2020/06/14 by Charles Fefferman, Jacob N. Shapiro, Fefferman, Charles L. +3 · 2 citations
Physics and Astronomy · Mathematics · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Quantum and electron transport phenomena
paper · pdf · doi:10.48550/arxiv.2006.08025
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.