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

The Journal of Chemical Physics
Anton V Sinitskiy, Gregory A Voth

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 ...Continue Reading

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Citations

Jan 8, 2018·The Journal of Chemical Physics·Anton V Sinitskiy, Gregory A Voth
Mar 17, 2018·The Journal of Chemical Physics·Igor PoltavskyAlexandre Tkatchenko
Jul 1, 2019·The Journal of Chemical Physics·Won Hee RyuGregory A Voth
Mar 17, 2018·The Journal of Chemical Physics·Michael J WillattStuart C Althorpe
Oct 4, 2018·The Journal of Chemical Physics·Luis M Sesé
Mar 17, 2018·The Journal of Chemical Physics·Yining HanGregory A Voth

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