University of Toronto
Physics Department
Quantum Optics and Condensed Matter

Abstract

Brownian motion is an important phenomenon in physics because its treatment elucidates systems that can interact with their surroundings. Although it has been more than ninety years since Einstein's seminal work on Brownian motion, the quantum description of this phenomenon presents unique problems. In particular, the quantum Brownian equation developed about fifteen years ago, which has since become the standard in the literature, is flawed: it does not preserve the positivity of the density operator describing the system of interest. Thus, the Uncertainty Principle, for example, is not necessarily obeyed.

In our talk, we will present some recent work (Phys. Rev. Lett., 77, p.2600 (1996)) which corrects this "positivity problem." In so doing, we demonstrate how dissipation can be treated quantum mechanically. One of the keys to our work involves choosing initial conditions that take into account correlations between the system of interest and its surroundings (in usual approaches, these correlations are neglected.) The quantum Brownian equation that we derive correctly predicts the relaxation to thermal equilibrium of a positive density operator describing the system of interest.

Contact: Prof. J.E. Sipe (416-978-4517)