Quantum Mechanics with Random Imaginary Scalar Potential

Details Quantum Mechanics with Random Imaginary Scalar Potential Quantum Mechanics with Random Imaginary Scalar Potential

1998-11-17

arxiv.org/abs/cond-mat/9811260v1

Europhys. Lett. 45, 290 (1999)

Physics

Condensed Matter

Disordered Systems and Neural Networks

10 pages, 1 eps figure

Scientific paper

10.1209/epl/i1999-00161-8

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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