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Localization Transitions in Non-Hermitian Quantum Mechanics

1996; American Physical Society; Volume: 77; Issue: 3 Linguagem: Inglês

10.1103/physrevlett.77.570

1092-0145

Naomichi Hatano, David R. Nelson,

Cold Atom Physics and Bose-Einstein Condensates

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.