https://doi.org/10.1140/epjb/e2004-00013-5
Dissipative evolution of quantum statistical ensembles and nonlinear response to a time-periodic perturbation
1
Institut de physique des nanostructures, École
Polytechnique Fédérale, CH-1015 EPF-Lausanne, Switzerland
2
Institut de théorie des phénomènes physiques, École
Polytechnique Fédérale, CH-1015 EPF-Lausanne, Switzerland
Corresponding author: a francois.reuse@epfl.ch
Received:
6
June
2003
Revised:
26
November
2003
Published online:
30
January
2004
We present a detailed discussion of the evolution of a
statistical ensemble of quantum mechanical systems coupled weakly
to a bath. The Hilbert space of the full system is given by the
tensor product between the Hilbert spaces associated with the
bath and the bathed system. The statistical states of the
ensemble are described in terms of density matrices. Supposing
the bath to be held at some – not necessarily thermal –
statistical equilibrium and tracing over the bath degrees of
freedom, we obtain reduced density matrices defining the
statistical states of the bathed system. The master equations
describing the evolution of these reduced density matrices are
derived under the most general conditions. On time scales that
are large with respect to the bath correlation time and
with respect to the reciprocal transition frequencies of the
bathed system, the resulting evolution of the reduced density
matrix of the bathed system is of Markovian type. The detailed
balance relations valid for a thermal equilibrium of the bath are
derived and the conditions for the validity of the
fluctuation-dissipation theorem are given. Based on the general
approach, we investigate the non-linear response of the bathed
subsystem to a time-periodic perturbation. Summing the
perturbation series we obtain the coherences and the populations
for arbitrary strengths of the perturbation.
PACS: 05.30.-d – Quantum statistical mechanics / 33.35.+r – Electron resonance and relaxation / 33.25.+k – Nuclear resonance and relaxation
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2003