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2192 results in Statistical Physics

Page 53 of 110

Complex Networks
  • Structure, Robustness and Function
  • Reuven Cohen, Shlomo Havlin
  • Published online:
    05 August 2013
    Print publication:
    08 July 2010
  • Examining important results and analytical techniques, this graduate-level textbook is a step-by-step presentation of the structure and function of complex networks. Using a range of examples, from the stability of the internet to efficient methods of immunizing populations, and from epidemic spreading to how one might efficiently search for individuals, this textbook explains the theoretical methods that can be used, and the experimental and analytical results obtained in the study and research of complex networks. Giving detailed derivations of many results in complex networks theory, this is an ideal text to be used by graduate students entering the field. End-of-chapter review questions help students monitor their own understanding of the materials presented.

Introduction to the Statistical Physics of Integrable Many-body Systems
  • Ladislav Šamaj, Zoltán Bajnok
  • Published online:
    05 June 2013
    Print publication:
    16 May 2013
  • Including topics not traditionally covered in literature, such as (1+1)-dimensional QFT and classical 2D Coulomb gases, this book considers a wide range of models and demonstrates a number of situations to which they can be applied. Beginning with a treatise of nonrelativistic 1D continuum Fermi and Bose quantum gases of identical spinless particles, the book describes the quantum inverse scattering method and the analysis of the related Yang–Baxter equation and integrable quantum Heisenberg models. It also discusses systems within condensed matter physics, the complete solution of the sine-Gordon model and modern trends in the thermodynamic Bethe ansatz. Each chapter concludes with problems and solutions to help consolidate the reader's understanding of the theory and its applications. Basic knowledge of quantum mechanics and equilibrium statistical physics is assumed, making this book suitable for graduate students and researchers in statistical physics, quantum mechanics and mathematical and theoretical physics.

  • 20 - Luttinger many-fermion model

  • from PART IV - STRONGLY CORRELATED ELECTRONS
  • Ladislav Šamaj, Zoltán Bajnok, Hungarian Academy of Sciences, Budapest
  • Book:
    Introduction to the Statistical Physics of Integrable Many-body Systems
    Published online:
    05 June 2013
    Print publication:
    16 May 2013, pp 333-361

  • Summary

    Low-temperature properties of 3D interacting fermion systems are well described by Landau's theory of Fermi liquids; for reviews see, e.g. [183, 184]. It involves only excitations of the system around the Fermi surface on energy scales small compared to the Fermi energy. Excitations are well described by quasi-particles which are in one-to-one correspondence with the bare particles. The bare-particle interaction does not break the qualitative picture of non-interacting system, but renormalizes the dynamical characteristics (the effective mass and the pair interaction) of quasi-particles. Within the microscopic Green function formalism, the existence of quasi-particles is equivalent to assuming that the self-energy correction Σ(k, ω) is regular (has only short-range contributions in time and space) close to the Fermi surface. The lifetime of quasi-particles τ α(εk−εF)−2 is long enough to consider them as well-defined eigenstates over long time-scales. The momentum occupation number of the bare particles exhibits a sharp discontinuity when crossing the Fermi momentum. The charge and spin degrees of freedom of quasi-particle always travel together.

    The Landau theory breaks down in 1D systems of interacting fermions which have a very specific Fermi surface consisting of two points ±kF. In such systems, the self-energy Σ(k, ω) no longer possesses the analytic properties required for introducing quasi-particles. In contrast to Fermi liquids, the momentum occupation number of the bare particles in the ground state is continuous at the Fermi momentum. Moreover, the charge and spin excitations are separated.

Page 53 of 110