https://doi.org/10.1140/epjst/e2015-02413-0
Review
An introduction to the problem of bridging quantum and classical dynamics
1 CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochime, Avenue Forel 2, 1015 Lausanne, Suisse
2 Dipartimento di Fisica, Università di Roma “La Sapienza”, Ple A. Moro 2, 00185 Roma, Italia
3 School of Physics, University College of Dublin UCD, Belfield, Dublin 4, Ireland
a e-mail: sara.bonella@epfl.ch
b e-mail: giovanni.ciccotti@roma1.infn.it
Received: 26 March 2015
Revised: 5 May 2015
Published online: 22 June 2015
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.
© EDP Sciences, Springer-Verlag, 2015
