The Defocusing Nonlinear Schr?dinger Equation

The Defocusing Nonlinear Schr?dinger Equation
Author: Panayotis G. Kevrekidis
Publisher: SIAM
Total Pages: 437
Release: 2015-08-04
Genre: Mathematics
ISBN: 1611973945

Bose?Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose?Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schr?dinger-type models that arise therein.?The Defocusing Nonlinear Schr?dinger Equation?is a broad study of nonlinear?excitations in self-defocusing nonlinear media. It summarizes state-of-the-art knowledge on the defocusing nonlinear Schr?dinger-type models in a single volume and contains a wealth of resources, including over 800 references to relevant articles and monographs and a meticulous index for ease of navigation.

Knots in Hellas '98 - Proceedings of the International Conference on Knot Theory and Its Ramifications

Knots in Hellas '98 - Proceedings of the International Conference on Knot Theory and Its Ramifications
Author: V. F. R. Jones
Publisher: World Scientific
Total Pages: 588
Release: 2000
Genre: Mathematics
ISBN: 9789812792679

There have been exciting developments in the area of knot theory in recent years. They include Thurston's work on geometric structures on 3-manifolds (e.g. knot complements), Gordon–Luecke work on surgeries on knots, Jones' work on invariants of links in S3, and advances in the theory of invariants of 3-manifolds based on Jones- and Vassiliev-type invariants of links. Jones ideas and Thurston's idea are connected by the following path: hyperbolic structures, PSL(2, C) representations, character varieties, quantization of the coordinate ring of the variety to skein modules (i.e. Kauffman, bracket skein module), and finally quantum invariants of 3-manifolds. This proceedings volume covers all those exciting topics.

Lattice Statistics And Mathematical Physics: Festschrift Dedicated To Professor Fa-yueh Wu On The Occasion Of His 70th Birthday, Proceedings Of Apctp-nankai Joint Symposium

Lattice Statistics And Mathematical Physics: Festschrift Dedicated To Professor Fa-yueh Wu On The Occasion Of His 70th Birthday, Proceedings Of Apctp-nankai Joint Symposium
Author: Mo-lin Ge
Publisher: World Scientific
Total Pages: 330
Release: 2002-11-06
Genre: Science
ISBN: 981448718X

This book contains thirty-six short papers on recent progress in a variety of subjects in mathematical and theoretical physics, written for the proceedings of a symposium in honor of the seventieth birthday of Professor F Y Wu, held at the Nankai Institute of Mathematics, October 7-11, 2001. The collection of papers is aimed at researchers, including graduate students, with an interdisciplinary interest and gives a brief introduction to many of the topics of current interest. These include new results on exactly solvable models in statistical mechanics, integrable through the Yang-Baxter equations, quantum groups, fractional statistics, random matrices, index theorems on the lattice, combinatorics, and other related topics.

Lattice Statistics and Mathematical Physics

Lattice Statistics and Mathematical Physics
Author: Jacques H. H. Perk
Publisher: World Scientific
Total Pages: 330
Release: 2002
Genre: Science
ISBN: 9812382038

"Papers presented at the Nankai Symposium on 'Lattice Statistics and Mathematical Physics ... took place at the Nankai Institute of Mathematics in Tianjin, China"--P. v.

Functional Integration

Functional Integration
Author: Cécile Dewitt-Morette
Publisher: Springer Science & Business Media
Total Pages: 436
Release: 2013-11-11
Genre: Science
ISBN: 1489903194

The program of the Institute covered several aspects of functional integration -from a robust mathematical foundation to many applications, heuristic and rigorous, in mathematics, physics, and chemistry. It included analytic and numerical computational techniques. One of the goals was to encourage cross-fertilization between these various aspects and disciplines. The first week was focused on quantum and classical systems with a finite number of degrees of freedom; the second week on field theories. During the first week the basic course, given by P. Cartier, was a presentation of a recent rigorous approach to functional integration which does not resort to discretization, nor to analytic continuation. It provides a definition of functional integrals simpler and more powerful than the original ones. Could this approach accommodate the works presented by the other lecturers? Although much remains to be done before answering "Yes," there seems to be no major obstacle along the road. The other courses taught during the first week presented: a) a solid introduction to functional numerical techniques (A. Sokal) and their applications to functional integrals encountered in chemistry (N. Makri). b) integrals based on Poisson processes and their applications to wave propagation (S. K. Foong), in particular a wave-restorer or wave-designer algorithm yielding the initial wave profile when one can only observe its distortion through a dissipative medium. c) the formulation of a quantum equivalence principle (H. Kleinert) which. given the flat space theory, yields a well-defined quantum theory in spaces with curvature and torsion.

Knots And Physics (Second Edition)

Knots And Physics (Second Edition)
Author: Louis H Kauffman
Publisher: World Scientific
Total Pages: 739
Release: 1994-01-15
Genre: Mathematics
ISBN: 9814502375

In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included.This book is an introduction to knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of knot theory, coupled with a quantum statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems.