Lower Bound on Quantum Tunneling for Strong Magnetic Fields
Abstract
We consider a particle bound to a twodimensional plane and a double well potential, subject to a perpendicular uniform magnetic field . The energy difference between the lowest two eigenvaluesthe eigenvalue splittingis 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.
 Publication:

arXiv eprints
 Pub Date:
 June 2020
 arXiv:
 arXiv:2006.08025
 Bibcode:
 2020arXiv200608025F
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 Quantum Physics
 EPrint:
 23 pages