Lower Bound on Quantum Tunneling for Strong Magnetic Fields

@article{Fefferman2020LowerBO,
  title={Lower Bound on Quantum Tunneling for Strong Magnetic Fields},
  author={Charles Fefferman and Jacob Shapiro and Michael I. Weinstein},
  journal={SIAM J. Math. Anal.},
  year={2020},
  volume={54},
  pages={1105-1130}
}
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… 

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