Order,Disorder and Chaos in Quantum Systems

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Publisher : Birkhäuser
ISBN 13 : 3034873069
Total Pages : 349 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Order,Disorder and Chaos in Quantum Systems by : Exner

Download or read book Order,Disorder and Chaos in Quantum Systems written by Exner and published by Birkhäuser. This book was released on 2013-03-08 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume collects the contributions to the conference "Order, disorder and chaos in quantum systems" which was held at Dubna last October. It is the third meeting in the series started three years ago in which we tried to put together mathematical physicists from the member and non-member countries of JINR with their colleagues from soviet universities and institutes using this international centre as a convenient basis. As in the previous cases, new faces, subj ects and ideas appeared but the spirit remained the same, relaxed and inspirative. Among this conference contributions, a majority should be listed in the "orderly" category. Being more specific, this means mostly various aspects of the theory of Schroedinger operators that has been always a core of quantum mechanics. In spite of the fact that it is studied already for several decades, there are still many interesting problems to solve as some of the lectures collected below witness. At the same time, the theory extends to some new areas motivated by physical problems ; let us mention Schroedinger operators in complicated spatial domains appearing in some parts of solid-state physics or various models using the concept of contact interactions. Our world is far from perfect and to keep a perfect order is difficult not only in everyday life but also in most physical systems. Theoreticians are used to take this fact into account introducing stochastic factors into their considerations.

Quantum Chaos

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Publisher : Cambridge University Press
ISBN 13 : 052143291X
Total Pages : 703 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis Quantum Chaos by : Giulio Casati

Download or read book Quantum Chaos written by Giulio Casati and published by Cambridge University Press. This book was released on 1995-04-27 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of our understanding of chaotic behaviour in quantum systems.

Mathematical Results in Quantum Mechanics

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Publisher : Birkhäuser
ISBN 13 : 3034885458
Total Pages : 346 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Mathematical Results in Quantum Mechanics by : M. Demuth

Download or read book Mathematical Results in Quantum Mechanics written by M. Demuth and published by Birkhäuser. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decades have demonstrated that quantum mechanics is an inexhaustible source of inspiration for contemporary mathematical physics. Of course, it seems to be hardly surprising if one casts a glance toward the history of the subject; recall the pioneering works of von Neumann, Weyl, Kato and their followers which pushed forward some of the classical mathematical disciplines: functional analysis, differential equations, group theory, etc. On the other hand, the evident powerful feedback changed the face of the "naive" quantum physics. It created a contem porary quantum mechanics, the mathematical problems of which now constitute the backbone of mathematical physics. The mathematical and physical aspects of these problems cannot be separated, even if one may not share the opinion of Hilbert who rigorously denied differences between pure and applied mathemat ics, and the fruitful oscilllation between the two creates a powerful stimulus for development of mathematical physics. The International Conference on Mathematical Results in Quantum Mechan ics, held in Blossin (near Berlin), May 17-21, 1993, was the fifth in the series of meetings started in Dubna (in the former USSR) in 1987, which were dedicated to mathematical problems of quantum mechanics. A primary motivation of any meeting is certainly to facilitate an exchange of ideas, but there also other goals. The first meeting and those that followed (Dubna, 1988; Dubna, 1989; Liblice (in the Czech Republic), 1990) were aimed, in particular, at paving ways to East-West contacts.

Quantum Mechanics from General Relativity

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Publisher : Springer Science & Business Media
ISBN 13 : 9400946643
Total Pages : 243 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Quantum Mechanics from General Relativity by : M. Sachs

Download or read book Quantum Mechanics from General Relativity written by M. Sachs and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a sequel to my earlier work, General Relativity and Matter [1], which will be referred to henceforth as GRM. The monograph, GRM, focuses on the full set of implications of General Relativity Theory, as a fundamental theory of matter in all domains, from elementary particle physics to cosmology. It is shown there to exhibit an explicit unification of the gravitational and electromagnetic fields of force with the inertial manifestations of matter, expressing the latter explicitly in terms of a covariant field theory within the structure of this general theory. This monograph will focus, primarily, on the special relativistic limit of the part of this general field theory of matter that deals with inertia, in the domain where quantum mechanics has been evoked in contemporary physics as a funda mental explanation for the behavior of elementary matter. Many of the results presented in this book are based on earlier published works in the journals, which will be listed in the Bibliography. These results will be presented here in an expanded form, with more discussion on the motivation and explanation for the theoretical development of the subject than space would allow in normal journal articles, and they will be presented in one place where there would then be a more unified and coherent explication of the subject.

Hilbert Space Operators in Quantum Physics

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Publisher : Springer Science & Business Media
ISBN 13 : 1402088701
Total Pages : 677 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Hilbert Space Operators in Quantum Physics by : Jirí Blank

Download or read book Hilbert Space Operators in Quantum Physics written by Jirí Blank and published by Springer Science & Business Media. This book was released on 2008-09-24 with total page 677 pages. Available in PDF, EPUB and Kindle. Book excerpt: The new edition of this book detailing the theory of linear-Hilbert space operators and their use in quantum physics contains two new chapters devoted to properties of quantum waveguides and quantum graphs. The bibliography contains 130 new items.

Singular Perturbations of Differential Operators

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Publisher : Cambridge University Press
ISBN 13 : 9780521779128
Total Pages : 454 pages
Book Rating : 4.7/5 (791 download)

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Book Synopsis Singular Perturbations of Differential Operators by : Sergio Albeverio

Download or read book Singular Perturbations of Differential Operators written by Sergio Albeverio and published by Cambridge University Press. This book was released on 2000-03-13 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a systematic mathematical study of differential (and more general self-adjoint) operators.

Binding and Scattering in Two-Dimensional Systems

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Publisher : Springer Science & Business Media
ISBN 13 : 3540666842
Total Pages : 224 pages
Book Rating : 4.5/5 (46 download)

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Book Synopsis Binding and Scattering in Two-Dimensional Systems by : J. Timothy Londergan

Download or read book Binding and Scattering in Two-Dimensional Systems written by J. Timothy Londergan and published by Springer Science & Business Media. This book was released on 1999-11-17 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is accessible to anyone with an undergraduate background in quantum mechanics, electromagnetism and some solid state physics. It describes in detail the properties of particles and fields in quasi-two-dimensional systems used to approximate realistic quantum heterostructures. Here the authors treat wires, i.e. they assume an infinite hard-wall potential for the system. They discuss bound states, the properties of transmission and reflection, conductance, etc. It is shown that the simple models developed in this book in detail are capable of understanding even complex physical phenomena. The methods are applied to optical states in photonic crystals, and similarities and differences between those and electronic states in quantum heterostructures and electromagnetic fields in waveguides are discussed.

Lectures on Probability Theory and Statistics

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Publisher : Springer
ISBN 13 : 3540449221
Total Pages : 294 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Lectures on Probability Theory and Statistics by : Sergio Albeverio

Download or read book Lectures on Probability Theory and Statistics written by Sergio Albeverio and published by Springer. This book was released on 2003-07-03 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In World Mathematical Year 2000 the traditional St. Flour Summer School was hosted jointly with the European Mathematical Society. Sergio Albeverio reviews the theory of Dirichlet forms, and gives applications including partial differential equations, stochastic dynamics of quantum systems, quantum fields and the geometry of loop spaces. The second text, by Walter Schachermayer, is an introduction to the basic concepts of mathematical finance, including the Bachelier and Black-Scholes models. The fundamental theorem of asset pricing is discussed in detail. Finally Michel Talagrand, gives an overview of the mean field models for spin glasses. This text is a major contribution towards the proof of certain results from physics, and includes a discussion of the Sherrington-Kirkpatrick and the p-spin interaction models.

Analysis as a Tool in Mathematical Physics

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Publisher : Springer Nature
ISBN 13 : 3030315312
Total Pages : 627 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Analysis as a Tool in Mathematical Physics by : Pavel Kurasov

Download or read book Analysis as a Tool in Mathematical Physics written by Pavel Kurasov and published by Springer Nature. This book was released on 2020-07-14 with total page 627 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boris Pavlov (1936-2016), to whom this volume is dedicated, was a prominent specialist in analysis, operator theory, and mathematical physics. As one of the most influential members of the St. Petersburg Mathematical School, he was one of the founders of the Leningrad School of Non-self-adjoint Operators. This volume collects research papers originating from two conferences that were organized in memory of Boris Pavlov: “Spectral Theory and Applications”, held in Stockholm, Sweden, in March 2016, and “Operator Theory, Analysis and Mathematical Physics – OTAMP2016” held at the Euler Institute in St. Petersburg, Russia, in August 2016. The volume also includes water-color paintings by Boris Pavlov, some personal photographs, as well as tributes from friends and colleagues.

Applied Chaos and Complexity Theory in Education

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Publisher : IGI Global
ISBN 13 : 1522504613
Total Pages : 322 pages
Book Rating : 4.5/5 (225 download)

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Book Synopsis Applied Chaos and Complexity Theory in Education by : Erçetin, ?efika ?ule

Download or read book Applied Chaos and Complexity Theory in Education written by Erçetin, ?efika ?ule and published by IGI Global. This book was released on 2016-05-23 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: As a field of mathematical study, chaos and complexity theory analyzes the state of dynamical systems by evaluating how they interact, evolve, and adapt. Though this theory impacts a variety of disciplines, it also has significant influence on educational systems and settings. Applied Chaos and Complexity Theory in Education examines the application of the theories of chaos and complexity in relation to educational systems and institutions. Featuring emergent research and perspectives on mathematical patterns in educational settings and instructional practices, this book is a comprehensive reference source for researchers, scholars, mathematicians, and graduate students.

Sturm?Liouville Operators, Their Spectral Theory, and Some Applications

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Publisher : American Mathematical Society
ISBN 13 : 1470476665
Total Pages : 946 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Sturm?Liouville Operators, Their Spectral Theory, and Some Applications by : Fritz Gesztesy

Download or read book Sturm?Liouville Operators, Their Spectral Theory, and Some Applications written by Fritz Gesztesy and published by American Mathematical Society. This book was released on 2024-09-24 with total page 946 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a detailed treatment of the various facets of modern Sturm?Liouville theory, including such topics as Weyl?Titchmarsh theory, classical, renormalized, and perturbative oscillation theory, boundary data maps, traces and determinants for Sturm?Liouville operators, strongly singular Sturm?Liouville differential operators, generalized boundary values, and Sturm?Liouville operators with distributional coefficients. To illustrate the theory, the book develops an array of examples from Floquet theory to short-range scattering theory, higher-order KdV trace relations, elliptic and algebro-geometric finite gap potentials, reflectionless potentials and the Sodin?Yuditskii class, as well as a detailed collection of singular examples, such as the Bessel, generalized Bessel, and Jacobi operators. A set of appendices contains background on the basics of linear operators and spectral theory in Hilbert spaces, Schatten?von Neumann classes of compact operators, self-adjoint extensions of symmetric operators, including the Friedrichs and Krein?von Neumann extensions, boundary triplets for ODEs, Krein-type resolvent formulas, sesquilinear forms, Nevanlinna?Herglotz functions, and Bessel functions.

Floquet Theory for Partial Differential Equations

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Publisher : Birkhäuser
ISBN 13 : 3034885733
Total Pages : 363 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Floquet Theory for Partial Differential Equations by : P.A. Kuchment

Download or read book Floquet Theory for Partial Differential Equations written by P.A. Kuchment and published by Birkhäuser. This book was released on 2012-12-06 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear differential equations with periodic coefficients constitute a well developed part of the theory of ordinary differential equations [17, 94, 156, 177, 178, 272, 389]. They arise in many physical and technical applications [177, 178, 272]. A new wave of interest in this subject has been stimulated during the last two decades by the development of the inverse scattering method for integration of nonlinear differential equations. This has led to significant progress in this traditional area [27, 71, 72, 111 119, 250, 276, 277, 284, 286, 287, 312, 313, 337, 349, 354, 392, 393, 403, 404]. At the same time, many theoretical and applied problems lead to periodic partial differential equations. We can mention, for instance, quantum mechanics [14, 18, 40, 54, 60, 91, 92, 107, 123, 157-160, 192, 193, 204, 315, 367, 412, 414, 415, 417], hydrodynamics [179, 180], elasticity theory [395], the theory of guided waves [87-89, 208, 300], homogenization theory [29, 41, 348], direct and inverse scattering [175, 206, 216, 314, 388, 406-408], parametric resonance theory [122, 178], and spectral theory and spectral geometry [103 105, 381, 382, 389]. There is a sjgnificant distinction between the cases of ordinary and partial differential periodic equations. The main tool of the theory of periodic ordinary differential equations is the so-called Floquet theory [17, 94, 120, 156, 177, 267, 272, 389]. Its central result is the following theorem (sometimes called Floquet-Lyapunov theorem) [120, 267].

From Phase Transitions to Chaos

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Publisher : World Scientific
ISBN 13 : 9789810209384
Total Pages : 608 pages
Book Rating : 4.2/5 (93 download)

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Book Synopsis From Phase Transitions to Chaos by : G‚za Gy”rgyi

Download or read book From Phase Transitions to Chaos written by G‚za Gy”rgyi and published by World Scientific. This book was released on 1992 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises about forty research papers and essays covering a wide range of subjects in the forefront of contemporary statistical physics. The contributors are renown scientists and leading authorities in several different fields. This book is dedicated to P‚ter Sz‚pfalusy on the occasion of his sixtieth birthday. Emphasis is placed on his two main areas of research, namely phase transitions and chaotic dynamical systems, as they share common aspects like the applicability of the probabilistic approach or scaling behaviour and universality. Several papers deal with equilibrium phase transitions, critical dynamics, and pattern formation. Also represented are disordered systems, random field systems, growth processes, and neural network. Statistical properties of interacting electron gases, such as the Kondo lattice, the Wigner crystal, and the Hubbard model, are treated. In the field of chaos, Hamiltonian transport and resonances, strange attractors, multifractal characteristics of chaos, and the effect of weak perturbations are discussed. A separate section is devoted to selected mathematical aspects of dynamical systems like the foundation of statistical mechanics, including the problem of ergodicity, and rigorous results on quantum chaos.

Classes of Linear Operators

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Publisher : Birkhäuser
ISBN 13 : 303488558X
Total Pages : 563 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Classes of Linear Operators by : Israel Gohberg

Download or read book Classes of Linear Operators written by Israel Gohberg and published by Birkhäuser. This book was released on 2013-03-09 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes constitute texts for graduate courses in linear operator theory. The reader is assumed to have a knowledge of both complex analysis and the first elements of operator theory. The texts are intended to concisely present a variety of classes of linear operators, each with its own character, theory, techniques and tools. For each of the classes, various differential and integral operators motivate or illustrate the main results. Although each class is treated seperately and the first impression may be that of many different theories, interconnections appear frequently and unexpectedly. The result is a beautiful, unified and powerful theory. The classes we have chosen are representatives of the principal important classes of operators, and we believe that these illustrate the richness of operator theory, both in its theoretical developments and in its applicants. Because we wanted the books to be of reasonable size, we were selective in the classes we chose and restricted our attention to the main features of the corresponding theories. However, these theories have been updated and enhanced by new developments, many of which appear here for the first time in an operator-theory text. In the selection of the material the taste and interest of the authors played an important role.

Operator Extensions, Interpolation of Functions and Related Topics

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Publisher : Birkhäuser
ISBN 13 : 303488575X
Total Pages : 225 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Operator Extensions, Interpolation of Functions and Related Topics by : A. Gheondea

Download or read book Operator Extensions, Interpolation of Functions and Related Topics written by A. Gheondea and published by Birkhäuser. This book was released on 2012-12-06 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since 1976 the Institute of Mathematics of the Romanian Academy (formerly the Department of Mathematics of INCREST) and the Faculty of Mathematics (formerly the Faculty of Sciences) of the University ofTimi~oara have organized several Con ferences on Operator Theory. These Conferences were held yearly in Timi~oara (or in Timi~oara and Herculane) and beginning with 1985 they were held in Bucharest (1985,1986), in Timi~oara (1988) and in Predeal (1990). At the beginning, these Conferences answered the need of a part of the Romanian Mathematical Community ofexploring other forms of survival, after the dissolution of the Institute of Mathematics in 1975. Soon, these meetings evolved to International Conferences with a broad participation and where important results in Operator Theory and Operator Algebras and their interplay with Complex Function Theory, Differential Equations, Mathematical Physics, System Theory, etc. were presented. The 14th Conference on Operator Theory was held between June 1st and June 5th 1992, at the University ofTimi~oara. It was partially supported by the Institute of Mathematics of the Romanian Academy and by the Faculty of Mathematics of the University ofTimi~oara. Another important contribution towards covering the costs of this meeting came from The Soros Foundation for an Open Society. Without this generous help the organizing of this event would be impossible. Since 1980, the Proceedings of OT Conferences were published by Birkhauser Verlag in the series Operator Theory: Advances and Applications. The abstracts of the talks were collected in the Conference Report, published by the University of Timi~oara.

Operator Theory and Boundary Eigenvalue Problems

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Publisher : Birkhäuser
ISBN 13 : 3034891067
Total Pages : 327 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Operator Theory and Boundary Eigenvalue Problems by : I. Gohberg

Download or read book Operator Theory and Boundary Eigenvalue Problems written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Workshop on Operator Theory and Boundary Eigenvalue Problems was held at the Technical University, Vienna, Austria, July 27 to 30, 1993. It was the seventh workshop in the series of IWOTA (International Workshops on Operator Theory and Applications). The main topics at the workshop were interpolation problems and analytic matrix functions, operator theory in spaces with indefinite scalar products, boundary value problems for differential and functional-differential equations and systems theory and control. The workshop covered different aspects, starting with abstract operator theory up to contrete applications. The papers in these proceedings provide an accurate cross section of the lectures presented at the workshop. This book will be of interest to a wide group of pure and applied mathematicians.

Operator Theory and Complex Analysis

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Publisher : Birkhäuser
ISBN 13 : 3034886063
Total Pages : 417 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Operator Theory and Complex Analysis by : T. Ando

Download or read book Operator Theory and Complex Analysis written by T. Ando and published by Birkhäuser. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: