Quantum mechanics with random imaginary scalar potential

A. V. Izyumov; B. D. Simons

doi:doi:10.1209/epl/i1999-00161-8

DOI: 10.1209/epl/i1999-00161-8

Europhys. Lett, 45 (3), pp. 290-295 (1999)

Quantum mechanics with random imaginary scalar potential

A. V. Izyumov and B. D. Simons

Cavendish Laboratory - Madingley Road, Cambridge, CB3 0HE, UK

(received 22 July 1998; accepted in final form 19 November 1998)

PACS. 05.40 ${\rm +j}$ - Fluctuation phenomena, random processes, and Brownian motion.
PACS. 05.45 ${\rm +b}$ - Theory and models of chaotic systems.
PACS. 36.20 ${\rm -r}$ - Macromolecules and polymer molecules.

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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