State-space distribution and dynamical flow for closed and open quantum systems

TL;DR

This paper introduces a formalism for analyzing open quantum systems using state space distributions, enabling a fluid-like description of quantum dynamics that separates classical and quantum uncertainties.

Contribution

It develops a novel state space distribution formalism for open quantum systems, providing explicit equations of motion and a fluid mechanics analogy for quantum dynamics.

Findings

The formalism accurately describes open quantum system dynamics.

The equations of motion resemble classical fluid dynamics.

Application to a two-level system confirms analytical consistency.

Abstract

We present a general formalism for studying the effects of dynamical heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that are shown to be consistent with the derived analytical results.