Quantum systems in Markovian environments

TL;DR

This paper introduces a mathematical framework for modeling quantum systems influenced by Markovian environments, accounting for state-dependent Hamiltonians and instantaneous transitions, with a focus on finite-dimensional systems.

Contribution

It develops a novel approach to model quantum systems with environment-dependent Hamiltonians and Markovian environmental changes, including instantaneous state transitions.

Findings

Framework for averaging over Markovian environments

Applicable to finite-dimensional quantum systems

Predicts expected observable values

Abstract

In this work, we develop a mathematical framework to model a quantum system whose Hamiltonian may depend on the state of changing environment, that evolves according to a Markovian process. When the environment changes its state, the quantum system may suffer a shock that produces an instantaneous transition among its states. The model that we propose can be readily adapted to more general settings.\\ To avoid collateral analytical issues, we consider the case of quantum systems with finite dimensional state space, in which case the observables are described by Hermitian matrices. We show how to average over the environment to predict the expected values of observables.