Quantum tunneling in deep potential wells and strong magnetic field revisited

Inspired by a recent paper${}^{\ast }$ by C. Fefferman, J. Shapiro and M. Weinstein, we investigate quantum tunneling for a Hamiltonian with a symmetric double well and a uniform magnetic field. In the simultaneous limit of strong magnetic field and deep potential wells with disjoint supports, tunneling occurs and we derive accurate estimates of its magnitude. ${}^{\ast }$[Lower bound on quantum tunneling for strong magnetic fields. SIAM J. Math. Anal. 54(1), 1105-1130 (2022).]