N° ANR-09-BLAN-0098-01

Starting 01/09/2009
Ending 31/08/2013

Headed by Stéphane ATTAL

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The aim of this project is to enhence collaborations between researchers of international level on the development of two complementary approaches of rigorous statistical mechanics for quantum open systems.

There exist actually two different approaches, two different groups of researchers, in mathematics as well as in physics, which study the behaviour of dissipative quantum systems. They are: the Hamiltonian approach and the Markovian approach.

Up to the last few years the connections and collaboration between these two groups of researchers have been very poor. Their techniques are very different but the problems they study are exactly the same. It has been one the successes of some of the members of this A.N.R. project to initiate, 7 years ago, discussions and collaborations between these two groups. Already, concrete results have been obtained (common publications, developments of new tools, collaborations with physicists, ...).

The aim of this A.N.R. is to help this group of researchers to increase their cooperation in order to solve some of the most challenging problems connected to rigourous quantum statistical mechanics. In particular, we have in mind: the Fourier's law for heat transport on quantum systems, the description of non-equilibrium steady states for simple spin models, the development of quantum Lanvegin equation techniques in order to describe the action of quantum heat baths.