Spectral Theory Of Random Schrodinger Operators

Author : R. Carmona,J. Lacroix
Publisher : Springer Science & Business Media
Page : 611 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244882

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Spectral Theory of Random Schrödinger Operators by R. Carmona,J. Lacroix Pdf

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.

Author : Reinhard Lang
Publisher : Unknown
Page : 136 pages
File Size : 51,7 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 3662191512

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Spectral Theory of Random Schrodinger Operators by Reinhard Lang Pdf

Author : René Carmona,Jean Lacroix
Publisher : Unknown
Page : 587 pages
File Size : 45,6 Mb
Release : 1990
Category : Schrèodinger operator
ISBN : 376433486X

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Spectral Theory of Random Schrödinger Operators by René Carmona,Jean Lacroix Pdf

Author : Reinhard Lang
Publisher : Springer
Page : 133 pages
File Size : 54,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540466277

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Spectral Theory of Random Schrödinger Operators by Reinhard Lang Pdf

The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.

Author : R. Carmona,J. LaCroix
Publisher : Unknown
Page : 620 pages
File Size : 47,9 Mb
Release : 1990-01-01
Category : Electronic
ISBN : 1461244897

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Spectral Theory of Random Schrodinger Operators by R. Carmona,J. LaCroix Pdf

Author : Rafael del Río,Carlos Villegas-Blas
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 47,7 Mb
Release : 2004
Category : Schrödinger operator
ISBN : 9780821832974

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Spectral Theory of Schrodinger Operators by Rafael del Río,Carlos Villegas-Blas Pdf

This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.

Author : Margherita Disertori,Werner Kirsch,Abel Klein
Publisher : SMF
Page : 244 pages
File Size : 52,7 Mb
Release : 2008
Category : Mathematics
ISBN : UOM:39015072684635

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Random Schrödinger Operators by Margherita Disertori,Werner Kirsch,Abel Klein Pdf

During the last thirty years, random Schrodinger operators, which originated in condensed matter physics, have been studied intensively and very productively. The theory is at the crossroads of a number of mathematical fields: the theory of operators, partial differential equations, the theory of probabilities, in particular the study of stochastic processes and that of random walks and Brownian motion in a random environment. This monograph aims to give the reader a panorama of the subject, from the now-classic foundations to very recent developments.

Author : Sergio Albeverio,Anindita Balslev,Ricardo Weder
Publisher : Springer Nature
Page : 316 pages
File Size : 44,8 Mb
Release : 2021-06-03
Category : Mathematics
ISBN : 9783030684907

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Schrödinger Operators, Spectral Analysis and Number Theory by Sergio Albeverio,Anindita Balslev,Ricardo Weder Pdf

This book gives its readers a unique opportunity to get acquainted with new aspects of the fruitful interactions between Analysis, Geometry, Quantum Mechanics and Number Theory. The present book contains a number of contributions by specialists in these areas as an homage to the memory of the mathematician Erik Balslev and, at the same time, advancing a fascinating interdisciplinary area still full of potential. Erik Balslev has made original and important contributions to several areas of Mathematics and its applications. He belongs to the founders of complex scaling, one of the most important methods in the mathematical and physical study of eigenvalues and resonances of Schrödinger operators, which has been very essential in advancing the solution of fundamental problems in Quantum Mechanics and related areas. He was also a pioneer in making available and developing spectral methods in the study of important problems in Analytic Number Theory.

Author : Reinhard Lang
Publisher : Springer
Page : 0 pages
File Size : 54,6 Mb
Release : 1991-12-11
Category : Mathematics
ISBN : 3540549757

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Spectral Theory of Random Schrödinger Operators by Reinhard Lang Pdf

The interplay between the spectral theory of Schr|dinger operators and probabilistic considerations forms the main theme of these notes, written for the non-specialist reader and intended to provide a brief and elementaryintroduction to this field. An attempt is made to show basic ideas in statu nascendi and to follow their evaluation from simple beginnings through to more advanced results. The term "genetic" in the title refers to this proceedure. The author concentrates on 2 topics which, in the history of the subject, have been of major conceptual importance - on the one hand the Laplacian is a random medium and the left end of its spectrum (leading to large deviation problems for Brownian motion and the link to thenotion of entropy) and on the other, Schr|dinger operators with general ergodic potentials in one-dimensional space. Ideas and concepts are explained in the simplest, possible setting and by means of a few characteristic problems with heuristic arguments preceding rigorous proofs.

Author : Ivan Veselic
Publisher : Springer Science & Business Media
Page : 151 pages
File Size : 42,9 Mb
Release : 2008-01-02
Category : Mathematics
ISBN : 9783540726890

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Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators by Ivan Veselic Pdf

This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.

Author : A. M. Berthier
Publisher : Pitman Publishing
Page : 332 pages
File Size : 55,8 Mb
Release : 1982
Category : Differential operators
ISBN : UCAL:B4304722

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Spectral Theory and Wave Operators for the Schrödinger Equation by A. M. Berthier Pdf

Author : Hans L. Cycon,Barry Simon
Publisher : Springer Science & Business Media
Page : 337 pages
File Size : 47,9 Mb
Release : 1987
Category : Computers
ISBN : 9783540167587

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Schrödinger Operators by Hans L. Cycon,Barry Simon Pdf

Are you looking for a concise summary of the theory of Schrödinger operators? Here it is. Emphasizing the progress made in the last decade by Lieb, Enss, Witten and others, the three authors don’t just cover general properties, but also detail multiparticle quantum mechanics – including bound states of Coulomb systems and scattering theory. This corrected and extended reprint contains updated references as well as notes on the development in the field over the past twenty years.

Author : Fritz Gesztesy
Publisher : American Mathematical Soc.
Page : 466 pages
File Size : 51,6 Mb
Release : 2007
Category : Mathematical physics
ISBN : 9780821842492

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Spectral Theory and Mathematical Physics: A Festschrift in Honor of Barry Simon's 60th Birthday by Fritz Gesztesy Pdf

This Festschrift had its origins in a conference called SimonFest held at Caltech, March 27-31, 2006, to honor Barry Simon's 60th birthday. It is not a proceedings volume in the usual sense since the emphasis of the majority of the contributions is on reviews of the state of the art of certain fields, with particular focus on recent developments and open problems. The bulk of the articles in this Festschrift are of this survey form, and a few review Simon's contributions to aparticular area. Part 1 contains surveys in the areas of Quantum Field Theory, Statistical Mechanics, Nonrelativistic Two-Body and $N$-Body Quantum Systems, Resonances, Quantum Mechanics with Electric and Magnetic Fields, and the Semiclassical Limit. Part 2 contains surveys in the areas of Random andErgodic Schrodinger Operators, Singular Continuous Spectrum, Orthogonal Polynomials, and Inverse Spectral Theory. In several cases, this collection of surveys portrays both the history of a subject and its current state of the art. A substantial part of the contributions to this Festschrift are survey articles on the state of the art of certain areas with special emphasis on open problems. This will benefit graduate students as well as researchers who want to get a quick, yet comprehensiveintroduction into an area covered in this volume.

Author : Michael Demuth,M. Krishna
Publisher : Springer Science & Business Media
Page : 224 pages
File Size : 41,5 Mb
Release : 2006-09-12
Category : Mathematics
ISBN : 9780817644390

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Determining Spectra in Quantum Theory by Michael Demuth,M. Krishna Pdf

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.

Author : Leonid Pastur,Alexander Figotin
Publisher : Springer
Page : 0 pages
File Size : 48,5 Mb
Release : 1992
Category : Science
ISBN : 3642743463

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Spectra of Random and Almost-Periodic Operators by Leonid Pastur,Alexander Figotin Pdf

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.