# Regensburg 2002 – wissenschaftliches Programm

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# DY: Dynamik und Statistische Physik

## DY 46: Poster

### DY 46.10: Poster

### Donnerstag, 14. März 2002, 15:30–18:00, D

**Coherent state path integral approach to dissipative quantum dynamics.** — •Alexey Novikov^{1,2}, Ulrich Kleinekathöfer^{1,2}, and Michael Schreiber^{1,2} — ^{1}Institut für Physik, Technische Universität, D-09107 Chemnitz, Germany — ^{2}International University Bremen, D-28725 Bremen

Employing the path integral technique the quantum
dynamics of systems with dissipation is investigated. The dissipation in
the system is described as a consequence of its coupling to a reservoir
consisting of an infinite or an finite number of harmonic oscillators.
Here we
calculated the matrix elements of operator of evolution using
path integrals in coherent state representation.

In contrast to the well-known Herman-Kluk method which
is usually used together with a phase
space representation
in the present alternative treatment
we use only a coherent state basis.

This approach can
be used for system Hamiltonians which are given in a
harmonic oscillator eigenstate
representation. The system-bath coupling is assumed to be bilinear.
We calculated the path integral in stationary-phase approximation, which
leads to exact results for a system of coupled harmonic oscillators.
In order to solve the equation of motion we diagonalized the
Lagrangian, which can be reduced to a Lagrangian of a number of
independent
oscillators by this diagonalization.

Using this treatment we consider quantum damped harmonic oscillator
within and without the rotating-wave approximation. The matrix elements of
density
operator has been calculated. We evaluated the relaxation in the system
at non-equilibrium initial condition.