Format:
Online-Ressource
,
digital
Edition:
Online-Ausg. Springer eBook Collection. Mathematics and Statistics Electronic reproduction; Available via World Wide Web
ISBN:
9783034804141
Series Statement:
Operator Theory: Advances and Applications 224
Content:
This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.?
Content:
This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.ai
Note:
Description based upon print version of record
,
Spectral Analysisof Quantum Hamiltonians; Contents; Preface; Remarks on Sojourn Time Estimates for Periodic Time-dependent Quantum Systems; 1. Introduction; 2. Energy-time Uncertainty Principle; 2.1. The autonomous case: a review; 2.2. The non-autonomous case; 3. A model; References; Continuity of Spectra in Rieffel's Pseudodifferential Calculus; Introduction; 1. Families of Rieffel quantized c*-algebras; 2. The Abelian case; 3. Spectral continuity for symbols; 4. Spectral continuity for operators; Framework; Acknowledgement; References; Stability of Matter
,
1. Introduction: The stability of quantum systems: A historical overview2. Stability of Matter: The classical proof of Lieb and Thirring; 2.1. Stability of the hydrogen atom in non-relativistic Quantum Mechanics; 2.2. Stability of a system of N electrons in non-relativistic Quantum Mechanics; 2.3. Stability of a many particle system via Thomas-Fermi; 2.4. Bibliographical Remarks; 3. Lieb-Thirring inequalities; 3.1. Use of commutation methods to prove the Lieb-Thirring inequalityfor γ = 3/2 in dimension 1; 3.2. The Eden-Foias bound [21]; 3.3. Bibliographical Remarks
,
4. The stability of matter for a relativistic toy model4.1. Bibliographical Remarks; References; On the Regularity of the Hausdorff Distance Between Spectra of Perturbed Magnetic Hamiltonians; 1. Introduction; 1.1. The setting and the main result; 2. Proof of Theorem 1.1; 2.1. The case α 〉 0; 2.2. The case α = 0; 3. Magnetic Hamiltonians; Acknowledgment; References; The Topological Bloch-Floquet Transform and Some Applications; 1. Introduction; 2. Some guiding examples; 3. The complete spectral theorem by von Neumann; 4. The nuclear spectral theorem by Maurin; 5. The wandering property
,
6. The generalized Bloch-Floquet transformConstruction of the wandering nuclear space; The transform; The decomposition; 7. Emergent geometry; Geometric vs. analytic viewpoint; Triviality, local triviality and vector bundle structure; Algebraic viewpoint; The Hilbert bundle emerging from the Bloch-Floquet decomposition; Decomposition of the observables and endomorphism sections; Appendix A. Gel'fand theory, joint spectrum and basic measures; Appendix B. Direct integralof Hilbert spaces; Acknowledgement; References; Discrete Schrödinger Operators with Random Alloy-type Potential
,
1. Introduction2. Discrete Anderson models with general alloy-type potential; 3. Localization properties; 4. The spectrum; 5. Averaging of determinants and resolvents; 5.1. Estimates on polynomials and resolvents; 5.2. Cartan estimates; 6. Wegner estimates; 7. Localization via fractional moment method; 7.1. Boundedness of fractional moments; 7.2. Decay of fractional moments; 7.3. Localization; 8. Localization via multiscale analysis; 8.1. Probabilistic estimates; 8.2. An application of Cartan's lemma; References
,
Operator Domains and SUSY Breaking in a Model of SUSYQM with a Singular Potential
,
Electronic reproduction; Available via World Wide Web
Additional Edition:
ISBN 9783034804134
Additional Edition:
Erscheint auch als Druck-Ausgabe Spectral analysis of quantum hamiltonians Basel [u.a.] : Birkhäuser/Springer, 2012 ISBN 9783034804134
Additional Edition:
ISBN 303480413X
Language:
English
Subjects:
Mathematics
Keywords:
Spektrum
;
Analyse
;
Hamilton-Operator
DOI:
10.1007/978-3-0348-0414-1
URL:
Volltext
(lizenzpflichtig)
Bookmarklink
