A resonance theory for open quantum systems with time-dependent dynamics

TL;DR

This paper introduces a resonance theory for open quantum systems with time-dependent Hamiltonians, providing a non-markovian dynamical representation valid over all times and demonstrating applications to spin-fermion systems with level crossings.

Contribution

It develops a novel resonance-based framework for analyzing open quantum systems with time-dependent dynamics, extending existing theories to non-markovian regimes.

Findings

Representation of dynamics via resonance energies and states

Applicable to systems with arbitrary energy level crossings

Provides transition probabilities over all times

Abstract

We develop a resonance theory to describe the evolution of open systems with time-dependent dynamics. Our approach is based on piecewise constant Hamiltonians: we represent the evolution on each constant bit using a recently developed dynamical resonance theory, and we piece them together to obtain the total evolution. The initial state corresponding to one time-interval with constant Hamiltonian is the final state of the system corresponding to the interval before. This results in a non-markovian dynamics. We find a representation of the dynamics in terms of resonance energies and resonance states associated to the Hamiltonians, valid for all times $t\geq 0$ and for small (but fixed) interaction strengths. The representation has the form of a path integral over resonances. We present applications to a spin-fermion system, where the energy levels of the spin may undergo rather arbitrary crossings in the course of time. In particular, we find the probability for transition between ground- and excited state at all times.