Collective Effects in Quantum Statistics of Radiation and Matter
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

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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
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

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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
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

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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
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

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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
Bose-Einstein Condensation

Author: A. Griffin

Publisher: Cambridge University Press

Published: 1996-07-13

Total Pages: 622

ISBN-13: 9780521589901

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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
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

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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.

Perspectives in Analysis
Perspectives in Analysis

Author: Michael Benedicks

Publisher: Springer Science & Business Media

Published: 2006-06-01

Total Pages: 382

ISBN-13: 3540304347

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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.

A Dressing Method in Mathematical Physics
A Dressing Method in Mathematical Physics

Author: Evgeny V. Doktorov

Publisher: Springer Science & Business Media

Published: 2007-05-19

Total Pages: 413

ISBN-13: 1402061404

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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. 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.