Semiclassical Dynamics in Phase Space: Time-Dependent Self-Consistent Field Approximation

Vladimir S. Filinov

Gerhard Stock

A semiclassical time-dependent self-consistent-field approach for the description of dissipative quantum phenomena is proposed. The total density operator is approximated by a semiclassical ansatz, which couples the system degrees of freedom to the bath degrees of freedom in a self-consistent manner, and is thus in the spirit of a classical-path description. The capability of the approach is demonstrated by comparing semiclassical calculations for a spin–boson model with an Ohmic bath to exact path-integral calculations. It is shown that the semiclassical model nicely reproduces the complex dissipative behavior of the spin–boson model for a large range of model parameters. The validity and accuracy of the semiclassical approach is discussed in some detail. It is shown that the method is essentially based on the assumption of complete randomization of nuclear phases. In particular, the assumption of phase randomization allows one to perform the trace over the bath variables through quasiclassical sampling of the nuclear initial conditions without invoking any further approximation.

Zong-Chao Yan, Tamar Seideman

We introduce a time-dependent self-consistent-field approach for studying the coupled rotational–translational motion of molecules subject to the macroscopic potential induced by a spatially inhomogeneous, polarized laser field. A hybrid classical-quantum-mechanical variation of the scheme is employed to investigate the possibility of simultaneously focussing the center-of-mass motion of molecules and aligning their figure axis in a field-free region of space. A semiclassical-quantum-mechanical variation is used to describe the rotational–translational dynamics of cold molecules confined to an optical trap.

Bill Poirier

Haobin Wang, Michael Thoss, William Hallowes Miller

An efficient method, the self-consistent hybrid method, is proposed for accurately simulating time-dependent quantum dynamics in complex systems. The method is based on an iterative convergence procedure for a dynamical hybrid approach. In this approach, the overall system is first partitioned into a “core” and a “reservoir” (an initial guess). The former is treated via an accurate quantum mechanical method, namely, the time-dependent multiconfiguration self-consistent field or multiconfiguration time-dependent Hartree approach, and the latter is treated via a more approximate method, e.g., classical mechanics, semiclassical initial value representations, quantum perturbation theories, etc. Next, the number of “core” degrees of freedom, as well as other variational parameters, is systematically increased to achieve numerical convergence for the overall quantum dynamics. The method is applied to two examples of quantum dissipative dynamics in the condensed phase: the spin-boson problem and the electronic resonance decay in the presence of a vibrational bath. It is demonstrated that the method provides a practical way of obtaining accurate quantum dynamical results for complex systems.