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The Sitges International School of Physics is the second one to be held in Spain on the Many Body Problem. The first one took place on Mallorca during the summer 1969. The aim of the school was mainly to direct the interest of professors and students of Spanish Universities tow~rds this concrete field of re search. For this purpose 55 ~specially prepared lectures were given by an eminent collection of lecturers. Besides, a school of this class contri butes to the scientific formation of many students from other countries. Also, in a meeting of this kind, personal contacts are born that favour future co~laboration between scientists. In view of the success of the first two schools, we intend to foster future international meetings on this subject until interest in it is consolidated in Spain. All the lectures given are published here except those of Professor P.C. Martin whose lec tures have previously been published. I would like to thank all those people who helped to make this school a success, and in particular: Prof. J.L. Villar-Palasi, Minister of Educa tion of Spain for sponsoring the school. Dr. R. Diez-Hochleitner, Undersecretary of the Ministry of Education for receiving the project of this school with such enthusiasm. v PREFACE Prof. E.Costa-Novella, Director General of Universities in Spain and Dr. F.Arias-Salgado who showed such interest and patience while assuring the necessary finance would be found for the school.
The Sitges International School of Physics is the second one to be held in Spain on the Many Body Problem. The first one took place on Mallorca during the summer 1969. The aim of the school was mainly to direct the interest of professors and students of Spanish Universities tow~rds this concrete field of re search. For this purpose 55 ~specially prepared lectures were given by an eminent collection of lecturers. Besides, a school of this class contri butes to the scientific formation of many students from other countries. Also, in a meeting of this kind, personal contacts are born that favour future co~laboration between scientists. In view of the success of the first two schools, we intend to foster future international meetings on this subject until interest in it is consolidated in Spain. All the lectures given are published here except those of Professor P.C. Martin whose lec tures have previously been published. I would like to thank all those people who helped to make this school a success, and in particular: Prof. J.L. Villar-Palasi, Minister of Educa tion of Spain for sponsoring the school. Dr. R. Diez-Hochleitner, Undersecretary of the Ministry of Education for receiving the project of this school with such enthusiasm. v PREFACE Prof. E.Costa-Novella, Director General of Universities in Spain and Dr. F.Arias-Salgado who showed such interest and patience while assuring the necessary finance would be found for the school.
Lectures on the Many-Body Problem is a compilation of papers delivered at the Fifth International School of Physics, held at Ravello, Italy in April 1963. The book is devoted to the techniques of many-body theory, which are used in finding solutions to difficult problems encountered in solid-state physics. The text discusses such topics as the discontinuities in the drift velocity of ions in liquid helium; density fluctuation excitations in many-particle systems; tunneling from a many-particle point of view; the mathematics of second quantization for systems of fermions; and correlation functions and macroscopic equations. Theoretical physicists will find the monograph invaluable.
Kinetic Theory, Volume 2: Irreversible Processes compiles the fundamental papers on the kinetic theory of gases. This book comprises the two papers by Maxwell and Boltzmann in which the basic equations for transport processes in gases are formulated, as well as the first derivation of Boltzmann's "H-theorem and problem of irreversibility. Other topics include the dynamical theory of gases; kinetic theory of the dissipation of energy; three-body problem and the equations of dynamics; theorem of dynamics and the mechanical theory of heat; and mechanical explanation of irreversible processes. This volume is beneficial to physics students in the advanced undergraduate or postgraduate level.
A dominant feature of our ordinary experience of the world is a sense of irreversible change: things lose form, people grow old, energy dissipates. On the other hand, a major conceptual scheme we use to describe the natural world, molecular dynamics, has reversibility at its core. The need to harmonize conceptual schemes and experience leads to several questions, one of which is the focus of this book. How does irreversibility at the macroscopic level emerge from the reversibility that prevails at the molecular level? Attempts to explain the emergence have emphasized probability, and assigned different probabilities to the forward and reversed directions of processes so that one direction is far more probable than the other. The conclu sion is promising, but the reasons for it have been obscure. In many cases the aim has been to find an explana tion in the nature of probability itself. Reactions to that have been divided: some think the aim is justified while others think it is absurd.
This book differs from its predecessor, Lieb & Mattis Mathematical Physics in One Dimension, in a number of important ways. Classic discoveries which once had to be omitted owing to lack of space — such as the seminal paper by Fermi, Pasta and Ulam on lack of ergodicity of the linear chain, or Bethe's original paper on the Bethe ansatz — can now be incorporated. Many applications which did not even exist in 1966 (some of which were originally spawned by the publication of Lieb & Mattis) are newly included. Among these, this new book contains critical surveys of a number of important developments: the exact solution of the Hubbard model, the concept of spinons, the Haldane gap in magnetic spin-one chains, bosonization and fermionization, solitions and the approach to thermodynamic equilibrium, quantum statistical mechanics, localization of normal modes and eigenstates in disordered chains, and a number of other contemporary concerns.
This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kinetic theory formulated from the viewpoint of nonequilibrium ensembles in both nonrelativistic and, in Vol. 2, relativistic contexts. Theories of macroscopic irreversible processes must strictly conform to the thermodynamic laws at every step and in all approximations that enter their derivation from the mechanical principles. Upholding this as the inviolable tenet, the author develops theories of irreversible transport processes in fluids (gases or liquids) on the basis of irreversible kinetic equations satisfying the H theorem. They apply regardless of whether the processes are near to or far removed from equilibrium, or whether they are linear or nonlinear with respect to macroscopic fluxes or thermodynamic forces. Both irreversible Boltzmann and generalized Boltzmann equations are used for deriving theories of irreversible transport equations and generalized hydrodynamic equations, which rigorously conform to the tenet. All observables described by the so-formulated theories therefore also strictly obey the tenet.