Determining Spectra In Quantum Theory

Author: Michael Demuth
Publisher: Springer Science & Business Media
ISBN: 0817644393
Size: 31.99 MB
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This work focuses on various known criteria in the spectral theory of selfadjoint operators. The concise, unified presentation is aimed at graduate students and researchers working in the spectral theory of Schrodinger operators with either fixed or random potentials. But given the large gap this book fills in the literature, it will serve a wider audience of mathematical physicists in its contribution to works in spectral theory.

Spectral Theory And Mathematical Physics

Author: Marius Mantoiu
Publisher: Birkhäuser
ISBN: 3319299921
Size: 27.16 MB
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The present volume contains the Proceedings of the International Conference on Spectral Theory and Mathematical Physics held in Santiago de Chile in November 2014. Main topics are: Ergodic Quantum Hamiltonians, Magnetic Schrödinger Operators, Quantum Field Theory, Quantum Integrable Systems, Scattering Theory, Semiclassical and Microlocal Analysis, Spectral Shift Function and Quantum Resonances. The book presents survey articles as well as original research papers on these topics. It will be of interest to researchers and graduate students in Mathematics and Mathematical Physics.

Hyperfinite Dirichlet Forms And Stochastic Processes

Author: Sergio Albeverio
Publisher: Springer Science & Business Media
ISBN: 9783642196591
Size: 64.30 MB
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This monograph treats the theory of Dirichlet forms from a comprehensive point of view, using "nonstandard analysis." Thus, it is close in spirit to the discrete classical formulation of Dirichlet space theory by Beurling and Deny (1958). The discrete infinitesimal setup makes it possible to study the diffusion and the jump part using essentially the same methods. This setting has the advantage of being independent of special topological properties of the state space and in this sense is a natural one, valid for both finite- and infinite-dimensional spaces. The present monograph provides a thorough treatment of the symmetric as well as the non-symmetric case, surveys the theory of hyperfinite Lévy processes, and summarizes in an epilogue the model-theoretic genericity of hyperfinite stochastic processes theory.

Random Operators

Author: Michael Aizenman
Publisher: American Mathematical Soc.
ISBN: 1470419130
Size: 52.79 MB
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This book provides an introduction to the mathematical theory of disorder effects on quantum spectra and dynamics. Topics covered range from the basic theory of spectra and dynamics of self-adjoint operators through Anderson localization--presented here via the fractional moment method, up to recent results on resonant delocalization. The subject's multifaceted presentation is organized into seventeen chapters, each focused on either a specific mathematical topic or on a demonstration of the theory's relevance to physics, e.g., its implications for the quantum Hall effect. The mathematical chapters include general relations of quantum spectra and dynamics, ergodicity and its implications, methods for establishing spectral and dynamical localization regimes, applications and properties of the Green function, its relation to the eigenfunction correlator, fractional moments of Herglotz-Pick functions, the phase diagram for tree graph operators, resonant delocalization, the spectral statistics conjecture, and related results. The text incorporates notes from courses that were presented at the authors' respective institutions and attended by graduate students and postdoctoral researchers.

Self Adjoint Extensions In Quantum Mechanics

Author: D.M. Gitman
Publisher: Springer Science & Business Media
ISBN: 0817646620
Size: 59.37 MB
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This exposition is devoted to a consistent treatment of quantization problems, based on appealing to some nontrivial items of functional analysis concerning the theory of linear operators in Hilbert spaces. The authors begin by considering quantization problems in general, emphasizing the nontriviality of consistent operator construction by presenting paradoxes to the naive treatment. It then builds the necessary mathematical background following it by the theory of self-adjoint extensions. By considering several problems such as the one-dimensional Calogero problem, the Aharonov-Bohm problem, the problem of delta-like potentials and relativistic Coulomb problemIt then shows how quantization problems associated with correct definition of observables can be treated consistently for comparatively simple quantum-mechanical systems. In the end, related problems in quantum field theory are briefly introduced. This well-organized text is most suitable for students and post graduates interested in deepening their understanding of mathematical problems in quantum mechanics. However, scientists in mathematical and theoretical physics and mathematicians will also find it useful.

Advances In The Theory Of Quantum Systems In Chemistry And Physics

Author: Philip E. Hoggan
Publisher: Springer Science & Business Media
ISBN: 9400720769
Size: 63.24 MB
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Advances in the Theory of Quantum Systems in Chemistry and Physics is a collection of 32 selected papers from the scientific contributions presented at the 15th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XV), held at Magdalene College, Cambridge, UK, from August 31st to September 5th, 2010. This volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a wide range of problems in chemistry, physics, and biology. The breadth and depth of the scientific topics discussed during QSCP-XV are gathered in seven sections: I. Fundamental Theory; II. Model Atoms; III. Atoms and Molecules with Exponential-Type Orbitals; IV. Density-Oriented Methods; V. Dynamics and Quantum Monte-Carlo Methodology; VI. Structure and Reactivity; VII. Complex Systems, Solids, Biophysics. Advances in the Theory of Quantum Systems in Chemistry and Physics is written for research students and professionals in Quantum systems of chemistry and physics. It also constitutes and invaluable guide for those wishing to familiarize themselves with research perspectives in the domain of quantum systems for thematic conversion or simply to gain insight into the methodological developments and applications to physics chemistry and biology that have actually become feasible by the end of 2010.

Quantum Systems In Chemistry And Physics

Author: Kiyoshi Nishikawa
Publisher: Springer Science & Business Media
ISBN: 9400752970
Size: 38.28 MB
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Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is a collection of 33 selected papers from the scientific contributions presented at the 16th International Workshop on Quantum Systems in Chemistry and Physics (QSCP-XVI), held at Ishikawa Prefecture Museum of Art in Kanazawa, Japan, from September 11th to 17th, 2011. The volume discusses the state of the art, new trends, and the future of methods in molecular quantum mechanics and their applications to a wide range of problems in physics, chemistry, and biology. The breadth and depth of the scientific topics discussed during QSCP-XVI appears in the classification of the contributions in six parts: I. Fundamental Theory II. Molecular Processes III. Molecular Structure IV. Molecular Properties V. Condensed Matter VI. Biosystems. Quantum Systems in Chemistry and Physics: Progress in Methods and Applications is written for advanced graduate students as well as for professionals in theoretical chemical physics and physical chemistry. The book covers current scientific topics in molecular, nano, material, and bio sciences and provides insights into methodological developments and applications of quantum theory in physics, chemistry, and biology that have become feasible at end of 2011.

Spectral Analysis Of Relativistic Operators

Author: A. A. Balinsky
Publisher: World Scientific
ISBN: 1848162189
Size: 64.57 MB
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Over the last decade, there has been considerable interest and progress in determining the spectral properties of various operators that take relativistic effects into account, with important implications for mathematics and physics. Difficulties are encountered in many-particle problems due to the lack of semiboundedness of the Dirac operator, and this has led to the investigation of operators like those of Chandrasekhar-Herbst and Brown-Ravenhall, which are semibounded under appropriate circumstances.This book contains an up-to-date, comprehensive and self-contained analysis of the spectral properties of these operators, providing the tools for anyone working in this area. Another major feature is the work of the authors on zero modes, a topic which has important significance for the stability of matter and other physical problems. Up until now, these topics have been scattered throughout the literature, without a systematic and cohesive treatment. The book will report largely on the progress on these topics published since 1992.

Vibronic Interactions And The Jahn Teller Effect

Author: Mihail Atanasov
Publisher: Springer Science & Business Media
ISBN: 9789400723849
Size: 19.49 MB
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The concepts of the Jahn-Teller effect and vibronic coupling are being applied to more and more systems in both chemistry and physics. Aspects of structural chemistry such as the distortion of the nuclear framework to a lower-symmetry conformation have received an increasing attention, as well as the dynamics on the coupled potential energy surfaces. The Jahn-Teller intersections are now recognized as prototype cases of conical intersections where the nuclear motion is known to be inherently nonadiabatic in nature and interchanges freely between the different potential energy surfaces. In the condensed phase especially, the significance of the Jahn-Teller effect has been increasingly appreciated, following the discovery of superconductivity in the fullerides and of very large ("colossal") magnetoresistance in the manganite perovskites. Indeed, these materials are particularly challenging since the Jahn-Teller interaction competes with electronic correlation effects. Vibronic Interactions and the Jahn-Teller Effect: Theory and Applications provides an in-depth discussion of the Jahn-Teller effect and vibronic interactions as reflected by the contributions presented at the XX International Conference on the Jahn-Teller effect, Fribourg, Switzerland, 2010. The following topics have been treated in a clear and concise way: • Complex topologies of Jahn-Teller effect and conical intersections • Multi-state vibronic interactions on strongly coupled potential energy surfaces • Interplay of vibronic and spin-orbit coupling • Strain in Jahn-Teller systems and cooperative Jahn-Teller effect • Orbital ordering and its relation to ferromagnetism, ferroelectricity and molecular magnets • The Jahn-Teller effect in icosahedral systems • The Jahn-Teller effect and high temperature superconductivity This book is of interest to a wide audience including academic and industrial theoretical and experimental physicists, chemists, spectroscopists, and crystallographers.