Ph. Blanchard

From quantum to quantum via decoherence

Various physical effects resulting from decoherence are discussed in the algebraic framework. In particular, it is shown that the environment may induce not only classical properties like superselection rules, pointer states or even classical behavior of the quantum system, but, what is more, it also allows the transition from statistical description of infinite quantum systems to quantum mechanics of systems with a finite number of degrees of freedom. It is shown that such transition holds for the quantum spin system in the thermodynamic limit interacting with the phonon field.

Modelling AIDS-Epidemics or any venereal disease on random graphs

The aim of this paper is to review and to report on general results dealing with the description of a new mathematical model based on the concept of random graphs. This stochastic model is intended to describe the dynamics of sexually transmitted diseases. For shortness and simplicity we will mainly concentrate on the case of the Human Immuno-Deficiency Virus (HIV) and AIDS. AIDS is a fatal, infectious disease for which there is now no cure, and its sufferers appear to remain infectious for life. Even though at present much of the numerical information needed is not available, the mathematical modelling of transmissions of infection in the context of the AIDS epidemics is nevertheless vital in investigating how changes in the various assumptions and parameter values would affect the course of the epidemic. This can h:lp to clarify what behavioural changes are needed, to test what mterventwn and preventiOn strategies should be pursued and what sort of data should be collected.

Quantum mechanics with event dynamics

Abstract Event generating algorithm corresponding to a linear master equation of Lindblads type is described and illustrated on two examples: that of a particle detector and of a fuzzy clock. Relation to other approaches to the foundations of quantum theory and to the description of quantum measurements is briefly discussed.

Stochastic variational principle and diffusion processes

In this paper, we give a method to construct diffusion process with constant diffusion coefficient by a stochastic variational principle. The result is very similar to the classical case. We discuss also the relation between our stochastic variational principle and the stochastic mechanics.

Smoothing Properties of the Heat Semigroups Associated to Hamiltonians Describing Point Interactions in One and Two Dimensions

Smoothing properties of the heat semigroups associated to Hamiltonians describing point interactions in one and two dimensions are investigated. A construction of Hamiltonians describing point interaction on Lp-spaces is then derived and a full description of their spectra is given. Particularly, we prove the p-independence of their spectra and the exponential growth of the p-norms of such semigroups for large time.

Stochastic jump processes associated with Dirac equation

We study the stochastic jump processes associated with the Dirac equation where the space derivatives are replaced by discrete approximations.

Trapping for Newtonian Diffusion Processes

In the first lecture I will try to explain a general mechanism for the formation of impenetrable barriers for diffusion processes (see [1]). I will consider a special class of diffusion processes, which we call Newtonian diffusions. This name is justified by the fact that such a diffusion process satisfies a Newton law in the mean. We will see how it is possible to define a mean stochastic acceleration a for diffusion processes. The Newton law in the mean

Decoherence, Classical Properties and Entanglement of Quantum Systems

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