Yan Pautrat

Transport properties of quasi-free fermions

Using the scattering approach to the construction of Non-Equilibrium Steady States proposed by Ruelle we study the transport properties of systems of independent electrons. We show that Landauer-Buttiker and Green-Kubo formulas hold under very general conditions.

Topics in non-equilibrium quantum statistical mechanics

1 Zentrum Mathematik M5, Technische Universitat Munchen, D-85747 Garching, Germany e-mail: hbar@ma.tum.de 2 Department of Mathematics and Statistics, McGill University, 805 Sherbrooke Street West, Montreal, QC, H3A 2K6, Canada e-mail: jaksic@math.mcgill.co 3 Laboratoire de Mathematiques, Universite Paris-Sud, 91405 Orsay cedex, France e-mail: yan.pautrat@math.u-psud.fr 4 CPT-CNRS, UMR 6207, Universite du Sud, Toulon-Var, B.P. 20132, 83957 La Garde Cedex, France e-mail: pillet@univ-tln.fr

Homogeneous Open Quantum Random Walks on a Lattice

We study open quantum random walks (OQRWs) for which the underlying graph is a lattice, and the generators of the walk are homogeneous in space. Using the results recently obtained in Carbone and Pautrat (Ann Henri Poincaré, 2015), we study the quantum trajectory associated with the OQRW, which is described by a position process and a state process. We obtain a central limit theorem and a large deviation principle for the position process. We study in detail the case of homogeneous OQRWs on the lattice

(n+1)

\mathbb {Z}^d

A quantum central limit theorem for sums of independent identically distributed random variables

Zd, with internal space

Second-order asymptotics for quantum hypothesis testing in settings beyond i.i.d.—quantum lattice systems and more

\mathfrak {h}=\mathbb {C}^2