Inhaltsangabe
1 Schrödinger and Dirac operators.- Discrete spectrum of the periodic Schrödinger operator for non-negative perturbations.- The discrete spectrum in a gap of the continuous one for compact supported perturbations.- Schrödinger operators with strong local magnetic perturbations: Existence of eigenvalues in gaps of the essential spectrum.- Regularity of the nodal sets of solutions to Schrödinger equations.- Results in the spectral theory of Schrödinger operators with wide potential barriers.- Stark ladders and perturbation theory.- Singular potentials: algebraization.- Asymptotic behavior of the resolvent of the Dirac operator.- Discrete spectrum of the perturbed Dirac operator.- 2 Generalized Schrödinger operators.- The spectrum of Schrödinger operators in Lp(Rd) and in C0(Rd).- On spectral properties of generalized Schrödinger operators.- A Fermi-type rule for contact embedded-eigenvalue perturbations.- A simple model for predissociation.- Scattering on several solenoids.- Hall conductance of Riemann surfaces.- 3 Stochastic spectral analysis.- Framework and results of stochastic spectral analysis.- Occupation time asymptotics to the decay of eigenfunctions.- Holomorphic semigroups and Schrödinger equations.- Some problems on submarkovian semigroups.- Smoothness estimates and uniqueness for the Dirichlet operator.- Trace ideal properties of perturbed Dirichlet semigroups.- Quantum dynamical semigroups.- 4 Many-body problems and statistical physics K.B. Sinha.- Limits of infinite order, dimensionality or number of components for random finite-difference operators.- Atoms at finite density and temperature and the spectra of reduced density matrices.- Quantum fluctuations in the many-body problem.- General Hamiltonians and model Hamiltonians.- Poisson fields representations in the statistical mechanics of conitinuous systems.- Exact ground states for quantum spin chains.- The spectrum of the spin-boson model.- A survey of Wigner-Poisson problems.- 5 Chaos.- Classical d’Alembert field in an one-dimensional pulsating region.- Irregular scattering in one-dimensional periodically driven systems.- Relatively random unitary operators.- 6 Operator theory and its application.- A trace formula for obstacles problems and applications.- Propagation in irregular optic fibres.- Singular perturbations, regularization and extension theory.- Adiabatic reduction theory. Semiclassical S-matrix for N-state one-dimensional systems.- The functional structure of the monodromy matrix for Harper’s equation.- Eigenfunction expansion of right definite multiparameter problems.- Singularly perturbed operators.- Some problems of p-adic quantum theory.
Reseña del editor
This book contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. Its purpose is to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book is addressed to the wide audience of mathematicians and physicists interested in contemporary quantum physics and associated mathematical problems. The reader will find sections not only on traditional subjects such as Schrödinger and Dirac operators and generalized Schrödinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications. Contributors: Schrödinger and Dirac operators: M.Sh. Birman, V. Grecchi, R. Hempel, M. Hoffmann-Ostenhof, Y. Saito, G. Stolz, M. Znojil · Generalized Schrödinger operators: J.-P. Antoine, J.F. Brasche, P. Duclos, R. Hempel, M. Klein, P. Stovicek · Stochastic spectral analysis: M. Demuth, V.A. Liskevich, E.M. Ouhabaz, P. Stollmann · Many-body problems and statistical physics: M. Fannes, R. Gielerak, M. Hübner, A.M. Khorunzhy, H. Lange, N. Macris, Yu.A. Petrina, K.B. Sinha, A. Verbeure · Chaos: J. Dittrich, P. Seba, K. Zyczkowski · Operator theory and its application: F. Bentosela, V. Buslaev, A.N. Kochubei, A.Yu. Konstantinov, V. Koshmanenko, H. Neidhardt, G. Nenciu, D. Robert
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