47162597
Recognizable sets of finite bilabelled transition systems
22241766
An extension of the notions of traces and of asynchronous automata
Nous generalisons la notion de trace, c'est-a-dire d'un element d'un monoide partiellement commutatif, en faisant dependre la relation de commutation entre lettres du contexte dans lequel elle est appliquee. Nous generalisons de facon correspondante la notion d'automate asynchrone et nous generalisons le theoreme de Zielonka a ces notions
24358839
Synchronized behaviours of processes and rational relations
SummarySynchronized behaviours of processes, specified in three different ways, are compared with rational relations.
123822351
The relaxation-time von Neumann-Poisson equation
This paper is concerned with the relaxation-time von Neumann-Poisson (or quantum Liouville-Poisson) equation in three spatial dimensions which describes the self-consistent time evolution of an open quantum mechanical system that include some relaxation mechanism. This model and the equivalent relaxation-time Wigner-Poisson system play an important role in the simulation of quantum semiconductor devices. We prove that the evolution is a positivity preserving map, satisfying the Lindblad condition. The nonlinear evolution problem is formulated as an abstract Cauchy problem in the space of Hermitian trace class operators. For initial density matrices with finite kinetic energy we prove the global-in-time existence and uniqueness of mild solutions. A key ingredient for our analysis is a new generalization of the Lieb-Thirring inequality for density matrix operators. We also present a local convergence result towards the steady state of the system.