Quantum Trajectories

Principal Investigator

Craig Savage

Department of Physics and Theoretical Physics

This project seeks to understand quantum chaos in open systems. We use the newly developed method of quantum trajectories to solve the relevant quantum mechanical master equations. The broader context of this work is the investigation of the nature of the interface between quantum and classical mechanics. Classical dynamical systems show chaos. We investigate the corresponding dynamics in quantum systems. A unique feature of our work is our consideration of open systems, that is systems interacting with environments. This is significant because classical systems are typically open. Our immediate goal is to find a criterion for chaotic dynamics which is applicable to both classical and quantum systems. To this end we are investigating an information theoretic criterion based on the sensitivity of chaotic systems to perturbations of parameters. The particular dynamical system we focus on is the second harmonic generator.

Projects

u57 - VPP, PC


What are the results to date and the future of the work?

We have published work on the second harmonic generator which establishes a link between the classical chaotic and quantum mechanical regimes. We now have preliminary evidence for the validity of an information theoretic criterion for quantum chaos. Our goal is to firmly establish the validity of this criterion.

What computational techniques are used?

The quantum trajectories code was developed in 1996 by Stuart Midgley as his theoretical physics honours research project. The quantum trajectories equation is quite similar to the Schrodinger equation. The code utilises recent algorithmic developments based on dynamically adapting the quantum mechanical basis to the current system state.

- Appendix A