Tunneling, the ability of a particle to transition from one potential well to another, is a basic phenomenon in elementary quantum mechanics. The time scale on which tunneling occurs is well studied in simplest cases, but in the presence of a strong magnetic field, much less is known.

We show that a strong magnetic field can sometimes completely eliminate tunneling, but under generic assumptions in a suitable regime we show that tunneling occurs, and we provide upper and lower bounds for the relevant time scale.

Joint work with Jacob Shapiro and Michael Weinstein.