• Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics

Random Operators


Author: Michael Aizenman,Simone Warzel
Publisher: American Mathematical Soc.
ISBN: 1470419130
Category: Functional analysis -- Miscellaneous applications of functional analysis -- Applications in quantum physics
Page: 326
View: 5326
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.

    • Mathematics

Random Operator Theory


Author: Reza Saadati
Publisher: Academic Press
ISBN: 0081009550
Category: Mathematics
Page: 82
View: 8828
Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. Explores random differentiation and random integral equations Delves into the study of random operator theory Discusses the concept of random Banach algebras and its applications

    • Mathematics

Random Linear Operators


Author: A.V. Skorohod
Publisher: Springer Science & Business Media
ISBN: 9781402003264
Category: Mathematics
Page: 200
View: 2508
It isn't that they can't see Approach your problems from the solution. the right end and begin with It is that they can't see the the answers. Then one day, perhaps you will find the problem. final question. G. K. Chesterton. The Scandal 'The Hermit Clad in Crane of Father Brown 'The Point of a Pin'. Feathers' in R. van Gulik's The Chinese Maze l1urders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

    • Computers

Random Integral Equations


Author: Bharucha-Reid
Publisher: Academic Press
ISBN: 008095605X
Category: Computers
Page: 266
View: 2098
Random Integral Equations


    • Mathematics

Random Operator Theory


Author: Reza Saadati
Publisher: Academic Press
ISBN: 0081009550
Category: Mathematics
Page: 82
View: 7242
Random Operator Theory provides a comprehensive discussion of the random norm of random bounded linear operators, also providing important random norms as random norms of differentiation operators and integral operators. After providing the basic definition of random norm of random bounded linear operators, the book then delves into the study of random operator theory, with final sections discussing the concept of random Banach algebras and its applications. Explores random differentiation and random integral equations Delves into the study of random operator theory Discusses the concept of random Banach algebras and its applications

    • Random matrices

Theory of Stochastic Canonical Equations


Author: Vi͡acheslav Leonidovich Girko
Publisher: Springer Science & Business Media
ISBN: 9781402000744
Category: Random matrices
Page: 463
View: 7731

    • Random operators

Random Schrodinger Operators


Author: Margherita Disertori,Werner Kirsch,Abel Klein
Publisher: N.A
ISBN: 9782856292549
Category: Random operators
Page: 213
View: 6122

    • Mathematics

Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators


Author: Ivan Veselic
Publisher: Springer Science & Business Media
ISBN: 3540726896
Category: Mathematics
Page: 142
View: 2920
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.

    • Mathematics

Proceedings of the St. Petersburg Mathematical Society


Author: O. A. Ladyzhenskaya
Publisher: American Mathematical Soc.
ISBN: 9780821806135
Category: Mathematics
Page: 250
View: 9856
This volume is devoted to analysis, probablility and applications. It includes useful surveys by Pastur on random operators and their applications, Feldman on harmonic analysis and analogues of Levi-Khinchin formulas on abelian groups, and Kerov on application of representation theory of symmetric groups to classical analysis. Also featured are products of random operators, convolution of abelian groups, orthogonal polynomials, and semiordered Banach spaces.

    • Political Science

The Operators

The Wild and Terrifying Inside Story of America's War in Afghanistan
Author: Michael Hastings
Publisher: Penguin
ISBN: 1101575484
Category: Political Science
Page: 432
View: 5631
The inspiration for the Netflix original movie War Machine, starring Brad Pitt, Tilda Swinton, and Ben Kingsley From the author of The Last Magazine, a shocking behind-the-scenes portrait of our military commanders, their high-stake maneuvers, and the politcal firestorm that shook the United States. In the shadow of the hunt for Bin Laden and the United States’ involvement in the Middle East, General Stanley McChrystal, the commanding general of international and U.S. forces in Afghanistan, was living large. His loyal staff liked to call him a “rock star.” During a spring 2010 trip, journalist Michael Hastings looked on as McChrystal and his staff let off steam, partying and openly bashing the Obama administration. When Hastings’s article appeared in Rolling Stone, it set off a political firestorm: McChrystal was unceremoniously fired. In The Operators, Hastings picks up where his Rolling Stone coup ended. From patrol missions in the Afghan hinterlands to senior military advisors’ late-night bull sessions to hotel bars where spies and expensive hookers participate in nation-building, Hastings presents a shocking behind-the-scenes portrait of what he fears is an unwinnable war. Written in prose that is at once eye-opening and other times uncannily conversational, readers of No Easy Day will take to Hastings’ unyielding first-hand account of the Afghan War and its cast of players.

    • Mathematics

Set Valued Mappings with Applications in Nonlinear Analysis


Author: Donal O'Regan,Ravi P. Agarwal
Publisher: CRC Press
ISBN: 9780203216491
Category: Mathematics
Page: 480
View: 2017
Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.

    • Mathematics

Spectral Theory of Random Schrödinger Operators


Author: R. Carmona,J. Lacroix
Publisher: Springer Science & Business Media
ISBN: 1461244889
Category: Mathematics
Page: 589
View: 7621
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.

    • Mathematics

Quantum Graphs and Their Applications

Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on Quantum Graphs and Their Applications, June 19-23, 2005, Snowbird, Utah
Author: Gregory Berkolaiko
Publisher: American Mathematical Soc.
ISBN: 0821837656
Category: Mathematics
Page: 307
View: 8485
This volume is a collection of articles dedicated to quantum graphs, a newly emerging interdisciplinary field related to various areas of mathematics and physics. The reader can find a broad overview of the theory of quantum graphs. The articles present methods coming from different areas of mathematics: number theory, combinatorics, mathematical physics, differential equations, spectral theory, global analysis, and theory of fractals. They also address various important applications, such as Anderson localization, electrical networks, quantum chaos, mesoscopic physics, superconductivity, optics, and biological modeling.

    • Distribution (Probability theory)

Mathematical Results in Quantum Mechanics

International Conference in Blossin (Germany), May 17-21, 1993
Author: Michael Demuth
Publisher: Springer Science & Business Media
ISBN: 9783764350253
Category: Distribution (Probability theory)
Page: 356
View: 2983
This book contains the proceedings of the International Conference on Mathematical Results in Quantum Mechanics held in Blossin, Germany, May 17-21, 1993. Its purpose is to draw attention to the recent developments in quantum mechanics and related mathematical problems. The book is addressed to the wide audience of mathematicians and physicists interested in contemporary quantum physics and associated mathematical problems. The reader will find sections not only on traditional subjects such as Schrödinger and Dirac operators and generalized Schrödinger generators, but also on stochastic spectral analysis, many-body problems and statistical physics, chaos, and operator theory and its applications. Contributors: Schrödinger and Dirac operators: M.Sh. Birman, V. Grecchi, R. Hempel, M. Hoffmann-Ostenhof, Y. Saito, G. Stolz, M. Znojil • Generalized Schrödinger operators: J.-P. Antoine, J.F. Brasche, P. Duclos, R. Hempel, M. Klein, P. Stovicek • Stochastic spectral analysis: M. Demuth, V.A. Liskevich, E.M. Ouhabaz, P. Stollmann • Many-body problems and statistical physics: M. Fannes, R. Gielerak, M. Hübner, A.M. Khorunzhy, H. Lange, N. Macris, Yu.A. Petrina, K.B. Sinha, A. Verbeure • Chaos: J. Dittrich, P. Seba, K. Zyczkowski • Operator theory and its application: F. Bentosela, V. Buslaev, A.N. Kochubei, A.Yu. Konstantinov, V. Koshmanenko, H. Neidhardt, G. Nenciu, D. Robert

    • Mathematics

Multi-scale Analysis for Random Quantum Systems with Interaction


Author: Victor Chulaevsky,Yuri Suhov
Publisher: Springer Science & Business Media
ISBN: 1461482267
Category: Mathematics
Page: 238
View: 4220
The study of quantum disorder has generated considerable research activity in mathematics and physics over past 40 years. While single-particle models have been extensively studied at a rigorous mathematical level, little was known about systems of several interacting particles, let alone systems with positive spatial particle density. Creating a consistent theory of disorder in multi-particle quantum systems is an important and challenging problem that largely remains open. Multi-scale Analysis for Random Quantum Systems with Interaction presents the progress that had been recently achieved in this area. The main focus of the book is on a rigorous derivation of the multi-particle localization in a strong random external potential field. To make the presentation accessible to a wider audience, the authors restrict attention to a relatively simple tight-binding Anderson model on a cubic lattice Zd. This book includes the following cutting-edge features: an introduction to the state-of-the-art single-particle localization theory an extensive discussion of relevant technical aspects of the localization theory a thorough comparison of the multi-particle model with its single-particle counterpart a self-contained rigorous derivation of both spectral and dynamical localization in the multi-particle tight-binding Anderson model. Required mathematical background for the book includes a knowledge of functional calculus, spectral theory (essentially reduced to the case of finite matrices) and basic probability theory. This is an excellent text for a year-long graduate course or seminar in mathematical physics. It also can serve as a standard reference for specialists.

    • Architecture

Stochastic Analysis and Random Maps in Hilbert Space


Author: A. A. Dorogovt͡sev
Publisher: VSP
ISBN: 9789067641630
Category: Architecture
Page: 109
View: 6512
This book is devoted to stochastic operators in Hilbert space. A number of models in modern probability theory apply the notion of a stochastic operator in explicit or latent form. In this book, objects from the Gaussian case are considered. Therefore, it is useful to consider all random variables and elements as functionals from the Wiener process or its formal derivative, i.e. white noise. The book consists of five chapters. The first chapter is devoted to stochastic calculus and its main goal is to prepare the tools for solving stochastic equations. In the second chapter the structure of stochastic equations, mainly the structure of Gaussian strong linear operators, is studied. In chapter 3 the definition of the action of the stochastic operator on random elements in considered. Chapter 4 deals with the mathematical models in which the notions of stochastic calculus arise and in the final chapter the equation with random operators is considered.