Nonlinear Dirac Equation in Bose-Einstein Condensates PDF Download
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Author: Laith H. Haddad
Publisher:
ISBN:
Category : Bose-Einstein condensation
Languages : en
Pages : 353
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Book Description
Author: Laith H. Haddad
Publisher:
ISBN:
Category : Bose-Einstein condensation
Languages : en
Pages : 353
Get Book Here
Book Description
Author: Victoriano Carmona
Publisher: Springer
ISBN: 3319667661
Category : Science
Languages : en
Pages : 428
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Book Description
This book is part of a two volume set which presents the analysis of nonlinear phenomena as a long-standing challenge for research in basic and applied science as well as engineering. It discusses nonlinear differential and differential equations, bifurcation theory for periodic orbits and global connections. The integrability and reversibility of planar vector fields and theoretical analysis of classic physical models are sketched. This first volume concentrates on the mathematical theory and computational techniques that are essential for the study of nonlinear science, a second volume deals with real-world nonlinear phenomena in condensed matter, biology and optics.
Author: Panayotis G. Kevrekidis
Publisher: Springer Science & Business Media
ISBN: 3540735917
Category : Science
Languages : en
Pages : 398
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Book Description
This book, written by experts in the fields of atomic physics and nonlinear science, covers the important developments in a special aspect of Bose-Einstein condensation, namely nonlinear phenomena in condensates. Topics covered include bright, dark, gap and multidimensional solitons; vortices; vortex lattices; optical lattices; multicomponent condensates; mathematical methods/rigorous results; and the beyond-the-mean-field approach.
Author: Nabile Boussaïd
Publisher: American Mathematical Soc.
ISBN: 1470443953
Category : Education
Languages : en
Pages : 297
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Book Description
This monograph gives a comprehensive treatment of spectral (linear) stability of weakly relativistic solitary waves in the nonlinear Dirac equation. It turns out that the instability is not an intrinsic property of the Dirac equation that is only resolved in the framework of the second quantization with the Dirac sea hypothesis. Whereas general results about the Dirac-Maxwell and similar equations are not yet available, we can consider the Dirac equation with scalar self-interaction, the model first introduced in 1938. In this book we show that in particular cases solitary waves in this model may be spectrally stable (no linear instability). This result is the first step towards proving asymptotic stability of solitary waves. The book presents the necessary overview of the functional analysis, spectral theory, and the existence and linear stability of solitary waves of the nonlinear Schrödinger equation. It also presents the necessary tools such as the limiting absorption principle and the Carleman estimates in the form applicable to the Dirac operator, and proves the general form of the Dirac-Pauli theorem. All of these results are used to prove the spectral stability of weakly relativistic solitary wave solutions of the nonlinear Dirac equation.
Author: Amandine Aftalion
Publisher: Springer Science & Business Media
ISBN: 081764492X
Category : Mathematics
Languages : en
Pages : 212
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Book Description
This book provides an up-to-date approach to the diagnosis and management of endocarditis based on a critical analysis of the recent studies. It is the only up-to-date clinically oriented textbook available on this subject. The book is structured in a format that is easy to follow, clinically relevant and evidence based. The author has a special interest in the application of ultrasound in the study of cardiac structure and function.
Author: Kuppuswamy Porsezian
Publisher: CRC Press
ISBN: 1351831100
Category : Science
Languages : en
Pages : 630
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Book Description
Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications presents a collection of breakthrough research portraying the odyssey of light from optical solitons to optical rogue waves in nonlinear optical fibers. The book provides a simple yet holistic view on the theoretical and application-oriented aspects of light, with a special focus on the underlying nonlinear phenomena. Exploring the very frontiers of light-wave technology, the text covers the basics of nonlinear fiberoptics and the dynamics of electromagnetic pulse propagation in nonlinear waveguides. It also highlights some of the latest advances in nonlinear optical fiber technology, discussing hidden symmetry reductions and Ablowitz–Kaup–Newell–Segur (AKNS) hierarchies for nonautonomous solitons, state-of-the-art Brillouin scattering applications, backpropagation, and the concept of eigenvalue communication—a powerful nonlinear digital signal processing technique that paves the way to overcome the current limitations of traditional communications methods in nonlinear fiber channels. Key chapters study the feasibility of the eigenvalue demodulation scheme based on digital coherent technology by throwing light on the experimental study of the noise tolerance of the demodulated eigenvalues, investigate matter wave solitons and other localized excitations pertaining to Bose–Einstein condensates in atom optics, and examine quantum field theory analogue effects occurring in binary waveguide arrays, plasmonic arrays, etc., as well as their ensuing nonlinear wave propagation. Featuring a foreword by Dr. Akira Hasegawa, the father of soliton communication systems, Odyssey of Light in Nonlinear Optical Fibers: Theory and Applications serves as a curtain raiser to usher in the photonics era. The technological innovations at the core of the book form the basis for the next generation of ultra-high speed computers and telecommunication devices.
Author: Shōsuke Sasaki
Publisher: Nova Novinka
ISBN: 9781616687540
Category : Science
Languages : en
Pages : 172
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Book Description
Bose--Einstein condensation was discovered in atomic gas systems, where Bose condensate occupies 100% of the total system at zero temperature. Liquid helium systems have been investigated based on the Landau theory, where the superfluid component of liquid helium is background flow. According to the Landau theory, it is doubtful that the superfluid component is a Bose condensate. In experiments, the probability of helium atoms with zero momentum is a few percent of the total liquid helium at ultra-low temperatures. However, the superfluid component occupies 100% of the liquid helium at zero temperature, as macroscopic observations indicate. This book introduces a quasi-particle representing an eigenstate of the total Hamiltonian.
Author: Alessandro Michelangeli
Publisher: Springer Nature
ISBN: 3030604535
Category : Science
Languages : en
Pages : 331
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Book Description
Since long over the decades there has been a large transversal community of mathematicians grappling with the sophisticated challenges of the rigorous modelling and the spectral and scattering analysis of quantum systems of particles subject to an interaction so much localised to be considered with zero range. Such a community is experiencing fruitful and inspiring exchanges with experimental and theoretical physicists. This volume reflects such spirit, with a diverse range of original contributions by experts, presenting an up-to-date collection of most relevant results and challenging open problems. It has been conceived with the deliberate two-fold purpose of serving as an updated reference for recent results, mathematical tools, and the vast related literature on the one hand, and as a bridge towards several key open problems that will surely form the forthcoming research agenda in this field.
Author: Keith Burnett (Ed); Mark Edwar
Publisher: DIANE Publishing
ISBN: 0788137409
Category :
Languages : en
Pages : 213
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Book Description
Among the most remarkable effects that quantum mechanics adds to the catalog of the thermal properties of matter is "condensation" of an ideal gas of identical particles into a single quantum state, the principle of which was discovered in the theory of statistical mechanics by Bose and Einstein in the 1920s. Bose-Einstein condensation (BEC) is a mechanism for producing a macroscopic quantum system, and is exemplary of the macroscopic quantum phenomena of superconductivity and superfluidity.These 15 papers provide an introduction to current work on BEC.
Author: Claude Daviau
Publisher:
ISBN: 9781907343582
Category : Mathematics
Languages : en
Pages : 0
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Book Description
Beginnings of quantum mechanics are revised and the author starts from the point where relativity and quantum mechanics were compatible. A modified wave equation for the electron is used. The relativistic invariance is then enlarged to a greater invariance group and the first consequences are studied. This invariance applies to the whole electromagnetism, including magnetic monopoles. Another space-time variety is seen which is very different from the usual relativistic space-time.
