Exact Green's functions for localized irreversible potentials

TL;DR

This paper derives exact Green's functions for a localized potential that breaks reversibility, illustrating quantum irreversibility and its differences from classical behavior, with potential applications to wave systems.

Contribution

It provides an analytical solution for the Green's function of a localized irreversible potential, revealing its meromorphic structure and implications for quantum irreversibility.

Findings

Analytical Green's function with meromorphic structure

Demonstration of quantum irreversibility effects

Differences between classical and wave-like irreversibility

Abstract

We study the quantum-mechanical problem of scattering caused by a localized obstacle that breaks spatial and temporal reversibility. Accordingly, we follow Maxwell's prescription to achieve a violation of the second law of thermodynamics by means of a momentum-dependent interaction in the Hamiltonian, resulting in what is known as Maxwell's demon. We obtain the energy-dependent Green's function analytically, as well as its meromorphic structure. The poles lead directly to the solution of the evolution problem, in the spirit of M. Moshinsky's work in the 1950s. Symmetric initial conditions are evolved in this way, showing important differences between classical and wave-like irreversibility in terms of collapses and revivals of wave packets. Our setting can be generalized to other wave operators, e.g. electromagnetic cavities in a classical regime.