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dc.contributor.authorHele, Timen
dc.contributor.authorWillatt, Michael Jen
dc.contributor.authorMuolo, Andreaen
dc.contributor.authorAlthorpe, Stuarten
dc.date.accessioned2015-05-22T09:10:27Z
dc.date.available2015-05-22T09:10:27Z
dc.date.issued2015-04-02en
dc.identifier.citationHele et al Journal of Chemical Physics 142, 134103 (2015). DOI: 10.1063/1.4916311en
dc.identifier.issn0021-9606
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/247931
dc.description.abstractWe show that a single change in the derivation of the linearized semiclassical-initial value representation (LSC-IVR or “classical Wigner approximation”) results in a classical dynamics which conserves the quantum Boltzmann distribution. We rederive the (standard) LSC-IVR approach by writing the (exact) quantum time-correlation function in terms of the normal modes of a free ring-polymer (i.e., a discrete imaginary-time Feynman path), taking the limit that the number of polymer beads N → ∞, such that the lowest normal-mode frequencies take their “Matsubara” values. The change we propose is to truncate the quantum Liouvillian, not explicitly in powers of ħ2 at ħ0 (which gives back the standard LSC-IVR approximation), but in the normal-mode derivatives corresponding to the lowest Matsubara frequencies. The resulting “Matsubara” dynamics is inherently classical (since all terms O(ħ2) disappear from the Matsubara Liouvillian in the limit N → ∞) and conserves the quantum Boltzmann distribution because the Matsubara Hamiltonian is symmetric with respect to imaginary-time translation. Numerical tests show that the Matsubara approximation to the quantum time-correlation function converges with respect to the number of modes and gives better agreement than LSC-IVR with the exact quantum result. Matsubara dynamics is too computationally expensive to be applied to complex systems, but its further approximation may lead to practical methods.
dc.description.sponsorshipT.J.H.H., M.J.W., and S.C.A. acknowledge funding from the U.K. Engineering and Physical Sciences Research Council. A.M. acknowledges the European Lifelong Learning Programme (LLP) for an Erasmus student placement scholarship. T.J.H.H. also acknowledges a Research Fellowship from Jesus College, Cambridge and helpful discussions with Dr. Adam Harper.
dc.languageEnglishen
dc.language.isoenen
dc.publisherAIP
dc.subjectBoltzmann equationsen
dc.subjectNormal modesen
dc.subjectMolecular dynamicsen
dc.subjectCorrelation functionsen
dc.subjectFourier transformsen
dc.titleBoltzmann-conserving classical dynamics in quantum time-correlation functions: “Matsubara dynamics”en
dc.typeArticle
dc.description.versionThis is the author accepted manuscript. The final version is available from AIP via http://dx.doi.org/10.1063/1.4916311en
prism.number134103en
prism.publicationDate2015en
prism.publicationNameJournal of Chemical Physicsen
prism.volume142en
dc.rioxxterms.funderEPSRC
rioxxterms.versionofrecord10.1063/1.4916311en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2015-04-02en
dc.contributor.orcidHele, Tim [0000-0003-2367-3825]
dc.contributor.orcidAlthorpe, Stuart [0000-0003-1288-8070]
dc.identifier.eissn1089-7690
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/I002499/1)


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