Dynamics and Thermodynamics of Systems with Long Range Interactions
Dynamics and Thermodynamics of Systems with Long Range Interactions

Author: Thierry Dauxois

Publisher: Springer

Published: 2008-01-11

Total Pages: 492

ISBN-13: 3540458352

DOWNLOAD EBOOK

Properties of systems with long range interactions are still poorly understood despite being of importance in most areas of physics. The present volume introduces and reviews the effort of constructing a coherent thermodynamic treatment of such systems by combining tools from statistical mechanics with concepts and methods from dynamical systems. Analogies and differences between various systems are examined by considering a large range of applications, with emphasis on Bose--Einstein condensates. Written as a set of tutorial reviews, the book will be useful for both the experienced researcher as well as the nonexpert scientist or postgraduate student.

Dynamics and Thermodynamics of Systems with Long Range Interactions: Theory and Experiments
Dynamics and Thermodynamics of Systems with Long Range Interactions: Theory and Experiments

Author: Alessandro Campa

Publisher: American Institute of Physics

Published: 2008-01-17

Total Pages: 402

ISBN-13:

DOWNLOAD EBOOK

The workshop was about the developments of the thermodynamical and dynamical behavior of many-body systems in which the interactions decay very slowly with the distance: they present very strange properties, not found in the other systems. The possibility of testing the theoretical ideas in laboratory systems was the most innovative issue.

Chaotic Dynamics and Thermodynamics of Periodic Systems with Long-range Forces
Chaotic Dynamics and Thermodynamics of Periodic Systems with Long-range Forces

Author: Pankaj Kumar

Publisher:

Published: 2016

Total Pages: 225

ISBN-13:

DOWNLOAD EBOOK

Gravitational and electromagnetic interactions form the backbone of our theoretical understanding of the universe. While, in general, such interactions are analytically inexpressible for three-dimensional infinite systems, one-dimensional modeling allows one to treat the long-range forces exactly. Not only are one-dimensional systems of profound intrinsic interest, physicists often rely on one-dimensional models as a starting point in the analysis of their more complicated higher-dimensional counterparts. In the analysis of large systems considered in cosmology and plasma physics, periodic boundary conditions are a natural choice and have been utilized in the study of one dimensional Coulombic and gravitational systems. Such studies often employ numerical simulations to validate the theoretical predictions, and in cases where theoretical relations have not been mathematically formulated, numerical simulations serve as a powerful method in characterizing the system's physical properties. In this dissertation, analytic techniques are formulated to express the exact phase-space dynamics of spatially-periodic one-dimensional Coulombic and gravitational systems. Closed-form versions of the Hamiltonian and the electric field are derived for single-component and two-component Coulombic systems, placing the two on the same footing as the gravitational counterpart. Furthermore, it is demonstrated that a three-body variant of the spatially-periodic Coulombic or gravitational system may be reduced isomorphically to a periodic system of a single particle in a two-dimensional rhombic potential. The analytic results are utilized for developing and implementing efficient computational tools to study the dynamical and the thermodynamic properties of the systems without resorting to numerical approximations. Event-driven algorithms are devised to obtain Lyapunov spectra, radial distribution function, pressure, caloric curve, and Poincare surface of section through an N-body molecular-dynamics approach. The simulation results for the three-body systems show that the motion exhibits chaotic, quasiperiodic, and periodic behaviors in segmented regions of the phase space. The results for the large versions of the single-component and two-component Coulombic systems show no clear-cut indication of a phase transition. However, as predicted by the theoretical treatment, the simulated temperature dependencies of energy, pressure as well as Lyapunov exponent for the gravitational system indicate a phase transition and the critical temperature obtained in simulation agrees well with that from the theory.

Complexity, Metastability And Nonextensivity - Proceedings Of The 31st Workshop Of The International School Of Solid State Physics
Complexity, Metastability And Nonextensivity - Proceedings Of The 31st Workshop Of The International School Of Solid State Physics

Author: Constantino Tsallis

Publisher: World Scientific

Published: 2005-09-23

Total Pages: 427

ISBN-13: 9814479187

DOWNLOAD EBOOK

A broad introduction and overview of current interdisciplinary studies on complexity, this volume is an ideal starting point for scientists and graduate students who wish to enter the field. The book features a diverse collection of the latest research work not found in a single volume elsewhere.Among the highly regarded contributors to the volume are the 2004 Boltzmann medalists E G D Cohen and H E Stanley; G Parisi, Boltzmann medalist in 1992 and Dirac medalist in 1999; and numerous internationally renowned experts, such as S Abe, F T Arecchi, J-P Bouchaud, A Coniglio, W Ebeling, P Grigolini, R Mantegna, M Paczuski, A Robledo, L Pietronero, A Vespignani, and T Vicsek.

Statistical Physics
Statistical Physics

Author: Nicolas Sator

Publisher: CRC Press

Published: 2023-08-09

Total Pages: 451

ISBN-13: 1000915565

DOWNLOAD EBOOK

This book presents an introduction to the main concepts of statistical physics, followed by applications to specific problems and more advanced concepts, selected for their pedagogical or practical interest. Particular attention has been devoted to the presentation of the fundamental aspects, including the foundations of statistical physics, as well as to the discussion of important physical examples. Comparison of theoretical results with the relevant experimental data (with illustrative curves) is present through the entire textbook. This aspect is facilitated by the broad range of phenomena pertaining to statistical physics, providing example issues from domains as varied as the physics of classical and quantum liquids, condensed matter, liquid crystals, magnetic systems, astrophysics, atomic and molecular physics, superconductivity and many more. This textbook is intended for graduate students (MSc and PhD) and for those teaching introductory or advanced courses on statistical physics. Key Features: A rigorous and educational approach of statistical physics illustrated with concrete examples. A clear presentation of fundamental aspects of statistical physics. Many exercises with detailed solutions. Nicolas Sator is Associate Professor at Sorbonne University, Paris, France. He is a member of the Laboratory of Theoretical Physics of Condensed Matter (LPTMC) and his research focuses on the physics of liquids. Nicolas Pavloff is Professor at Paris-Saclay University, France. He is a member of Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS) and his domain of research is quantum fluid theory. Lénaïc Couëdel is Professor at the University of Sasktchewan, Saskatoon, Canada and researcher at CNRS, France. His research area is plasma physics with a focus on complex plasma crystals.

Nanoscale Thermodynamics
Nanoscale Thermodynamics

Author: Signe Kjelstrup

Publisher: MDPI

Published: 2021-09-01

Total Pages: 168

ISBN-13: 3036511687

DOWNLOAD EBOOK

This Special Issue concerns the development of a theory for energy conversion on the nanoscale, namely, nanothermodynamics. The theory has been applied to porous media, small surfaces, clusters or fluids under confinement. The number of unsolved issues in these contexts is numerous and the present efforts are only painting part of the broader picture. We attempt to answer the following: How far down in scale does the Gibbs equation apply? Which theory can replace it beyond the thermodynamic limit? It is well known that confinement changes the equation of state of a fluid, but how does confinement change the equilibrium conditions themselves? This Special Issue explores some of the roads that were opened up for us by Hill with the idea of nanothermodynamics. The experimental progress in nanotechnology is advancing rapidly. It is our ambition with this book to inspire an increased effort in the development of suitable theoretical tools and methods to help further progress in nanoscience. All ten contributions to this Special Issue can be seen as efforts to support, enhance and validate the theoretical foundation of Hill.

Physics of Long-range Interacting Systems
Physics of Long-range Interacting Systems

Author: Alessandro Campa

Publisher: Oxford University Press, USA

Published: 2014

Total Pages: 429

ISBN-13: 0199581932

DOWNLOAD EBOOK

This book deals with an important class of many-body systems: those where the interaction potential decays slowly for large inter-particle distances; in particular, systems where the decay is slower than the inverse inter-particle distance raised to the dimension of the embedding space. Gravitational and Coulomb interactions are the most prominent examples, however it has become clear that long-range interactions are more common than previously thought. A satisfactory understanding of properties, generally considered as oddities only a couple of decades ago, has now been reached: ensemble inequivalence, negative specific heat, negative susceptibility, ergodicity breaking, out-of-equilibrium quasi-stationary-states, anomalous diffusion. The book, intended for Master and PhD students, tries to gradually acquaint the reader with the subject. The first two parts describe the theoretical and computational instruments needed to address the study of both equilibrium and dynamical properties of systems subject to long-range forces. The third part of the book is devoted to applications of such techniques to the most relevant examples of long-range systems.

Symmetry Breaking
Symmetry Breaking

Author: Franco Strocchi

Publisher: Springer Science & Business Media

Published: 2005-02-21

Total Pages: 220

ISBN-13: 9783540213185

DOWNLOAD EBOOK

The intriguing mechanism of spontaneous symmetry breaking is a powerful innovative idea at the basis of most of the recent developments in theoretical physics, from statistical mechanics to many-body theory to elementary particles theory; for infinitely extended systems a symmetric Hamiltonian can account for non symmetric behaviours, giving rise to non symmetric realizations of a physical system. In the first part of this book, devoted to classical field theory, such a mechanism is explained in terms of the occurrence of disjoint sectors and their stability properties and of an improved version of the Noether theorem. For infinitely extended quantum systems, discussed in the second part, the mechanism is related to the occurrence of disjoint pure phases and characterized by a symmetry breaking order parameter, for which non perturbative criteria are discussed, following Wightman, and contrasted with the standard Goldstone perturbative strategy. The Goldstone theorem is discussed with a critical look at the hypotheses that emphasizes the crucial role of the dynamical delocalization induced by the interaction range. The Higgs mechanism in local gauges is explained in terms of the Gauss law constraint on the physical states. The mathematical details are kept to the minimum required to make the book accessible to students with basic knowledge of Hilbert space structures. Much of the material has not appeared in other textbooks.

Kinetic Theory and Transport Phenomena
Kinetic Theory and Transport Phenomena

Author: Rodrigo Soto

Publisher: Oxford University Press

Published: 2016-10-20

Total Pages: 277

ISBN-13: 0191025143

DOWNLOAD EBOOK

One of the questions about which humanity has often wondered is the arrow of time. Why does temporal evolution seem irreversible? That is, we often see objects break into pieces, but we never see them reconstitute spontaneously. This observation was first put into scientific terms by the so-called second law of thermodynamics: entropy never decreases. However, this law does not explain the origin of irreversibly; it only quantifies it. Kinetic theory gives a consistent explanation of irreversibility based on a statistical description of the motion of electrons, atoms, and molecules. The concepts of kinetic theory have been applied to innumerable situations including electronics, the production of particles in the early universe, the dynamics of astrophysical plasmas, quantum gases or the motion of small microorganisms in water, with excellent quantitative agreement. This book presents the fundamentals of kinetic theory, considering classical paradigmatic examples as well as modern applications. It covers the most important systems where kinetic theory is applied, explaining their major features. The text is balanced between exploring the fundamental concepts of kinetic theory (irreversibility, transport processes, separation of time scales, conservations, coarse graining, distribution functions, etc.) and the results and predictions of the theory, where the relevant properties of different systems are computed.

Dynamics and Thermodynamics in Hierarchically Organized Systems
Dynamics and Thermodynamics in Hierarchically Organized Systems

Author: P. Auger

Publisher: Elsevier

Published: 2013-10-22

Total Pages: 223

ISBN-13: 1483287270

DOWNLOAD EBOOK

One of the most fundamental and efficient ways of conceptualizing complex systems is to organize them hierarchically. A hierarchically organized system is represented by a network of interconnected subsystems, each of which has its own network of subsystems, and so on, until some elementary subsystems are reached that are not further decomposed. This original and important book proposes a general mathematical theory of a hierarchical system and shows how it can be applied to very different topics such as physics (Hamiltonian systems), biology (coupling the molecular and the cellular levels), ecology (coupling the individual, population and ecosystem), and economics (coupling the sectoral, regional and national levels). The first attempt to develop mathematical frameworks for conceptualizing such systems only appeared in the early 1970s, and it took another decade before these mathematical frameworks were applied to various specific contexts of the sciences of the natural. Much of this work has been pioneered by the author, and he presents a more thorough work which will have a major impact on shifting current thinking in the sciences of the natural to a more holistic basis in which several levels of hierarchically organized systems are viewed in an integrated fashion.