Mathematical Results in Quantum Mechanics

by Dittrich, Jaroslav; Exner, Pavel; Tater, Milos

• ISBN13: 9783764360979
• ISBN10: 3764360976
• Format: Hardcover
• Copyright: 1999-04-01
• Publisher: Birkhauser

Summary

This book contains the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic, from June 22 to 26, 1998. The purpose is to draw attention to recent developments in quantum mechanics stemming from its numerous applications, and to related mathematical problems and techniques.This volume is addressed to the broad audience of mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions. The reader will find new results on Schrödinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, as well as on interesting new physical systems such as photonic crystals, quantum dots and wires

Table of Contents

Preface
An adiabatic theorem without a gap condition	p. 3
Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum	p. 13
Spectral problems in the theory of photonic crystals	p. 33
Optimal eigenvalues for some Laplacians and Schrodinger operators depending on curvature	p. 47
The spectral shift operator	p. 59
On the scattering operator for the Schrodinger equation with a time-dependent potential	p. 91
H[subscript -2]-construction and some applications	p. 99
Scattering with time periodic potentials and cyclic states	p. 107
Some geometry related to decay properties of the resolvent of a class of symmetric operators	p. 117
On some asymptotic formulas in the strong localization regime of the theory of disordered systems	p. 129
Spectral measures and category	p. 149
Quantum dots. A survey of rigorous results	p. 161
A simple model of concentrated nonlinearity	p. 183
Anomalous electron trapping by magnetic flux tubes and electric current vortices	p. 191
On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain	p. 197
Some aspects of generalized contact interaction in one-dimensional quantum mechanics	p. 203
Traces and trace norms for semigroup differences	p. 209
About a resolvent formula	p. 221
The determinant anomaly in low-dimensional quantum systems	p. 227
Linear Boltzmann equation as the weak coupling limit of the random Schrodinger equation	p. 233
Coexistence of different spectral types for almost periodic Schrodinger equations in dimension one	p. 243
Dynamical localization for random Schrodinger operators and an application to the almost Mathieu operator	p. 253
On fractal structure of the spectrum for periodic point perturbations of the Schrodinger operator with a uniform magnetic field	p. 259
A Weyl-Berry formula for the scattering operator associated to self-similar potentials on the line	p. 267
Localization and Lifshitz tails for random quantum waveguides	p. 275
Birman-Schwinger analysis for bound states in a pair of parallel quantum waveguides with a semitransparent boundary	p. 281
On the absolute continuity of spectra of periodic elliptic operators	p. 291
Hardy inequalities for magnetic Dirichlet forms	p. 299
Adiabatic curvature, chaos and the deformation of Riemann surfaces	p. 307
Operator interpretation of resonances arising in spectral problems for 2 x 2 matrix Hamiltonians	p. 315
On the operator-norm convergence of the Trotter-Kato product formula	p. 323
A particular case of the inverse problem for the Sturm-Liouville equation with parameter dependent potential	p. 335
One-dimensional Schrodinger operators with decaying potentials	p. 343
Stability of limiting absorption under singular perturbations	p. 351
Existence of averaging integrals for self-adjoint operators	p. 359
Monotonicity versus non-monotonicity in random operators	p. 365
A model in perturbation theory	p. 373
Band gap of the spectrum in periodically curved quantum waveguides	p. 379
A list of other talks	p. 385
A list of participants	p. 389
Table of Contents provided by Blackwell. All Rights Reserved.