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The European Physical Journal Special Topics

, Volume 224, Issue 12, pp 2305–2320 | Cite as

An introduction to the problem of bridging quantum and classical dynamics

  • S. Bonella
  • G. Ciccotti
Review A. Representation of Molecular Systems Across Scales
Part of the following topical collections:
  1. Discussion and Debate: Recurrent Problems in Scale Bridging Techniques in Molecular Simulation – What are the Current Options?

Abstract

Simulating the exact quantum dynamics of realistic interacting systems is presently a task beyond reach but for the smallest of them, as the numerical cost for solving the time-dependent Schrödinger equation scales exponentially with the number of degrees of freedom. Mixed quantum-classical methods attempt to solve this problem by starting from a full quantum description of the system and subsequently partitioning the degrees of freedom in two subsets: the quantum subsystem and the bath. A classical limit is then taken for the bath while preserving, at least approximately, the quantum evolution of the subsystem. A key, as yet not fully resolved, theoretical question is how to do so by constructing a consistent description of the overall dynamics. An exhaustive review of this class of methods is beyond the scope of this paper and we shall limit ourselves to present, as an example, a specific approach, known as the LANDM-Map method. The method stems from an attempt at taking a rigorous limit for the classical degrees of freedom starting from a path integral formulation of the full quantum problem. The results that we discuss are not new, but our intent here is to present them as an introduction to the problem of mixed quantum classical dynamics. We shall also indicate a broad classification of the available approaches, their limitations, and some open questions in this field.

Keywords

European Physical Journal Special Topic Molecular Simulation Time Correlation Function Nuclear Position Path Integral Representation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.CECAM Centre Européen de Calcul Atomique et MoléculaireÉcole Polytechnique Fédérale de Lausanne, BatochimeLausanneSuisse
  2. 2.Dipartimento di FisicaUniversità di Roma “La Sapienza”RomaItalia
  3. 3.School of PhysicsUniversity College of Dublin UCDDublin 4Ireland

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