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 - Fluctuation phenomena, random
processes, and Brownian motion.
PACS. 05.45 - Theory and models of chaotic systems.
PACS. 36.20 - Macromolecules and polymer molecules.
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.