Tunneling effect induced by a curved magnetic edge

Abstract

Experimentally observed magnetic fields with nanoscale variations are theoretically modeled by a piece-wise constant function with jump discontinuity along a smooth curve, the magnetic edge. Assuming the edge is a closed curve with an axis of symmetry and the field is sign changing and with exactly two distinct values, we prove that semi-classical tunneling occurs and calculate the magnitude of this tunneling effect. This paper is dedicated to Elliott H. Lieb on the occasion of his 90th birthday.