Dissipative time evolution of observables in non-equilibrium statistical quantum systems |
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Authors: | H Nachbagauer |
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Institution: | Institut für Theoretische Physik, Universit?t Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany, DE
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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.
Received: 21 July 1998 / Revised version: 28 September 1998 / Published online: 2 November 1998 |
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