Joint IAS/PU Analysis Seminar
4:30pm|Simonyi Hall 101 and Remote Access
Topic: Quantum Tunneling and Its Absence in Deep Wells and Strong Magnetic Fields
Speaker: Jacob Shapiro
Affiliation: Princeton University
Date: December 02, 2024
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.