On the irreversible dynamics emerging from quantum resonances

TL;DR

This paper analyzes the long-term behavior of quantum systems with stationary and metastable states, decomposing their evolution into stationary, exponentially decaying, and polynomially decaying parts, applicable to open systems and complex models.

Contribution

It introduces a decomposition of quantum propagators into stationary, exponential, and polynomial decay components using the Feshbach map, applicable beyond spectral deformation limitations.

Findings

Decomposition of quantum dynamics into distinct decay components.

Explicit decay rates and directions derived from resonance energies.

Application to the spin-boson model at arbitrary coupling strength.

Abstract

We consider the dynamics of quantum systems which possess stationary states as well as slowly decaying, metastable states arising from the perturbation of bound states. We give a decomposition of the propagator into a sum of a stationary part, one exponentially decaying in time and a polynomially decaying remainder. The exponential decay rates and the directions of decay in Hilbert space are determined, respectively, by complex resonance energies and by projections onto resonance states. Our approach is based on an elementary application of the Feshbach map. It is applicable to open quantum systems and to situations where spectral deformation theory fails. We derive a detailed description of the dynamics of the spin-boson model at arbitrary coupling strength.