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Mathematical Results in Quantum Mechanics : QMath7 Conference, Prague, June 22-26, 1998 - Jaroslav Dittrich

Mathematical Results in Quantum Mechanics

QMath7 Conference, Prague, June 22-26, 1998

By: Jaroslav Dittrich (Editor), Pavel Exner (Editor), Milos Tater (Editor)


Published: 1st April 1999
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This book constitutes the proceedings of the QMath 7 Conference on Mathematical Results in Quantum Mechanics held in Prague, Czech Republic in June, 1998. The volume addresses mathematicians and physicists interested in contemporary quantum physics and associated mathematical questions, presenting new results on Schr‚ÄĚdinger and Pauli operators with regular, fractal or random potentials, scattering theory, adiabatic analysis, and interesting new physical systems such as photonic crystals, quantum dots and wires.

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

ISBN: 9783764360979
ISBN-10: 3764360976
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 398
Published: 1st April 1999
Publisher: Birkhauser Verlag AG
Country of Publication: CH
Dimensions (cm): 24.77 x 17.15  x 2.54
Weight (kg): 0.89