Ehrenfest dynamics is purity non-preserving: a necessary ingredient for decoherence

We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we int...

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Bibliographic Details
Published in:The Journal of chemical physics 2012-08, Vol.137 (5), p.054106-054106
Main Authors: Alonso, J L, Clemente-Gallardo, J, Cuchí, J C, Echenique, P, Falceto, F
Format: Article
Language:English
Subjects:
Algorithms
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
DISTRIBUTION
Dynamic tests
Dynamical systems
Dynamics
Electronics
EVOLUTION
Formalism
IMPURITIES
INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY
PURE STATES
Purity
QUANTUM MECHANICS
Quantum Theory
SCHROEDINGER EQUATION
Solutions - chemistry
Thermodynamics
Trajectories
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Summary:We discuss the evolution of purity in mixed quantum/classical approaches to electronic nonadiabatic dynamics in the context of the Ehrenfest model. As it is impossible to exactly determine initial conditions for a realistic system, we choose to work in the statistical Ehrenfest formalism that we introduced in Alonso et al. [J. Phys. A: Math. Theor. 44, 396004 (2011)]. From it, we develop a new framework to determine exactly the change in the purity of the quantum subsystem along with the evolution of a statistical Ehrenfest system. In a simple case, we verify how and to which extent Ehrenfest statistical dynamics makes a system with more than one classical trajectory, and an initial quantum pure state become a quantum mixed one. We prove this numerically showing how the evolution of purity depends on time, on the dimension of the quantum state space D, and on the number of classical trajectories N of the initial distribution. The results in this work open new perspectives for studying decoherence with Ehrenfest dynamics.
ISSN:0021-9606
1089-7690
DOI:10.1063/1.4737861