Nose-Hoover sampling of quantum entangled distribution functions

TL;DR

This paper extends quantum thermostated dynamics to many-particle systems, incorporating quantum entanglement effects like Bose attraction and Pauli blocking, and discusses ergodicity issues in these models.

Contribution

It generalizes quantum thermostated equations of motion to indistinguishable particles, accounting for quantum entanglement and symmetry effects.

Findings

Derived isothermal equations for bosons and fermions with new quantum terms.

Identified Bose-attraction and Pauli-blocking effects in quantum dynamics.

Discussed ergodicity challenges in quantum thermostated systems.

Abstract

While thermostated time evolutions stand on firm grounds and are widely used in classical molecular dynamics (MD) simulations, similar methods for quantum MD schemes are still lacking. In the special case of a quantum particle in a harmonic potential, it has been shown that the framework of coherent states permits to set up equations of motion for an isothermal quantum dynamics. In the present article, these results are generalized to indistinguishable quantum particles. We investigate the consequences of the (anti-)symmetry of the many-particle wavefunction which leads to quantum entangled distribution functions. The resulting isothermal equations of motion for bosons and fermions contain new terms which cause Bose-attraction and Pauli-blocking. Questions of ergodicity are discussed for different coupling schemes.