Jacob Shapiro | PIMS - Pacific Institute for the Mathematical Sciences

Princeton University

https://web.math.princeton.edu/~shapiro/

Speaker at the Spring Time in Mathematical Quantum Physics Workshop ( UBC, May 2025)

Title: Quantum Tunneling And Its Absence In Deep Wells And Strong Magnetic Fields

Abstract: New results on quantum tunneling between deep potential wells, in the presence of a strong constant magnetic field are presented. This includes a family of double well potentials containing examples for which the low-energy eigenvalue splitting vanishes, and hence quantum tunneling is eliminated. Further, by deforming within this family, the magnetic ground state can be made to transition from symmetric to anti-symmetric. For generic double wells in a certain regime, tunneling is not suppressed, and a lower bound for the eigenvalue splitting is given. Joint with Fefferman and Weinstein.

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