Quantum-Classical Dynamics and Statistical
Mechanics by Partial Wigner Approach

 

GIOVANNI CICCOTTI
Department of Physics
University of ROMA ``La Sapienza''
Roma 00185, Italy
giovanni.ciccotti@roma1.infn.it

[ Slides ]

Abstract:

Based on a partial Wigner transform we present a scheme for carrying out quantum-classical evolution of many-body systems, formulate their statistical mechanical description and find ways to compute equilibrium and time-dependent expectation values. The evolution equations for the density matrix, or for the dynamical variables, are expressed in an adiabatic basis and the evolution is determined by an ensemble of surface-hopping trajectories. The quantum-classical form of the canonical equilibrium density is discussed (considering possible ways to circumvent the difficulties associated with lacking an explicit expression for it). The formulation of non-equilibrium statistical mechanics and time-dependent equilibrium properties is given together with a discussion of the expressions for quantum-classical transport coefficients and of the properties of time correlation functions.

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