Vojkan Jaksic
Department of Mathematics
McGill University
FERMI GOLDEN RULE FOR OPEN QUANTUM SYSTEM
The Fermi Golden Rule computations play an important role in
quantum field theory and quantum statistical mechanics.
In this minicourse I will
discuss how these computations can be made rigorous for
a class of open quantum systems. This class includes
PauliFierz systems, which
arise as an approximation to nonrelativistic QED, and which
have been subject of many studies in the recent literature.
I plan to discuss the following topics:

Banach space Level Shift Operators (LSO). Dynamical
and spectral Fermi Golden Rule.

Open quantum systems. Liouvilleans. PauliFierz systems.

Davies generator.

The LSO for
standard and CLiouvillean. Applications
to spectral theory.
 Relations between the Davies generator and the LSO for
standard and CLiouvillean.

Ergodic theory of LSO. Complete positivity, detailed balance,
thermodynamical stability.
Bibliography
This minicourse is primarily based on the recent joint work
with Jan Derezinski (in preparation). The additional references
are:
 Davies E.B.: Markovian master equations. Commun. Math.
Phys. 39, 91 (1974).

Gorini V., Frigerio A., Veri M., Kossakowski A., Sudarshan
E.C.G.: Properties of quantum markovian master equations.
Rep. Math. Phys. 13, 149 (1978).
 Lebowitz J., Spohn H.: Irreversible thermodynamics for quantum
systems weakly coupled to thermal reservoirs. Adv. Chem. Phys. 39,
109 (1978).
 Derezinski J., Jaksic V.: Spectral theory of
PauliFierz operators. J. Func. Anal. 180, 241 (2000).
 Jaksic V., Pillet C.A.: Mathematical theory of nonequilibrium
quantum statistical mechanics. J. Stat. Phys. 108, 787 (2002).

Derezinski J., Jaksic V.: Return to equilibrium for PauliFierz systems,
to appear in Ann. Henri Poincare, mparc 03242.