Lower Bound on Quantum Tunneling for Strong Magnetic Fields
Lower Bound on Quantum Tunneling for Strong Magnetic Fields
复制标题
强磁场量子隧道的下界
DOI：
10.1137/21m1429412
复制
发表时间：
2020
期刊：
影响因子：
--
通讯作者：
M. Weinstein
中科院分区：
文献类型：
--
作者：
C. Fefferman;Jacob Shapiro;M. Weinstein
我们考虑了受垂直均匀磁场约束的粒子受二维平面和双势垒势的约束。最低的两个本征值之间的能量差--本征值分裂--与两个井间的隧道几率有关。在磁场强度和势垒深度都很大的情况下，我们得到了这种分裂的上下界。主要的步骤是给出井间跳跃概率的下限，这是固体物理紧束缚模型中的一个关键参数。
We consider a particle bound to a two-dimensional plane and a double well potential, subject to a perpendicular uniform magnetic field . The energy difference between the lowest two eigenvalues--the eigenvalue splitting--is related to the tunneling probability between the two wells. We obtain upper and lower bounds on this splitting in the regime where both the magnetic field strength and the depth of the wells are large. The main step is a lower bound on the hopping probability between the wells, a key parameter in tight binding models of solid state physics.