Solving the Wigner equation with signed particle Monte Carlo for chemically relevant potentials

Abstract

Expanding the set of stable, accurate, and scalable methods for simulating molecular quantum dynamics is important for accelerating the computational exploration of molecular processes. In this paper, we adapt the signed particles Monte Carlo algorithm for solving the transient Wigner equation to scenarios of chemical interest. This approach was used in the past to study electronic processes in semi-conductors, but to the best of our knowledge, it had never been applied to molecular modeling. We present the algorithm and demonstrate its excellent performance on harmonic and double well potentials for electronic and nuclear systems. We explore the stability of the algorithm, discuss the choice of hyper-parameters, and cautiously speculate that it may be used in quantum molecular dynamics simulations.

Weyl–Wigner description of massless Dirac plasmas: ab initio quantum plasmonics for monolayer graphene

“…For parabolic systems, with dispersion relation E(k) = 2 k 2 /(2m 2 * ), we would have the local kinetic operator K{W} = ( k/m * ) • ∇W, which would lead to the well-known Wigner-Moyal equation describing, e.g. quantum plasmas in metallic or semi-conductor systems [49][50][51][52][53][54][55][56]. Equation (32) reads as one of the important results of this paper, for it is the quantum analogue of the well-known Boltzmann equation for a Dirac system.…”