induction may be proved to decay exponentially from its value on the surface of the cylinder. An important role is played by a theorem on the pointwise monotonicity of the ground state wave-function on the potential.