### Speaker

Mr
Pawel 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. This old and seemingly clichéd
system-environment model has been re-considered many, many times by each next
generation of physicists. However, it is still difficult to find a transparent
presentation of this fundamental issue of the quantum statistical physics. 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.
We study the celebrated model of a quantum open system $S$, i.e. a quantum
harmonic oscillator of mass $M$ and
eigenfrequency $\omega_0$ . It is in contact with a heat bath $B$ modeled as a collection of independent quantum harmonic
oscillators which form thermostat of temperature $T$ being in an equilibrium Gibbs canonical state.
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 for energy - potential and kinetic - which
we have obtained.

### Primary author

Mr
Pawel Bialas
(Department of Theoretical Physics, University of Silesia)

### Co-author

Prof.
Jerzy Łuczka
(University of Silesia, Katowice)