2018 Impact factor 4.843
Particles and Fields
Eur. Phys. J. C 8, 171-182
DOI 10.1007/s100529801041

Dissipative time evolution of observables in non-equilibrium statistical quantum systems

H. Nachbagauer

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.


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