Non-Markovian quantum dynamics: correlated projection superoperators and Hilbert space averaging.
The time-convolutionless (TCL) projection operator technique allows a systematic analysis of the non-Markovian quantum dynamics of open systems. We present a class of projection superoperators that project the states of the total system onto certain correlated system-environment states. It is shown that the application of the TCL technique to this class of correlated superoperators enables the nonperturbative treatment of the dynamics of system-environment models for which the standard approach fails in any finite order of the coupling strength. We demonstrate further that the correlated superoperators correspond to the idea of a best guess of conditional quantum expectations, which is determined by a suitable Hilbert-space average. The general approach is illustrated by means of the model of a spin that interacts through randomly distributed couplings with a finite reservoir consisting of two energy bands. Extensive numerical simulations of the full Schrödinger equation of the model reveal the power and efficiency of the method.
Physikalisches Institut, Universität Freiburg, Hermann-Herder-Strasse 3, D-79104 Freiburg, Germany. breuer@physik.uni-freiburg.de
Heinz-Peter
HP
Breuer
Jochen
J
Gemmer
Mathias
M
Michel