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Collective Effects in Quantum Statistics of Radiation and Matter
Author: V.N. Popov
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 228
ISBN-13: 9400929838
DOWNLOAD EBOOK →Material particles, electrons, atoms, molecules, interact with one another by means of electromagnetic forces. That is, these forces are the cause of their being combined into condensed (liquid or solid) states. In these condensed states, the motion of the particles relative to one another proceeds in orderly fashion; their individual properties as well as the electric and magnetic dipole moments and the radiation and absorption spectra, ordinarily vary little by comparison with their properties in the free state. Exceptiotls are the special so-called collective states of condensed media that are formed under phase transitions of the second kind. The collective states of matter are characterized to a high degree by the micro-ordering that arises as a result of the interaction between the particles and which is broken down by chaotic thermal motion under heating. Examples of such pheonomena are the superfluidity of liquid helium, and the superconductivity and ferromagnetism of metals, which exist only at temperatures below the critical temperature. At low temperature states the particles do not exhibit their individual characteristics and conduct themselves as a single whole in many respects. They flow along capillaries in ordered fashion and create an undamped current in a conductor or a macroscopic magnetic moment. In this regard the material acquires special properties that are not usually inherent to it.
Operator Theory with a Random Potential, and Some Questions of Statistical Physics
Author: Viktor Nikolaevich Popov
Publisher: American Mathematical Soc.
Published: 1991
Total Pages: 278
ISBN-13: 9780821831397
DOWNLOAD EBOOK →This collection is devoted to problems of operator theory with a random potential and a number of problems of statistical physics. For the Schrodinger operator with a potential randomly depending on time, mean wave operators, and the mean scattering operator are computed, and it is shown that the averaged dynamics behaves like free dynamics in the limit of infinite time. Results of applying the method of functional integration to some problems of statistical physics are presented: the theory of systems with model Hamiltonians and their dynamics, ferromagnetic systems of spin 1/2, Coulomb and quantum crystals. This collection is intended for specialists in spectral theory and statistical physics.
Interaction Of Electromagnetic Field With Condensed Matter
Author: Nickolai N Bogolubov Jr
Publisher: World Scientific
Published: 1990-06-30
Total Pages: 338
ISBN-13: 9814507318
DOWNLOAD EBOOK →This book covers a wide range of topics on the interaction of alternating magnetic field with condensed matter, including superradiant process, proton echo, gamma resonance, scattering of light by condensed matter near critical points, electromagnetically induced phase transitions and some mathematical problems describing the phenomena mentioned.
Mathematical Foundations of Quantum Statistical Mechanics
Author: D.Y. Petrina
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 460
ISBN-13: 940110185X
DOWNLOAD EBOOK →This monograph is devoted to quantum statistical mechanics. It can be regarded as a continuation of the book "Mathematical Foundations of Classical Statistical Mechanics. Continuous Systems" (Gordon & Breach SP, 1989) written together with my colleagues V. I. Gerasimenko and P. V. Malyshev. Taken together, these books give a complete pre sentation of the statistical mechanics of continuous systems, both quantum and classical, from the common point of view. Both books have similar contents. They deal with the investigation of states of in finite systems, which are described by infinite sequences of statistical operators (reduced density matrices) or Green's functions in the quantum case and by infinite sequences of distribution functions in the classical case. The equations of state and their solutions are the main object of investigation in these books. For infinite systems, the solutions of the equations of state are constructed by using the thermodynamic limit procedure, accord ing to which we first find a solution for a system of finitely many particles and then let the number of particles and the volume of a region tend to infinity keeping the density of particles constant. However, the style of presentation in these books is quite different.
Bose-Einstein Condensation
Author: A. Griffin
Publisher: Cambridge University Press
Published: 1996-07-13
Total Pages: 622
ISBN-13: 9780521589901
DOWNLOAD EBOOK →The first book devoted to Bose-Einstein condensation (BEC) as an interdisciplinary subject.
Path Integration: Trieste 1991, Lectures On - Proceedings Of The Adriatico Research Conference
Author: H A Cerdeira
Publisher: World Scientific
Published: 1993-02-27
Total Pages: 602
ISBN-13: 9814554537
DOWNLOAD EBOOK →This is a collection of pedagogical lectures and research papers that were presented during a combined course/conference program held at the International Centre for Theoretical Physics in Trieste in the summer of 1991. The lectures begin from an elementary level and were intended to bring student participants to the point where they could appreciate the research conference that came at the end of program.
Darboux Transformations in Integrable Systems
Author: Chaohao Gu
Publisher: Springer Science & Business Media
Published: 2006-07-09
Total Pages: 317
ISBN-13: 1402030886
DOWNLOAD EBOOK →The Darboux transformation approach is one of the most effective methods for constructing explicit solutions of partial differential equations which are called integrable systems and play important roles in mechanics, physics and differential geometry. This book presents the Darboux transformations in matrix form and provides purely algebraic algorithms for constructing the explicit solutions. A basis for using symbolic computations to obtain the explicit exact solutions for many integrable systems is established. Moreover, the behavior of simple and multi-solutions, even in multi-dimensional cases, can be elucidated clearly. The method covers a series of important equations such as various kinds of AKNS systems in R1+n, harmonic maps from 2-dimensional manifolds, self-dual Yang-Mills fields and the generalizations to higher dimensional case, theory of line congruences in three dimensions or higher dimensional space etc. All these cases are explained in detail. This book contains many results that were obtained by the authors in the past few years. Audience: The book has been written for specialists, teachers and graduate students (or undergraduate students of higher grade) in mathematics and physics.
Algebraic and Geometric Methods in Mathematical Physics
Author: Anne Boutet de Monvel
Publisher: Springer Science & Business Media
Published: 2013-11-11
Total Pages: 471
ISBN-13: 940170693X
DOWNLOAD EBOOK →Proceedings of the Kaciveli Summer School, Crimea, Ukraine, 1993
Perspectives in Analysis
Author: Michael Benedicks
Publisher: Springer Science & Business Media
Published: 2006-06-01
Total Pages: 382
ISBN-13: 3540304347
DOWNLOAD EBOOK →The Conference “Perspectives in Analysis” was held during May 26–28, 2003 at the Royal Institute of Technology in Stockholm, Sweden. The purpose of the conference was to consider the future of analysis along with its relations to other areas of mathematics and physics, and to celebrate the seventy-?fth birthday of Lennart Carleson. The scienti?c theme was one with which the name of Lennart Carleson has been associated for over ?fty years. His modus operandi has long been to carry out a twofold approach to the selection of research problems. First one should look for promising new areas of ana- sis, especially those having close contact with physically oriented problems of geometric character. The second step is to select a core set of problems that require new techniques for their resolutions. After making a central contri- tion, Lennart would usually move on to a new area, though he might return to the topic of his previous work if new techniques were developed that could break old mathematical log jams. Lennart’s operating approach is based on fundamental realities of modern mathematics as well as his own inner c- victions. Here we ?rst refer to an empirical fact of mathematical research: All topics have a ?nite half-life, with ?fteen years being an upper bound for most areas. After that time it is usually a good idea to move on to so- thing new.
