### Speaker

Paweł Bialas
(Department of Theoretical Physics, University of Silesia)

### Description

Models which contain quantum particle coupled to its environment were
analysed many times over recent years or even decades. Nonetheless this old and seemingly well known
problem contains some unknown aspects and have not been solved in the general
case. Furthermore by analysing behaviour of quantum Brownian motion one could
attempt to find answer for many fundamental questions concerning the very
essence of the quantum world, investigate transport phenomena or consider the nature and
properties of quantum information.
The topic of quantum Brownian motion is fundamental for many
fields of physics, for instance in statistical physics, condensed matter and
atomic physics.
There are plenty of methods for analysing such systems for instance path
integrals method, van Kampen method or generalised Langevin equation method. In
our considerations we utilise the last listed method and as a starting point in
our analysis we took quantum fluctuation-dissipation theorem.
We would like to present some of interesting properties exhibited by such
systems and exact, analytical results which we have obtained. In our investigations we were focused mainly on the kinetic energy of Brownian particle in long-time limit and general formula for autocorrelation function.

### Primary author

Paweł Bialas
(Department of Theoretical Physics, University of Silesia)

### Co-author

Jerzy Łuczka
(Department of Theoretical Physics, University of Silesia)