Interdisciplinary Physics Science at the Edge
FRIDAY 11:30 a.m. October 30th
1400 BPS
The Classical and Quantum Mechanism of Decoherence and the Quantum-Classical Path Integral Formulation
Nancy Makri
Departments of Chemistry and Physics
University of Illinois
The path integral formulation of time-dependent quantum
mechanics provides the ideal framework for rigorous quantum-classical or quantum-semiclassical
treatments, as the spatially localized, trajectory-like nature of the quantum
paths circumvents the need for
mean-field-type assumptions. However, the number of system
paths grows exponentially with the number of propagation steps. In addition, each path of the quantum
system generally gives rise to a distinct classical solvent trajectory. This exponential proliferation of trajectories with propagation time is the quantum-classical
manifestation of time nonlocality, familiar from
influence functional approaches.
A quantum-classical path integral (QCPI)
methodology has been developed. The starting point is the identification of two components in the effects induced on a quantum system
by a polyatomic environment. The first, “classical decoherence
mechanism” dominates completely at high temperature/low-frequency
solvents and/or when the system- environment interaction is weak.
Within the QCPI framework, the
memory associated with classical decoherence is removable. A second, nonlocal in time, “quantum
decoherence process” is also operative at low temperatures, although the contribution of the classical decoherence
mechanism
continues to play the most prominent role. The classical decoherence is analogous to the treatment of light absorption via
an oscillating dipole,
while quantum
decoherence is primarily associated with spontaneous emission, whose description requires quantization of the radiation field. The QCPI
methodology takes advantage of the
memory-free nature of system-independent solvent trajectories to account for all classical decoherence effects on the dynamics
of the quantum system
in an inexpensive fashion. Inclusion of the residual quantum
decoherence is accomplished via phase factors in the path integral expression, which is amenable to large time steps and iterative
decompositions.
The
methodology has been used to perform
an all-atom simulation of the ferrocene- ferrocenium
charge transfer process in liquid hexane with unprecedented accuracy. Comparison of the simulation results to those obtained by
mapping the solvent on an effective harmonic bath demonstrates the accuracy of linear response theory in this system.
Shawna Prater / Secretary
Astrophysics Group
Michigan State University
567 Wilson Road, Room 3261
Biomedical Physical Sciences Bldg
East Lansing, MI 48824-2320
Ph: (517) 884-5601 Fax (517) 432-8802
[log in to unmask],
[log in to unmask]