Quantum to classical limit of open systems

TL;DR

This paper reviews how open quantum systems transition to classical behavior using decoherence theory and the Weyl-Wigner-Moyal transformation, identifying preferred states and classical trajectories.

Contribution

It introduces a method to define preferred states and classical trajectories via the analytical extension of the Hamiltonian and WWM, advancing understanding of quantum-classical transition.

Findings

Identification of poles in Hamiltonian extension explains non-unitary evolution.

Definition of Moving Preferred Basis for decoherence.

Weyl-Wigner-Moyal of preferred states approximates classical trajectories.

Abstract

We present a complete review of the quantum-to-classical limit of open systems by means of the theory of decoherence and the use of the Weyl-Wigner-Moyal (WWM) transformation. We show that the analytical extension of the Hamiltonian provides a set of poles that can be used to (a) explain the non-unitary evolution of the relevant system and (b) completely define the set of preferred states that constitute the mixture into which the system decoheres: the Moving Preferred Basis. Moreover, we show that the WWM of these states are the best candidates to obtain the trajectories in the classical phase-space.