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.
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)
INTRODUCTION The most widely used test to identify undesired effects of drugs on the central and the peripheral nervous system is the neurobehavioural observation battery adapted from that first described by Irwin in mice. As a neurobehavioural assessment is based on observations; thus, all factors involved need to be controlled and standardised to make the… (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)
We prove new formulae for the wave operators for a Friedrichs scattering system with a rank one perturbation , and we derive a topological version of Levinson's theorem for this model.
We propose to interpret Levinson's theorem as an index theorem. This exhibits its topological nature. It furthermore leads to a more coherent explanation of the corrections due to resonances at thresholds.
We study Levinson type theorems for the family of Aharonov-Bohm models from different perspectives. The first one is purely analytical involving the explicit calculation of the wave-operators and allowing to determine precisely the various contributions to the left hand side of Levinson's theorem, namely those due to the scattering operator, the terms at… (More)