The heat kernel for two Aharonov-Bohm solenoids in a uniform magnetic field

Abstract

A non-relativistic quantum model is considered with a point particle carrying a charge $e$ and moving on the plane pierced by two infinitesimally thin Aharonov-Bohm solenoids and subjected to a perpendicular uniform magnetic field of magnitude $B$. Relying on a technique due to Schulman and Sunada which is applicable to Schrödinger operators on multiply connected configuration manifolds a formula is derived for the corresponding heat kernel. As an application of the heat kernel formula, an approximate asymptotic expressions are derived for the lowest eigenvalue lying above the first Landau level and for the corresponding eigenfunction while assuming that $|eB|R^2/(\hslash c)$ is large where $R$ is the distance between the two solenoids.

References in corpus (4)

• Nonrelativistic molecular models under external magnetic and AB flux fields
• On the Dirac and Pauli operators with several Aharonov-Bohm solenoids
• Generalized Bloch analysis and propagators on Riemannian manifolds with a discrete symmetry
• Noncommutative Bloch analysis of Bochner Laplacians with nonvanishing gauge fields