New Phase Space Formulations and Quantum Dynamics Approaches

TL;DR

This paper advances the phase space formulation of quantum mechanics by developing a new constrained coordinate-momentum framework, enabling practical trajectory-based quantum dynamics simulations for complex systems.

Contribution

It introduces a novel weighted constraint phase space approach for discrete-variable quantum systems, enhancing the representation and simulation of quantum dynamics in composite systems.

Findings

Numerical tests validate the effectiveness of the new trajectory-based methods.

The approach accurately describes dynamical processes in gas and condensed phases.

It provides a practical framework for complex quantum system simulations.

Abstract

We report recent progress on the phase space formulation of quantum mechanics with coordinate-momentum variables, focusing more on new theory of (weighted) constraint coordinate-momentum phase space for discrete-variable quantum systems. This leads to a general coordinate-momentum phase space formulation of composite quantum systems, where conventional representations on infinite phase space are employed for continuous variables. It is convenient to utilize (weighted) constraint coordinate-momentum phase space for representing the quantum state and describing nonclassical features. Various numerical tests demonstrate that new trajectory-based quantum dynamics approaches derived from the (weighted) constraint phase space representation are useful and practical for describing dynamical processes of composite quantum systems in gas phase as well as in condensed phase.