This talk is on a joint work with B. Helffer. Inspired by a recent paper* 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.  
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*[Lower bound on quantum tunneling for strong magnetic fields, SIAM J. Math. Anal. 54(1), 1105-1130 (2022).]