Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schr dinger Equation AM 154 written by Spyridon Kamvissis and published by Princeton University Press. This book was released on 2003-08-18 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book represents the first asymptotic analysis, via completely integrable techniques, of the initial value problem for the focusing nonlinear Schrödinger equation in the semiclassical asymptotic regime. This problem is a key model in nonlinear optical physics and has increasingly important applications in the telecommunications industry. The authors exploit complete integrability to establish pointwise asymptotics for this problem's solution in the semiclassical regime and explicit integration for the underlying nonlinear, elliptic, partial differential equations suspected of governing the semiclassical behavior. In doing so they also aim to explain the observed gradient catastrophe for the underlying nonlinear elliptic partial differential equations, and to set forth a detailed, pointwise asymptotic description of the violent oscillations that emerge following the gradient catastrophe. To achieve this, the authors have extended the reach of two powerful analytical techniques that have arisen through the asymptotic analysis of integrable systems: the Lax-Levermore-Venakides variational approach to singular limits in integrable systems, and Deift and Zhou's nonlinear Steepest-Descent/Stationary Phase method for the analysis of Riemann-Hilbert problems. In particular, they introduce a systematic procedure for handling certain Riemann-Hilbert problems with poles accumulating on curves in the plane. This book, which includes an appendix on the use of the Fredholm theory for Riemann-Hilbert problems in the Hölder class, is intended for researchers and graduate students of applied mathematics and analysis, especially those with an interest in integrable systems, nonlinear waves, or complex analysis.
Download or read book Semiclassical Soliton Ensembles for the Focusing Nonlinear Schr dinger Equation written by Spyridon Kamvissis and published by . This book was released on 2002 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Discrete Orthogonal Polynomials AM 164 written by J. Baik and published by Princeton University Press. This book was released on 2007-01-02 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the theory and applications of discrete orthogonal polynomials--polynomials that are orthogonal on a finite set. Unlike other books, Discrete Orthogonal Polynomials addresses completely general weight functions and presents a new methodology for handling the discrete weights case. J. Baik, T. Kriecherbauer, K. T.-R. McLaughlin & P. D. Miller focus on asymptotic aspects of general, nonclassical discrete orthogonal polynomials and set out applications of current interest. Topics covered include the probability theory of discrete orthogonal polynomial ensembles and the continuum limit of the Toda lattice. The primary concern throughout is the asymptotic behavior of discrete orthogonal polynomials for general, nonclassical measures, in the joint limit where the degree increases as some fraction of the total number of points of collocation. The book formulates the orthogonality conditions defining these polynomials as a kind of Riemann-Hilbert problem and then generalizes the steepest descent method for such a problem to carry out the necessary asymptotic analysis.
Download or read book Rogue and Shock Waves in Nonlinear Dispersive Media written by Miguel Onorato and published by Springer. This book was released on 2016-09-19 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained set of lectures addresses a gap in the literature by providing a systematic link between the theoretical foundations of the subject matter and cutting-edge applications in both geophysical fluid dynamics and nonlinear optics. Rogue and shock waves are phenomena that may occur in the propagation of waves in any nonlinear dispersive medium. Accordingly, they have been observed in disparate settings – as ocean waves, in nonlinear optics, in Bose-Einstein condensates, and in plasmas. Rogue and dispersive shock waves are both characterized by the development of extremes: for the former, the wave amplitude becomes unusually large, while for the latter, gradients reach extreme values. Both aspects strongly influence the statistical properties of the wave propagation and are thus considered together here in terms of their underlying theoretical treatment. This book offers a self-contained graduate-level text intended as both an introduction and reference guide for a new generation of scientists working on rogue and shock wave phenomena across a broad range of fields in applied physics and geophysics.
Download or read book Semi classical Analysis for Nonlinear Schr dinger Equations written by Rmi Carles and published by World Scientific. This book was released on 2008 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes review recent results on the high-frequency analysis of nonlinear Schrdinger equations in the presence of an external potential. The book consists of two relatively independent parts: WKB analysis, and caustic crossing. In the first part, the basic linear WKB theory is constructed and then extended to the nonlinear framework. The most difficult supercritical case is discussed in detail, together with some of its consequences concerning instability phenomena. Applications of WKB analysis to functional analysis, in particular to the Cauchy problem for nonlinear Schrdinger equations, are also given. In the second part, caustic crossing is described, especially when the caustic is reduced to a point, and the link with nonlinear scattering operators is investigated.These notes are self-contained and combine selected articles written by the author over the past ten years in a coherent manner, with some simplified proofs. Examples and figures are provided to support the intuition, and comparisons with other equations such as the nonlinear wave equation are provided.
Download or read book Wigner Measure and Semiclassical Limits of Nonlinear Schr dinger Equations written by Ping Zhang and published by American Mathematical Soc.. This book was released on 2008 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is based on a course entitled ``Wigner measures and semiclassical limits of nonlinear Schrodinger equations,'' which the author taught at the Courant Institute of Mathematical Sciences at New York University in the spring of 2007. The author's main purpose is to apply the theory of semiclassical pseudodifferential operators to the study of various high-frequency limits of equations from quantum mechanics. In particular, the focus of attention is on Wigner measure and recent progress on how to use it as a tool to study various problems arising from semiclassical limits of Schrodinger-type equations. At the end of each chapter, the reader will find references and remarks about recent progress on related problems. The book is self-contained and is suitable for an advanced graduate course on the topic.
Download or read book Mathematical Reviews written by and published by . This book was released on 2004 with total page 1574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Condensed Matter Field Theory written by Alexander Altland and published by Cambridge University Press. This book was released on 2010-03-11 with total page 785 pages. Available in PDF, EPUB and Kindle. Book excerpt: This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Download or read book Wave Turbulence written by Sergey Nazarenko and published by Springer Science & Business Media. This book was released on 2011-02-12 with total page 287 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wave Turbulence refers to the statistical theory of weakly nonlinear dispersive waves. There is a wide and growing spectrum of physical applications, ranging from sea waves, to plasma waves, to superfluid turbulence, to nonlinear optics and Bose-Einstein condensates. Beyond the fundamentals the book thus also covers new developments such as the interaction of random waves with coherent structures (vortices, solitons, wave breaks), inverse cascades leading to condensation and the transitions between weak and strong turbulence, turbulence intermittency as well as finite system size effects, such as “frozen” turbulence, discrete wave resonances and avalanche-type energy cascades. This book is an outgrow of several lectures courses held by the author and, as a result, written and structured rather as a graduate text than a monograph, with many exercises and solutions offered along the way. The present compact description primarily addresses students and non-specialist researchers wishing to enter and work in this field.
Download or read book Introduction to Quantum Optics written by Gilbert Grynberg and published by Cambridge University Press. This book was released on 2010-09-02 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering a number of important subjects in quantum optics, this textbook is an excellent introduction for advanced undergraduate and beginning graduate students, familiarizing readers with the basic concepts and formalism as well as the most recent advances. The first part of the textbook covers the semi-classical approach where matter is quantized, but light is not. It describes significant phenomena in quantum optics, including the principles of lasers. The second part is devoted to the full quantum description of light and its interaction with matter, covering topics such as spontaneous emission, and classical and non-classical states of light. An overview of photon entanglement and applications to quantum information is also given. In the third part, non-linear optics and laser cooling of atoms are presented, where using both approaches allows for a comprehensive description. Each chapter describes basic concepts in detail, and more specific concepts and phenomena are presented in 'complements'.
Download or read book Electromagnetic Noise and Quantum Optical Measurements written by Hermann A. Haus and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews: "Haus’ book provides numerous insights on topics of wide importance, and contains much material not available elsewhere in book form. [...] an indispensable resource for those working in quantum optics or electronics." Optics & Photonics News
Download or read book The Mother Body Phase Transition in the Normal Matrix Model written by Pavel M. Bleher and published by American Mathematical Soc.. This book was released on 2020-09-28 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this present paper, the authors consider the normal matrix model with cubic plus linear potential.
Download or read book A Dressing Method in Mathematical Physics written by Evgeny V. Doktorov and published by Springer Science & Business Media. This book was released on 2007-05-30 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph systematically develops and considers the so-called "dressing method" for solving differential equations (both linear and nonlinear), a means to generate new non-trivial solutions for a given equation from the (perhaps trivial) solution of the same or related equation. The primary topics of the dressing method covered here are: the Moutard and Darboux transformations discovered in XIX century as applied to linear equations; the Bäcklund transformation in differential geometry of surfaces; the factorization method; and the Riemann-Hilbert problem in the form proposed by Shabat and Zakharov for soliton equations, plus its extension in terms of the d-bar formalism. Throughout, the text exploits the “linear experience” of presentation, with special attention given to the algebraic aspects of the main mathematical constructions and to practical rules of obtaining new solutions. Various linear equations of classical and quantum mechanics are solved by the Darboux and factorization methods. An extension of the classical Darboux transformations to nonlinear equations in 1+1 and 2+1 dimensions, as well as its factorization, are also discussed in detail. What’s more, the applicability of the local and non-local Riemann-Hilbert problem-based approach and its generalization in terms of the d-bar method are illustrated via various nonlinear equations.
Download or read book Quantum Mechanics for Scientists and Engineers written by David A. B. Miller and published by Cambridge University Press. This book was released on 2008-04-21 with total page 575 pages. Available in PDF, EPUB and Kindle. Book excerpt: If you need a book that relates the core principles of quantum mechanics to modern applications in engineering, physics, and nanotechnology, this is it. Students will appreciate the book's applied emphasis, which illustrates theoretical concepts with examples of nanostructured materials, optics, and semiconductor devices. The many worked examples and more than 160 homework problems help students to problem solve and to practise applications of theory. Without assuming a prior knowledge of high-level physics or classical mechanics, the text introduces Schrödinger's equation, operators, and approximation methods. Systems, including the hydrogen atom and crystalline materials, are analyzed in detail. More advanced subjects, such as density matrices, quantum optics, and quantum information, are also covered. Practical applications and algorithms for the computational analysis of simple structures make this an ideal introduction to quantum mechanics for students of engineering, physics, nanotechnology, and other disciplines. Additional resources available from www.cambridge.org/9780521897839.
Download or read book Ultrashort Laser Pulse Phenomena written by Jean-Claude Diels and published by Elsevier. This book was released on 2006-09-21 with total page 675 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ultrashort Laser Pulse Phenomena, Second Edition serves as an introduction to the phenomena of ultra short laser pulses and describes how this technology can be used to examine problems in areas such as electromagnetism, optics, and quantum mechanics. Ultrashort Laser Pulse Phenomena combines theoretical backgrounds and experimental techniques and will serve as a manual on designing and constructing femtosecond ("faster than electronics") systems or experiments from scratch. Beyond the simple optical system, the various sources of ultrashort pulses are presented, again with emphasis on the basic concepts and how they apply to the design of particular sources (dye lasers, solid state lasers, semiconductor lasers, fiber lasers, and sources based on frequency conversion). Provides an easy to follow guide through "faster than electronics" probing and detection methods THE manual on designing and constructing femtosecond systems and experiments Discusses essential technology for applications in micro-machining, femtochemistry, and medical imaging
Download or read book Semiclassical Analysis written by Maciej Zworski and published by American Mathematical Soc.. This book was released on 2012 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: "...A graduate level text introducing readers to semiclassical and microlocal methods in PDE." -- from xi.
Download or read book Springer Handbook of Lasers and Optics written by Frank Träger and published by Springer Science & Business Media. This book was released on 2012-05-05 with total page 1704 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new edition features numerous updates and additions. Especially 4 new chapters on Fiber Optics, Integrated Optics, Frequency Combs and Interferometry reflect the changes since the first edition. In addition, major complete updates for the chapters: Optical Materials and Their Properties, Optical Detectors, Nanooptics, and Optics far Beyond the Diffraction Limit. Features Contains over 1000 two-color illustrations. Includes over 120 comprehensive tables with properties of optical materials and light sources. Emphasizes physical concepts over extensive mathematical derivations. Chapters with summaries, detailed index Delivers a wealth of up-to-date references.
