Dynamical aspects in the Quantizer-Dequantizer formalism

TL;DR

This paper explores how the quantizer-dequantizer formalism can embed quantum state manifolds and provide classical-like, potentially nonlinear, descriptions of quantum dynamics, with applications to Weyl systems and coherent states.

Contribution

It demonstrates the embedding of quantum state manifolds into the formalism and shows how invariant manifolds yield classical-like nonlinear dynamics.

Findings

Embedding of quantum state manifolds via quantizer-dequantizer systems

Invariant manifolds lead to classical-like nonlinear evolution

Illustration with Weyl systems and coherent states

Abstract

The use of the quantizer-dequantizer formalism to describe the evolution of a quantum system is reconsidered. We show that it is possible to embed a manifold in the space of quantum states of a given auxiliary system by means of an appropriate quantizer-dequantizer system. If this manifold of states is invariant with respect to some unitary evolution, the quantizer-dequantizer system provides a classical-like realization of such dynamics, which in general is non linear. Integrability properties are also discussed. Weyl systems and generalized coherente states are used as a simple illustration of these ideas.