One-Dimensional Ergodic Schrodinger Operators: I. General Theory, David Damanik, Jake Fillman

Автор: Fibich Gadi
Название: Nonlinear Schrodinger Equation
ISBN: 3319127470 ISBN-13(EAN): 9783319127477
Издательство: Springer
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Описание: The Nonlinear Schrodinger Equation

Автор: David Damanik, Jake Fillman
Название: One-Dimensional Ergodic Schrodinger Operators: I. General Theory
ISBN: 1470470861 ISBN-13(EAN): 9781470470869
Издательство: Mare Nostrum (Eurospan)
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Цена: 71060.00 T
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Описание: The theory of one-dimensional ergodic operators involves a beautiful synthesis of ideas from dynamical systems, topology, and analysis. Additionally, this setting includes many models of physical interest, including those operators that model crystals, disordered media, or quasicrystals. This field has seen substantial progress in recent decades, much of which has yet to be discussed in textbooks.Beginning with a refresher on key topics in spectral theory, this volume presents the basic theory of discrete one-dimensional Schrodinger operators with dynamically defined potentials. It also includes a self-contained introduction to the relevant aspects of ergodic theory and topological dynamics.This text is accessible to graduate students who have completed one-semester courses in measure theory and complex analysis. It is intended to serve as an introduction to the field for junior researchers and beginning graduate students as well as a reference text for people already working in this area. It is well suited for self-study and contains numerous exercises (many with hints).

Автор: Hayato Nawa, Hiroaki Kikuchi, Slim Ibrahim, Takafumi Akahori
Название: Global Dynamics Above the Ground State Energy for the Combined Power-Type Nonlinear Schrodinger Equations with Energy-Critical Growth at Low Frequencies
ISBN: 1470448726 ISBN-13(EAN): 9781470448721
Издательство: Mare Nostrum (Eurospan)
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Цена: 80390.00 T
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Описание: Focuses on the combined power-type nonlinear Schrodinger equations with energy-critical growth, and studies the solutions slightly above the ground state threshold at low frequencies to obtain a so-called nine-set theory developed by Nakanishi and Schlag.

Автор: Yulia Karpeshina, Roman Shterenberg
Название: Extended States for the Schrodinger Operator with Quasi-Periodic Potential in Dimension Two
ISBN: 1470435438 ISBN-13(EAN): 9781470435431
Издательство: Mare Nostrum (Eurospan)
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Цена: 83160.00 T
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Описание: Considers a Schrodinger operator $H=-\Delta +V(\vec x)$ in dimension two with a quasi-periodic potential $V(\vec x)$. The authors prove that the absolutely continuous spectrum of $H$ contains a semiaxis and there is a family of generalized eigenfunctions at every point of this semiaxis with the following properties.

Автор: Carles Remi
Название: Semi-Classical Analysis for Nonlinear Schrodinger Equations: Wkb Analysis, Focal Points, Coherent States (Second Edition)
ISBN: 981122790X ISBN-13(EAN): 9789811227905
Издательство: World Scientific Publishing
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Описание: The second edition of this book consists of three parts.

Автор: Agmon Shmuel
Название: Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrodinger Operations. (MN-29)
ISBN: 0691613672 ISBN-13(EAN): 9780691613673
Издательство: Wiley
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Цена: 31680.00 T
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Описание: Mathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper

Автор: Valentino A. Simpao
Название: Understanding the Schrodinger Equation: Some [Non]Linear Perspectives
ISBN: 1536176621 ISBN-13(EAN): 9781536176629
Издательство: Nova Science
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Описание: The current offering from Nova Science Publishers titled Understanding the Schrodinger Equation: Some [Non]Linear Perspectives is a collection of selectively invited manuscripts from some of the worlds leading workers in quantum dynamics; particularly as concerning Schrodingers wavefunction formalism. The work is dedicated to providing an illustrative sketch of a few of the numerous and sundry aspects of the Schrodinger equation; ranging from a new pedagogical teaching approach, to technical applications and foundational considerations. Towards this end, the work is generally of a theoretical nature; expounding various physical aspects of both linear and nonlinear Schrodinger systems and their attendant mathematical developments. Expressly, the book contains A chapter meant to give a new pedagogical paradigm for teaching an understanding of quantum mechanics, via the Schrodinger equation as an extension of probability theory. A chapter addressing the Schrodinger equation written in the second quantization formalism, derived from first principles; towards a deeper understanding of classical-quantum correspondence. A chapter discussing the connection between the Schrodinger equation and one of the most intuitive research fields in classical mechanics: the theory of nonlinear water waves. A chapter which investigates wave solutions of the generalized nonlinear time-dependent Schrodinger-like equation describing a cosmogonical body formation. A chapter addressing the nonlinear Schrodinger equation: a mathematical model with its wide-ranging applications and analytical results. A chapter investigating analytical self-similar and traveling-wave solutions of the Madelung equations obtained from the Schrodinger equation. A chapter which puts forth a novel paradigm of infinite dimensional quantum phase space extension of the Schrodinger equation. A chapter which discusses a metaplectic Bohmian formalism from classical (Hamiltons equations) to quantum physics (Schrodingers equation): the Metatron. The book is written in a lucid style, nicely marrying physical intuition with mathematical insight. As such, it should be of interest to workers in Schrodinger theory and related areas, and generally, to those who seek a deeper understanding of some of the linear and nonlinear perspectives of the Schrodinger equation.

Автор: Urbański Roy Munday Mariusz Mario
Название: Ergodic Theory - Finite and Infinite, Thermodynamic Formalism, Symbolic Dynamics and Distance Expanding Maps
ISBN: 3110702649 ISBN-13(EAN): 9783110702644
Издательство: Walter de Gruyter
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Цена: 275170.00 T
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Описание:

The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.

Автор: Sara Munday, Marc Kessebohmer, Bernd Otto Stratmann
Название: Infinite Ergodic Theory of Numbers
ISBN: 3110439417 ISBN-13(EAN): 9783110439410
Издательство: Walter de Gruyter
Цена: 61920.00 T
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Описание: By connecting dynamical systems and number theory, this graduate textbook on ergodic theory acts as an introduction to a highly active area of mathematics, where a variety of strands of research open up. The text explores various concepts in infinite ergodic theory, always using continued fractions and other number-theoretic dynamical systems as illustrative examples. Contents:PrefaceMathematical symbolsNumber-theoretical dynamical systemsBasic ergodic theoryRenewal theory and ?-sum-level setsInfinite ergodic theoryApplications of infinite ergodic theoryBibliographyIndex

Автор: Ya. Sinai,
Название: Introduction to ergodic theory,
ISBN: 0691081824 ISBN-13(EAN): 9780691081823
Издательство: Wiley
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Цена: 73920.00 T
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Описание: This monograph examines new areas of ergodic theory, describing entropy theory, elements of the renormalization group method in the theory of dynamical systems, the splitting of separatrices, and problems related to the theory of hyperbolic dynamical systems.

Автор: Pei-Dong Liu; Min Qian
Название: Smooth Ergodic Theory of Random Dynamical Systems
ISBN: 3540600043 ISBN-13(EAN): 9783540600046
Издательство: Springer
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Цена: 41920.00 T
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Описание: This text studies ergodic-theoretic aspects of random dynamical systems, for example, deterministic systems with noise. It aims to present a systematic treatment of a series of recent results concerning invariant measures, entropy and Lyapunov exponents of such systems.

Автор: Alexander M. Blokh, Leonid A. Bunimovich, Paul H. Jung, Lex G. Oversteegen, Yakov G. Sinai
Название: Dynamical Systems, Ergodic Theory, and Probability: In Memory of Kolya Chernov
ISBN: 1470427737 ISBN-13(EAN): 9781470427733
Издательство: Mare Nostrum (Eurospan)
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Цена: 110880.00 T
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Описание: Contains the proceedings of the Conference on Dynamical Systems, Ergodic Theory, and Probability, held in May 2015, at the University of Alabama. The book is devoted to recent advances in the theory of chaotic and weakly chaotic dynamical systems and its applications to statistical mechanics. The papers present new original results as well as comprehensive surveys.