Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Annals of Physics

Complex Semiclassical Description of Scattering Problem in Systems with 1.5 Degrees of Freedom

Kin’ya Takahashi, Kensuke S. Ikeda

Published Jul 1, 2000• 23 citations
Publisher
DOI
10.1006/aphy.2000.6050

Related papers

Semiclassical description of scattering with internal degrees of freedom

Sara Cruz-Barrios, Joaquín Gómez-Camacho

Nuclear Physics A•Jun 1, 1998•4 citations

A semiclassical self-consistent-field approach to dissipative dynamics: The spin–boson problem

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.

The Journal of Chemical Physics•Jul 22, 1995•113 citations

Semiclassical Description of Scattering

Kenneth W. Ford, JOHN ARCHIBALD WHEELER

Annals of Physics•Apr 1, 2000•22 citations

Semiclassical normalization of a path integral for a multichannel scattering problem

Alvin P. Penner, R. Wallace

The evaluation of a Feynman path integral is discussed for a scattering problem in which some degrees of freedom of the system are treated classically, while others are treated quantum mechanically. The path integral is of the type $K(0, {t}^{\ensuremath{'}\ensuremath{'}}; 0, {t}^{\ensuremath{'}})$, and is of interest in a multichannel semiclassical collision theory previously developed by Pechukas. It is shown that this path integral can be evaluated precisely in practice, despite the presence of noncausal terms in the integrand.

Physical Review A•Jan 1, 1975•10 citations

Semiclassical description of scattering

Kenneth W. Ford, JOHN ARCHIBALD WHEELER

Annals of Physics•Jul 1, 1959•767 citations

High-energy, semiclassical scattering processes

Bernard A. Lippmann

Annals of Physics•May 1, 1957•17 citations
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.
The evaluation of a Feynman path integral is discussed for a scattering problem in which some degrees of freedom of the system are treated classically, while others are treated quantum mechanically. The path integral is of the type $K(0, {t}^{\ensuremath{'}\ensuremath{'}}; 0, {t}^{\ensuremath{'}})$, and is of interest in a multichannel semiclassical collision theory previously developed by Pechukas. It is shown that this path integral can be evaluated precisely in practice, despite the presence of noncausal terms in the integrand.