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 in 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 originally due to Schulman, Laidlaw and DeWitt which is applicable to Schrodinger operators on multiply connected configuration manifolds a formula is derived for the corresponding heat kernel. As an application of the heat kernel formula, approximate asymptotic expressions are derived for the lowest eigenvalue lying above the first Landau level and for the corresponding eigenfunction while assuming that | e B | R 2 / ( ħ c ) is large, where R is the distance between the two solenoids.