# Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems

## Abstract

We have developed a method that recasts the time-propagation of dynamic, mutually interacting quantum-mechanical wavefunctions principally as the time-evolution of many classical particles. Our approach utilizes an approximation of Feynman path integrals, known as the semiclassical method, to reduce the path integral to only the 'classical' paths connecting the wavefunction at one time step to the next. In exchange for simplifying the path sampling, each classical path's contribution gains a determinant term dependent on the path and its environment. Like virtual particles in quantum field theory, 'virtual classical particles' are said to follow these classical paths. Pushing these virtual classical particles provides the necessary data to evolve quantum wavefunctions in time. Particle-based techniques implemented on parallel computers can then be used to propagate quantum systems using this alternative method.

- Authors:

- Dauger Research, Inc., P.O. Box 3074, Huntington Beach, CA 92605 (United States) and UCLA Plasma Physics Group, Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States). E-mail: d@daugerresearch.com
- UCLA Plasma Physics Group, Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States)

- Publication Date:

- OSTI Identifier:
- 20687261

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 209; Journal Issue: 2; Other Information: DOI: 10.1016/j.jcp.2005.03.028; PII: S0021-9991(05)00187-7; Copyright (c) 2005 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; FEYNMAN PATH INTEGRAL; LAGRANGIAN FUNCTION; MATHEMATICAL EVOLUTION; QUANTUM FIELD THEORY; QUANTUM MECHANICS; SEMICLASSICAL APPROXIMATION; TRAJECTORIES; VIRTUAL PARTICLES; WAVE FUNCTIONS

### Citation Formats

```
Dauger, D.E., Decyk, V.K., and Dawson, J.M.
```*Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems*. United States: N. p., 2005.
Web. doi:10.1016/j.jcp.2005.03.028.

```
Dauger, D.E., Decyk, V.K., & Dawson, J.M.
```*Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems*. United States. doi:10.1016/j.jcp.2005.03.028.

```
Dauger, D.E., Decyk, V.K., and Dawson, J.M. Tue .
"Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems". United States.
doi:10.1016/j.jcp.2005.03.028.
```

```
@article{osti_20687261,
```

title = {Using semiclassical trajectories for the time-evolution of interacting quantum-mechanical systems},

author = {Dauger, D.E. and Decyk, V.K. and Dawson, J.M.},

abstractNote = {We have developed a method that recasts the time-propagation of dynamic, mutually interacting quantum-mechanical wavefunctions principally as the time-evolution of many classical particles. Our approach utilizes an approximation of Feynman path integrals, known as the semiclassical method, to reduce the path integral to only the 'classical' paths connecting the wavefunction at one time step to the next. In exchange for simplifying the path sampling, each classical path's contribution gains a determinant term dependent on the path and its environment. Like virtual particles in quantum field theory, 'virtual classical particles' are said to follow these classical paths. Pushing these virtual classical particles provides the necessary data to evolve quantum wavefunctions in time. Particle-based techniques implemented on parallel computers can then be used to propagate quantum systems using this alternative method.},

doi = {10.1016/j.jcp.2005.03.028},

journal = {Journal of Computational Physics},

number = 2,

volume = 209,

place = {United States},

year = {Tue Nov 01 00:00:00 EST 2005},

month = {Tue Nov 01 00:00:00 EST 2005}

}