Spectra Of Random And Almost Periodic Operators
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Spectra Of Random And Almost Periodic Operators
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Author : Leonid Pastur
language : en
Publisher: Springer
Release Date : 1992
Spectra Of Random And Almost Periodic Operators written by Leonid Pastur and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.
In the last fifteen years the spectral properties of the Schrodinger equation and of other differential and finite-difference operators with random and almost-periodic coefficients have attracted considerable and ever increasing interest. This is so not only because of the subject's position at the in tersection of operator spectral theory, probability theory and mathematical physics, but also because of its importance to theoretical physics, and par ticularly to the theory of disordered condensed systems. It was the requirements of this theory that motivated the initial study of differential operators with random coefficients in the fifties and sixties, by the physicists Anderson, 1. Lifshitz and Mott; and today the same theory still exerts a strong influence on the discipline into which this study has evolved, and which will occupy us here. The theory of disordered condensed systems tries to describe, in the so-called one-particle approximation, the properties of condensed media whose atomic structure exhibits no long-range order. Examples of such media are crystals with chaotically distributed impurities, amorphous substances, biopolymers, and so on. It is natural to describe the location of atoms and other characteristics of such media probabilistically, in such a way that the characteristics of a region do not depend on the region's position, and the characteristics of regions far apart are correlated only very weakly. An appropriate model for such a medium is a homogeneous and ergodic, that is, metrically transitive, random field.
Almost Periodic Operators And Related Nonlinear Integrable Systems
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Author : V. A. Chulaevskiĭ
language : en
Publisher: Manchester University Press
Release Date : 1989
Almost Periodic Operators And Related Nonlinear Integrable Systems written by V. A. Chulaevskiĭ and has been published by Manchester University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Spectral Analysis Of Differential Operators
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Author : Fedor S. Rofe-Beketov
language : en
Publisher: World Scientific
Release Date : 2005
Spectral Analysis Of Differential Operators written by Fedor S. Rofe-Beketov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This is the first monograph devoted to the Sturm oscillatory theory for infinite systems of differential equations and its relations with the spectral theory. It aims to study a theory of self-adjoint problems for such systems, based on an elegant method of binary relations. Another topic investigated in the book is the behavior of discrete eigenvalues which appear in spectral gaps of the Hill operator and almost periodic SchrAdinger operators due to local perturbations of the potential (e.g., modeling impurities in crystals). The book is based on results that have not been presented in other monographs. The only prerequisites needed to read it are basics of ordinary differential equations and operator theory. It should be accessible to graduate students, though its main topics are of interest to research mathematicians working in functional analysis, differential equations and mathematical physics, as well as to physicists interested in spectral theory of differential operators."
Methods Of Spectral Analysis In Mathematical Physics
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Author : Jan Janas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-16
Methods Of Spectral Analysis In Mathematical Physics written by Jan Janas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-16 with Science categories.
The volume contains the proceedings of the OTAMP 2006 (Operator Theory, Analysis and Mathematical Physics) conference held at Lund University in June 2006. The conference was devoted to the methods of analysis and operator theory in modern mathematical physics. The following special sessions were organized: Spectral analysis of Schrödinger operators; Jacobi and CMV matrices and orthogonal polynomials; Quasi-periodic and random Schrödinger operators; Quantum graphs.
Spectral Analysis Of Quantum Hamiltonians
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Author : Rafael Benguria
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-06-30
Spectral Analysis Of Quantum Hamiltonians written by Rafael Benguria and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-06-30 with Mathematics categories.
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.
Integrable Systems And Random Matrices
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Author : Jinho Baik
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Integrable Systems And Random Matrices written by Jinho Baik and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
This volume contains the proceedings of a conference held at the Courant Institute in 2006 to celebrate the 60th birthday of Percy A. Deift. The program reflected the wide-ranging contributions of Professor Deift to analysis with emphasis on recent developments in Random Matrix Theory and integrable systems. The articles in this volume present a broad view on the state of the art in these fields. Topics on random matrices include the distributions and stochastic processes associated with local eigenvalue statistics, as well as their appearance in combinatorial models such as TASEP, last passage percolation and tilings. The contributions in integrable systems mostly deal with focusing NLS, the Camassa-Holm equation and the Toda lattice. A number of papers are devoted to techniques that are used in both fields. These techniques are related to orthogonal polynomials, operator determinants, special functions, Riemann-Hilbert problems, direct and inverse spectral theory. Of special interest is the article of Percy Deift in which he discusses some open problems of Random Matrix Theory and the theory of integrable systems.
Orthogonal Polynomials On The Unit Circle Spectral Theory
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Author : Barry Simon
language : en
Publisher: American Mathematical Soc.
Release Date : 2005
Orthogonal Polynomials On The Unit Circle Spectral Theory written by Barry Simon and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.
This two-part book is a comprehensive overview of the theory of probability measures on the unit circle, viewed especially in terms of the orthogonal polynomials defined by those measures. A major theme involves the connections between the Verblunsky coefficients (the coefficients of the recurrence equation for the orthogonal polynomials) and the measures, an analog of the spectral theory of one-dimensional Schrödinger operators. Among the topics discussed along the way are the asymptotics of Toeplitz determinants (Szegö's theorems), limit theorems for the density of the zeros of orthogonal polynomials, matrix representations for multiplication by z (CMV matrices), periodic Verblunsky coefficients from the point of view of meromorphic functions on hyperelliptic surfaces, and connections between the theories of orthogonal polynomials on the unit circle and on the real line.
An Introduction To Statistical Analysis Of Random Arrays
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Author : V. L. Girko
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05
An Introduction To Statistical Analysis Of Random Arrays written by V. L. Girko and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Mathematics categories.
No detailed description available for "An Introduction to Statistical Analysis of Random Arrays".
Determining Spectra In Quantum Theory
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Author : Michael Demuth
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-12
Determining Spectra In Quantum Theory written by Michael Demuth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-09-12 with Mathematics categories.
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 Of Random Schr Dinger Operators
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Author : R. Carmona
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Spectral Theory Of Random Schr Dinger Operators written by R. Carmona and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Since the seminal work of P. Anderson in 1958, localization in disordered systems has been the object of intense investigations. Mathematically speaking, the phenomenon can be described as follows: the self-adjoint operators which are used as Hamiltonians for these systems have a ten dency to have pure point spectrum, especially in low dimension or for large disorder. A lot of effort has been devoted to the mathematical study of the random self-adjoint operators relevant to the theory of localization for disordered systems. It is fair to say that progress has been made and that the un derstanding of the phenomenon has improved. This does not mean that the subject is closed. Indeed, the number of important problems actually solved is not larger than the number of those remaining. Let us mention some of the latter: • A proof of localization at all energies is still missing for two dimen sional systems, though it should be within reachable range. In the case of the two dimensional lattice, this problem has been approached by the investigation of a finite discrete band, but the limiting pro cedure necessary to reach the full two-dimensional lattice has never been controlled. • The smoothness properties of the density of states seem to escape all attempts in dimension larger than one. This problem is particularly serious in the continuous case where one does not even know if it is continuous.