Algebraically Self-Consistent Quasiclassical Approximation on Phase Space

Grad, J., Shaul Mukamel, YiJing Yan

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.

Seiya Nishiyama, Takao Komatsu

To clear up both algebraic and geometric structures for integrable systems derived from self-consistent field theory, in particular, geometric aspect of the random-phase-approximation (RPA) equation is exhibited on the basis of the viewpoint of symmetry of the evolution equation. The RPA equation for an infinite-dimensional Grassmannian is constructed.

Eugeni P. Gordov, Stanislav D. Tvorogov

Oleg Zaitsev, Romanas Narevich, R. E. Prange

L. Bányai, A. M. Bundaru, H. Haug

We treat the problem of self-consistently interacting bosons in the presence of a finite (but macroscopic) potential well within a quasiclassical approximation for the normal component and the order parameter. We solve the equilibrium problem and show that condensation actually occurs in two steps: one already at low densities with Bose condensation only in the well, and another one corresponding to the usual condensation in bulk. The peak and width of the distribution of trapped particles in the well display a distinct signature of the local condensation. A possible connection to recent experiments with excitons is discussed.