There is a connection between the Weyl pseudodifferential calculus and crossed product C *-algebras associated with certain dynamical systems. And in fact both topics are involved in the quantization of a non-relativistic particle moving in R N. Our paper studies the situation in which a variable magnetic field is also present. The Weyl calculus has to be… (More)
We review the spectral and the scattering theory for the Aharonov-Bohm model on R 2. New formulae for the wave operators and for the scattering operator are presented. The asymptotics at high and at low energy of the scattering operator are computed.
In this note Levinson theorems for Schrödinger operators in R n with one point interaction at 0 are derived using the concept of winding numbers. These results are based on new expressions for the associated wave operators.
We study generalised magnetic Schrödinger operators of the form H h (A, V) = h(Π A) + V , where h is an elliptic symbol, Π A = −i∇ − A, with A a vector potential defining a variable magnetic field B, and V is a scalar potential. We are mainly interested in anisotropic functions B and V. The first step is to show that these operators are affiliated to… (More)
In the framework of one dimensional potential scattering we prove that, modulo a compact term, the wave operators can be written in terms of a universal operator and of the scattering operator. The universal operator is related to the one dimensional Hilbert transform and can be expressed as a function of the generator of dilations. As a consequence, we… (More)
We present some improvements in the method of the weakly conjugate operator, one variant of the Mourre theory. When applied to certain two-body Schrödinger operators, this leads to a limiting absorption principle that is uniform on the positive real axis.
Armstrong, Gleitman, and Gleitman (1983) reported shorter categorization times for members of well-defined categories judged more typical. They concluded that these effects could not originate in a graded, similarity-based category representation and consequently that the typicality effects obtained with natural categories might not be indicative of such a… (More)
Pancreatic tumors are the gastrointestinal cancer with the worst prognosis in humans and with a survival rate of 5% at 5 years. Nowadays, no chemotherapy has demonstrated efficacy in terms of survival for this cancer. Previous study focused on the development of a new therapy by non thermal plasma showed significant effects on tumor growth for colorectal… (More)
The material presented here covers two talks given by the authors at the conference Operator Algebras and Mathematical Physics organised in Bucharest in August 2005. The first one was a review given by J. Kellendonk on the relation between bulk and boundary topolog-ical invariants in physical systems. In the second talk S. Richard described an application… (More)
The paper is a presentation of recent investigations on potential scattering in R 3. We advocate a new formula for the wave operators and deduce the various outcomes that follow from this formula. A topological version of Levinson's theorem is proposed by interpreting it as an index theorem.