Stochastic Aspects of the Quantum Dynamics

Sergio A Albeverio, Ph. Combe, M. Sirugue-Collin

Georgin Moiseevich Zaslavskiî

Г.М. Заславский

Walter T. Strunz

The interaction of a quantum system with a many degree of freedom environment entails damping and the loss of quantum coherence. In these two lectures we focus on two aspects of open quantum system dynamics. First, we present decoherence as a dynamical phenomenon and determine the corresponding time scales, discuss an experiment and the nature of robust states, and mention universal properties of short-time decoherence of macroscopic superpositions. Secondly, in analogy to the classical description of open systems in terms of Langevin equations, we present a stochastic approach to open quantum system dynamics in terms of a stochastic Schrödinger equation. We give a microscopic derivation that allows us to generalize the stochastic approach to non-Markovian situations. We discuss a convolutionless formulation of our theory and finally, we focus on the quantised version of Brownian motion as an often-employed example.

Zbigniew Haba

Takeshi Saito, Toshihico Arimitsu

By extending the quantum stochastic Liouville equation formulated by one of the authors (T. A.) within Non-Equilibrium Thermo Field Dynamics (NETFD), it is shown that, by means of stochastic Heisenberg equation, one can construct a unified framework of stochastic differential equations for quantum systems with the quantum white noise of non-thermal ensemble. A new aspect is given to deal with the difficulties attending quantum Langevin equations.