HARMONIC BROWNIAN MOTION

Charlotte Bigg

Setsuo Taniguchi

A Wiener integral approach to the non-commutative harmonic oscillator, i.e. an approach via Brownian motions and matrix-valued stochastic differential equations, will be given. Such an approach is a continuation and an extension of the one made by the author in an earlier paper (Kyushu J. Math. 62 (2008), 63-68).

Ilya Sinayskiy, Francesco Petruccione

The microscopic derivation of a new type of Brownian motion, namely open quantum Brownian motion (OQBM) is presented. The quantum master equation for OQBM is derived for a weakly driven system interacting with a decoherent environment. Examples of the dynamics for initial Gaussian and non-Gaussian distributions are presented. Both examples demonstrate convergence of the OQBM dynamics to Gaussian distributions.

Richard Becker

Aniello Lampo, Miguel Ángel García March, Maciej Lewenstein

Marcus V. S. Bonança, Sebastian Deffner, Gert-Ludwig Ingold

This article presents a brief account of Amir O. Caldeira's contributions to the theory of quantum Brownian motion. Motivated by its importance, we outline the description of Brownian motion in the quantum regime following Caldeira's first works. In this context, we particularly highlight the effect of dissipation on the tunneling rate out of a metastable state. We then journey along the alternative ways to approach quantum Brownian motion developed by Caldeira during his career, which go beyond the so-called Caldeira-Leggett model. We conclude by summarizing some of Caldeira's contributions to contemporary fields such as the theory of quantum decoherence and quantum thermodynamics, that were strongly inspired by his eponymous approach to quantum Brownian motion.