Stochastic Aspects of Classical and Quantum Systems: Proceedings of the 2nd French-German Encounter in Mathematics and Physics, held in Marseille, France, March 28 - April 1, 1983

by Sergio Albeverio (Editor)

L'Equation de Schrödinger quand h tend vers zero; une approche probabiliste.- Rearrangement Gaussien de fonctions.- Electrons of a solid in an external electric field.- An intrinsic approach to the evolution of quantum observables in terms of stochastic processes on phase space.- Diffusions and central limit theorems.- Random Schrödinger operators and the density of states.- Ergodic properties of the Lozi map.- Proprietes spectrales pour des hamiltoniens presque-periodiques.- A solvable almost periodic Schrödinger operator.- On the absence of breakdown of symmetry for the plane rotator model with long range unbounded random interaction.- Stratonovich solution of a quantum stochastic differential equation describing light emission and absorption.- Analytic expansion of Lyapunov exponents associated to the Schrödinger operator.- Reduction of non linear problems to Schrödinger or heat Formation of kepler orbits, singular solutions for hydrodynamical equations.- Quantum mechanical low energy scattering in terms of diffusion processes.

244 pages, Paperback

First published March 1, 1985

About the author

Sergio Albeverio (born 17 January 1939) is a Swiss mathematician and mathematical physicist working in numerous fields of mathematics and its applications. In particular he is known for his work in probability theory, analysis (including infinite dimensional, non-standard, and stochastic analysis), mathematical physics, and in the areas algebra, geometry, number theory, as well as in applications, from natural to social-economic sciences.

He initiated (with Raphael Høegh-Krohn) a systematic mathematical theory of Feynman path integrals and of infinite dimensional Dirichlet forms and associated stochastic processes (with applications particularly in quantum mechanics, statistical mechanics and quantum field theory). He also gave essential contributions to the development of areas such as p-adic functional and stochastic analysis as well as to the singular perturbation theory for differential operators. Other important contributions concern constructive quantum field theory and representation theory of infinite dimensional groups. He also initiated a new approach to the study of galaxy and planets formation inspired by stochastic mechanics.