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Localization transitions in non-Hermitian quantum mechanics

Naomichi Hatano·David R. Nelson
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Abstract

We study the localization transitions which arise in both one and two dimensions when quantum mechanical particles described by a random Schrödinger 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.

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Naomichi Hatano, David R. Nelson. 1996-03-26. Localization transitions in non-Hermitian quantum mechanics. https://doi.org/10.1103/physrevlett.77.570

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