**Workshops and Seminars, Year 2008**

**10 - 06 - 2008 **ore 11:00 - Aula seminari III piano

Oswaldo GONZALEZ GAXIOLA (UAM, México): *On the generator of the solution of a Quantum Stochastic Differential Equation and their defect indices
*

If the Hamiltonian is a bounded selfadjoint operator, we give a simple alternative characterization of the infinitesimal generator iC of the unitary group associated with a Quantum Stochastic Differential Equation (QSDE). By using the defect indices of the symmetric operator C, we give a sufficient condition that assures that iC is the restriction of a generator of a strongly continuous semigroup of isometries in the case when the Hamiltonian is an unbounded symmetric operator.

**21 - 05 - 2008 **ore 14:30 - Aula seminari III piano

L.P. MARTINEZ (UAM, México): *The Asymmetric Quantum Exclusion Semigroup*

We consider a model of electrical conductivity in a lattice deduced by L. Accardi and S. Kozyrev from the stochastic limit of a general system of spins interacting with a boson field. We search for diagonal (or classical) invariant states of the associated Quantum Markov Semigroup and show that:
a) They correspond with invariant measures of a classical asymmetric exclusion process.
b) Associated with every energy function, there exists infinitely many invariant states.
c) Any element in the closed convex hull of the above states satisfies a quantum detailed balance condition.
d) Any initial state is driven by the asymmetric exclusion QMS to an equilibrium state.

**11 - 04 - 2008 **ore 14:30 - Aula seminari III piano

Ameur DHAHRI (Paris Dauphine): *Quantum Stochastic Differential Equations with jump noises*