恒定磁场中自由带电玻色子基态的迈斯纳效应
The Meissner effect in the ground state of free charged Bosons in a constant magnetic field
摘要：
在半经典近似下，严格地研究了圆柱体内外加恒定磁场中的自由荷电玻色子模型，它是少数几个可以解析处理的局部规范协变系统之一.该模型首先由Schafroth研究，适用于描述物理空间中的准束缚电子对，即所谓的Schafroth对，它出现在某些化合物中。在半经典问题解存在的假设下，得到了基态（g.s.）当前$<\vec{j}(\vec{x})>$的期望值是伦敦形式，即，$<\vec{j}(\vec{x})> = -c |ϕ_{0}(\vec{x})|^{2} \vec{A}(\vec{x})$，其中c为正常数，$\vec{A}$为矢量势，$ϕ_{0}$为单粒子g. s。波函数以及一些规律性的假设，磁感应强度可以被证明从其在圆柱体表面上的值按指数衰减。一个重要的作用是由一个定理的点态单调性的基态波函数的潜力。
英文摘要：
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., $<\vec{j}(\vec{x})> = -c |ϕ_{0}(\vec{x})|^{2} \vec{A}(\vec{x})$, where c is a positive constant, $\vec{A}$ the vector potential and $ϕ_{0}$ 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.
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