Quantum Mechanics with Random Imaginary Scalar Potential

Abstract

We study spectral properties of a non-Hermitian Hamiltonian describing a quantum particle propagating in a random imaginary scalar potential. Cast in the form of an effective field theory, we obtain an analytical expression for the ensemble averaged one-particle Green function from which we obtain the density of complex eigenvalues. Based on the connection between non-Hermitian quantum mechanics and the statistical mechanics of polymer chains, we determine the distribution function of a self-interacting polymer in dimensions $d>4$.

10 pages, 1 eps figure

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Cited by in corpus (8)

• Random Matrices close to Hermitian or unitary: overview of methods and results
• Light Localization induced by Random Imaginary Permittivities
• "Single Ring Theorem" and the Disk-Annulus Phase Transition
• Anomalous localization enhancement in one-dimensional non-Hermitian disordered lattices
• Optimal Fluctuations and Tail States of non-Hermitian Operators
• "Lifshitz tails" and extended states in an Imaginary random potential
• Field theory of self-avoiding walks in random media
• Optimal Fluctuations and Tail States of non-Hermitian Operators