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Quantum Mechanics with Random Imaginary Scalar Potential

A. V. Izyumov·B. D. Simons
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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 $d>4$.

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BibTeXRIS

A. V. Izyumov, B. D. Simons. 1998-11-17. Quantum Mechanics with Random Imaginary Scalar Potential. https://doi.org/10.1209/epl%2Fi1999-00161-8

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