A reductionist perspective on quantum statistical mechanics: Coarse-graining of path integrals

Abstract

Computational modeling of the condensed phase based on classical statistical mechanics has been rapidly developing over the last few decades and has yielded important information on various systems containing up to millions of atoms. However, if a system of interest contains important quantum effects, well-developed classical techniques cannot be used. One way of treating finite temperature quantum systems at equilibrium has been based on Feynman's imaginary time path integral approach and the ensuing quantum-classical isomorphism. This isomorphism is exact only in the limit of infinitely many classical quasiparticles representing each physical quantum particle. In this work, we present a reductionist perspective on this problem based on the emerging methodology of coarse-graining. This perspective allows for the representations of one quantum particle with only two classical-like quasiparticles and their conjugate momenta. One of these coupled quasiparticles is the centroid particle of the quantum path integral quasiparticle distribution. Only this quasiparticle feels the potential energy function. The other quasiparticle directly provides the observable averages of quantum mechanical operators. The theory offers a simplified perspective on quantum statistical mechanics, revealing its most reductionist connection to classical statistical physics. By doing so, it can facilitate a simpler representation of certain quantum effects in complex molecular environments.

Approximating Matsubara dynamics using the planetary model: Tests on liquid water and ice

“…Unlike RPMD and CMD, the planetary model therefore has the potential to treat non-linear time-correlation functions (TCFs), which (at low enough temperatures) depend explicitly on the dynamical fluctuations. 20 [Note that a related method 21 was developed at around the same time as the planetary model, but this uses a different type of locally harmonic force on the fluctuation particle (called a 'pseudoparticle'), 22 and has so far been restricted to static applications. ]…”

Quantum mechanics/coarse-grained molecular mechanics (QM/CG-MM)

“…Recently, the CG methodology has been generalized to quantum systems. 38 In the present work though, we focus on modeling systems without non-adiabatic transitions in the surroundings. As for the restriction to non-adiabatic processes in the QM part, it seems less obligatory from the conceptual viewpoint, but useful for notational convenience.…”

“…is another characteristic of the I-th CG site (molecule) in vacuum in the electronic state nsurr defined by Eq (38). in the main text.…”

Real Space Triplets in Quantum Condensed Matter: Numerical Experiments Using Path Integrals, Closures, and Hard Spheres

“…The PI formalism is perfectly suited for performing path integral Monte Carlo (PIMC) and molecular dynamics (PIMD) computer simulations of quantum N-particle systems at nonzero temperatures . With due attention to the special characteristics of quantum averages [33,38,[44][45][46][47], the latter PI simulations can follow classical-like procedures [56][57][58][59][60]. To illustrate this situation, it is sufficient to recall the most basic PI description in the canonical ensemble ( , , ) of an actual quantum monatomic system in which exchange interactions can be neglected.…”