Canonical mean-field molecular dynamics derived from quantum mechanics

11/22/2021
∙
by   Xin Huang, et al.
∙
0
∙

Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature the ab initio molecular dynamics potential energy is based on the ground state electron eigenvalue problem and the accuracy has been proven to be đ’Ē(M^-1), provided the first electron eigenvalue gap is sufficiently large compared to the given temperature and M is the ratio of nuclei and electron masses. For higher temperature eigenvalues corresponding to excited electron states are required to obtain đ’Ē(M^-1) accuracy and the derivations assume that all electron eigenvalues are separated, which for instance excludes conical intersections. This work studies a mean-field molecular dynamics approximation where the mean-field Hamiltonian for the nuclei is the partial trace h:=Tr(H e^-β H)/Tr(e^-β H) with respect to the electron degrees of freedom and H is the Weyl symbol corresponding to a quantum many body Hamiltonian H. It is proved that the mean-field molecular dynamics approximates canonical quantum correlation observables with accuracy đ’Ē(M^-1+ tĪĩ^2), for correlation time t where Īĩ^2 is related to the variance of mean value approximation h. The proof of this estimate does not rely on diagonalizing the electron operator and consequently coinciding electron eigenvalues are allowed. Furthermore, the proof derives a precise asymptotic representation of the Weyl symbol of the Gibbs density operator using a path integral formulation.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

∙ 02/02/2020

Mean Field Theory for the Quantum Rabi Model, Inconsistency to the Rotating Wave Approximation

Considering well localized atom, the mean field theory (MFT) was applied...
∙ 01/25/2022

Convex Analysis of the Mean Field Langevin Dynamics

As an example of the nonlinear Fokker-Planck equation, the mean field La...
∙ 12/11/2017

DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics

Recent developments in many-body potential energy representation via dee...
∙ 08/22/2018

Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective

The free energy is a key quantity of interest in Ising models, but unfor...
∙ 12/10/2020

Detecting Structured Signals in Ising Models

In this paper, we study the effect of dependence on detecting a class of...
∙ 06/16/2020

Multi-level Monte Carlo path integral molecular dynamics for thermal average calculation in the nonadiabatic regime

With the path integral approach, the thermal average in a multi-electron...
∙ 04/19/2021

Ensemble equivalence for mean field models and plurisubharmonicity

We show that entropy is globally concave with respect to energy for a ri...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.