Semiclassical Physics

ISBN-13: 9780813340845 / Angielski / Miękka / 2003 / 484 str.

Matthias Brack; Rajat Bhaduri

Opis

Semiclassical Physics explores the fascinating and deep connection between classical motion and quantum fluctuations. The book conveys a way of describing quantum effects in a physical system using the periodic orbit theory of Gutzwiller, which focuses on the classical dynamics of the system. The authors seek to demonstrate its usefulness for understanding quantum fluctuations in interacting many-body systems, exhibiting the close link of the shorter classical periodic orbits with the partly resolved shell fluctuations. The extended Thomas-Fermi model is developed in detail and shown to describe the average properties of finite fermion systems in a self-consistent mean-field approach. The new, updated paperback edition includes: Basic introduction to semiclassical physics for the general reader Elementary derivation of the Gutzwiller trace formula for chaotic systems; thorough discussion of its extensions to mixed and integrable systems, uniform approximations, and diffractive corrections Unified presentation of extended Thomas-Fermi model, Wigner-Kirkwood expansion, Weyl and Euler-MacLaurin expansions, and Strutinsky averaging Relations of the Gutzwiller theory to the Selberg trace formula and Bogomolny's transfer-matrix method Applications to finite fermion systems in nuclear, atomic and condensed matter physics Analytical examples and educational problems with hints to their solution Appendices to facilitate further detailed study The book addresses graduate students with a basic knowledge of classical and quantum mechanics and scientists with an interest in semiclassical methods. The approach is informal, guided largely by simple solvable models and by practical applications to real physical phenomena.

Spis treści

Editor’s Foreword -- Preface to the Paperback Edition -- Preface -- Introduction -- Quantization of integrable systems -- The single-particle level density -- The extended Thomas-Fermi model -- Gutzwiller’s trace formula for isolated orbits -- Extensions of the Gutzwiller theory -- Quantization of nonintegrable systems -- Shells and periodic orbits in finite fermion systems -- Concluding remarks -- The self-consistent mean field approach -- Inverse Laplace transforms -- More about the monodromy matrix -- Calculation of Maslov indices for isolated orbits

O autorze

Brack, Matthias | Bhaduri, Rajat