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Session 8. Dynamic Systems with Fractional and Time Scale Derivatives
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Time Flow in Interacting Many Body Systems |
Rudolf Hilfer, University of Stuttgart, Germany
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The time evolution for closed quantum many body systems is usually given as a one-parameter
group of unitary operators on a Hilbert space representing a group of automorphisms on an underlying
\(C^{*}\) -algebra of observables. Dissipative processes, irreversible phenomena, decay of unstable
particles, approach to thermodynamic equilibrium or quantum measurement processes are difficult
to accommodate within this framework. For infinite systems the characterization of completeness
or incompleteness of this dynamical prescription is poorly understood and constitutes a nontrivial
first step in the analysis of the dynamics of such systems. The time evolution of macroscopic states
(or mixtures) for classical and quantum many body systems in statistical physics need not correspond
to a translation group or semigroup. Instead convolution semigroups appears generically.
The presentation will discuss the implications of this result for the foundations of nonequilibrium
statistical physics as well as possible applications to experiment.
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