DOI 10.1007/s100529801041
Dissipative time evolution of observables in non-equilibrium statistical quantum systems
Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
Received: 21 July 1998 / Revised version: 28 September 1998 / Published online: 2 November 1998
Abstract
We discuss differential- versus
integral-equation based methods describing out-of thermal
equilibrium systems and emphasize the importance of a well
defined reduction to statistical observables. Applying the
projection operator approach,
we investigate on the time evolution of expectation values of linear
and quadratic polynomials in position and momentum for a
statistical anharmonic oscillator with quartic potential.
Based on the exact integro-differential equations of motion, we
study the first and naive second order approximation which
breaks down at secular time-scales. A method is proposed to
improve the expansion by a non-perturbative resummation of
all quadratic operator correlators consistent with energy
conservation for all times. Motion cannot be described by
an effective Hamiltonian local in time reflecting non-unitarity
of the dissipative entropy generating evolution. We
numerically integrate the consistently improved equations
of motion for large times. We relate entropy to the uncertainty
product, both being expressible in terms of the observables
under consideration.
Copyright Springer-Verlag
