عنوان

Mathematical Results in Quantum Mechanics :

(Number (ISBN

3034887450

(Number (ISBN

9783034887458

Number

b553491

Title Proper

Mathematical Results in Quantum Mechanics :

General Material Designation

[Book]

Other Title Information

QMath7 Conference, Prague, June 22-26, 1998

First Statement of Responsibility

edited by Jaroslav Dittrich, Pavel Exner, Miloš Tater.

Place of Publication, Distribution, etc.

Basel

Name of Publisher, Distributor, etc.

Birkhäuser Basel

Date of Publication, Distribution, etc.

1999

Specific Material Designation and Extent of Item

(404 pages)

Series Title

Operator theory, advances and applications, 108.

Text of Note

I Plenary talks --;An adiabatic theorem without a gap condition --;Two-dimensional periodic Pauli operator. The effective masses at the lower edge of the spectrum --;Spectral problems in the theory of photonic crystals --;Optimal eigenvalues for some Laplacians and Schrödinger operators depending on curvature --;The spectral shift operator --;On the scattering operator for the Schrödinger equation with a time-dependent potential --;H_2-construction and some applications --;Scattering with time periodic potentials and cyclic states --;Some geometry related to decay properties of the resolvent of a class of symmetric operators --;On some asymptotic formulas in the strong localization regime of the theory of disordered systems --;Spectral measures and category --;Quantum dots. A survey of rigorous results --;II Session talks --;A simple model of concentrated nonlinearity --;Anomalous electron trapping by magnetic flux tubes and electric current vortices --;On the absolutely continuous energy distribution of a quantum mechanical system in a bounded domain --;Some aspects of generalized contact interaction in one-dimensional quantum mechanics --;Traces and trace norms for semigroup differences. --;About a resolvent formula --;The determinant anomaly in low-dimensional quantum systems --;Linear Boltzmann equation as the weak coupling limit of the random Schrödinger equation --;Coexistence of different spectral types for almost periodic Schrödinger equations in dimension one --;Dynamical localization for random Schrödinger operators and an application to the almost Mathieu operator --;On fractal structure of the spectrum for periodic point perturbations of the Schrödinger operator with a uniform magnetic field --;A Weyl-Berry formula for the scattering operator associated to self-similar potentials on the line --;Localization and Lifshitz tails for random quantum waveguides --;Birman-Schwinger analysis for bound states in a pair of parallel quantum waveguides with a semitransparent boundary --;On the absolute continuity of spectra of periodic elliptic operators --;Hardy inequalities for magnetic Dirichlet forms --;Adiabatic curvature, chaos and the deformation of Riemann surfaces --;Operator interpretation of resonances arising in spectral problems for 2 x 2 matrix Hamiltonians --;On the operator-norm convergence of the Trotter-Kato product formula --;A particular case of the inverse problem for the Sturm-Liouville equation with parameter dependent potential --;One-dimensional Schrödinger operators with decaying potentials --;Stability of limiting absorption under singular perturbations --;Existence of averaging integrals for self-adjoint operators --;Monotonicity versus non-monotonicity in random operators --;A model in perturbation theory --;Band gap of the spectrum in periodically curved quantum waveguides --;A list of other talks --;A list of participants.

Text of Note

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 Schrdinger 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.

Mathematical physics -- Congresses.

Mathematical physics.

Quantum theory -- Mathematics -- Congresses.

edited by Jaroslav Dittrich, Pavel Exner, Miloš Tater.

J Dittrich

Miloš Tater

Pavel Exner

Electronic name

[Book]

Y