Localization transitions in non-Hermitian quantum mechanics

Abstract

We study the localization transitions which arise in both one and two dimensions when quantum mechanical particles described by a random Schr\"odinger equation are subjected to a constant imaginary vector potential. A path-integral formulation relates the transition to flux lines depinned from columnar defects by a transverse magnetic field in superconductors. The theory predicts that the transverse Meissner effect is accompanied by stretched exponential relaxation of the field into the bulk and a diverging penetration depth at the transition.