Quantum mechanics with random imaginary scalar potential
Cavendish Laboratory - Madingley Road, Cambridge, CB3 0HE, UK
Accepted: 19 November 1998
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.
PACS: 05.40.+j – Fluctuation phenomena, random processes, and Brownian motion / 05.45.+b – Theory and models of chaotic systems / 36.20.-r – Macromolecules and polymer molecules
© EDP Sciences, 1999