Quantum Tunneling and the Aharonov-Bohm effect

2024/07/23 by Helffer, Bernard, Kachmar, Ayman · 1 citation
#35P20 #81Q10 #81U26 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2407.16524

Abstract

We investigate a Hamiltonian with radial potential wells and an Aharonov-Bohm vector potential with two poles. Assuming that the potential wells are symmetric, we derive the semi-classical asymptotics of the splitting between the ground and second state energies. The flux effects due to the Aharonov-Bohm vector potential are of lower order compared to the contributions coming from the potential wells.

Cited by

• Low-lying eigenvalues in the semiclassical limit of a Schrödinger operator with an inverse square potential, and non-asymptotic a-zeros of Kummer functions

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