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Statistical Mechanics of Superconductivity

  • Textbook
  • © 2015

Overview

Authors:
  1. Takafumi Kita

    1. Department of Physics, Hokkaido University, Sapporo, Japan

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  • Familiarizes readers with major concepts and techniques of modern theoretical physics through the study of superconductivity
  • Provides careful and detailed mathematical derivations understandable by beginners
  • Guides students of superconductivity on which topics to study in mathematics and modern theoretical physics
  • Demonstrates clearly both the coherence of the Cooper-pair condensation and the origin of superfluidity

Part of the book series: Graduate Texts in Physics (GTP)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
    Download chapter PDF

  2. Review of Thermodynamics

    • Takafumi Kita
    Pages 1-12

  3. Basics of Equilibrium Statistical Mechanics

    • Takafumi Kita
    Pages 13-23

  4. Quantum Mechanics of Identical Particles

    • Takafumi Kita
    Pages 25-41

  5. Statistical Mechanics of Ideal Gases

    • Takafumi Kita
    Pages 43-60

  6. Density Matrices and Two-Particle Correlations

    • Takafumi Kita
    Pages 61-71

  7. Hartree–Fock Equations and Landau’s Fermi-Liquid Theory

    • Takafumi Kita
    Pages 73-89

  8. Attractive Interaction and Bound States

    • Takafumi Kita
    Pages 91-99

  9. Mean-Field Equations of Superconductivity

    • Takafumi Kita
    Pages 101-123

  10. BCS Theory

    • Takafumi Kita
    Pages 125-141

  11. Superfluidity, Meissner Effect, and Flux Quantization

    • Takafumi Kita
    Pages 143-157

  12. Responses to External Perturbations

    • Takafumi Kita
    Pages 159-174

  13. Tunneling, Density of States, and Josephson Effect

    • Takafumi Kita
    Pages 175-187

  14. P-Wave Superfluidity

    • Takafumi Kita
    Pages 189-200

  15. Gor’kov, Eilenberger, and Ginzburg–Landau Equations

    • Takafumi Kita
    Pages 201-227

  16. Abrikosov’s Flux-Line Lattice

    • Takafumi Kita
    Pages 229-246

  17. Surfaces and Vortex Cores

    • Takafumi Kita
    Pages 247-263

  18. Solutions to Problems

    • Takafumi Kita
    Pages 265-286

  19. Back Matter

    Pages 287-289
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Keywords

About this book

This book provides a theoretical, step-by-step comprehensive explanation of superconductivity for undergraduate and graduate students who have completed elementary courses on thermodynamics and quantum mechanics. To this end, it adopts the unique approach of starting with the statistical mechanics of quantum ideal gases and successively adding and clarifying elements and techniques indispensible for understanding it. They include the spin-statistics theorem, second quantization, density matrices, the Bloch–De Dominicis theorem, the variational principle in statistical mechanics, attractive interaction and bound states. Ample examples of their usage are also provided in terms of topics from advanced statistical mechanics such as two-particle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermi-liquid theory, among others. With these preliminaries, the fundamental mean-field equations of superconductivity are derived with maximum mathematicalclarity based on a coherent state in terms of the Cooper-pair creation operator, a quasiparticle field for describing the excitation and the variational principle in statistical mechanics. They have the advantage that the phase coherence due to the Cooper-pair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classic s-wave superconductors and its extension to the p-wave superfluidity of 3He. Later, the mean-field equations are simplified to the Eilenberger and Ginzburg–Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov’s flux-line lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of p-wave superfluidity in liquid 3He. The book serves as a standard reference for advanced courses of statistical mechanics withexercises along with detailed answers.

Reviews

“This book has a unique approach to formulating mean field theory of superconductivity especially in a way most useful for studying inhomogeneous and/or unconventional superconductors. Building up from the fundamental laws of thermodynamics and the basic techniques of statistical mechanics such that it is readable for students, it develops the Bogoliubov-de Gennes formalism of superconductivity. The book culminates in derivation of the quasiclassical theory of superconductivity and its application to description of vortex states. While it is informative and useful for researchers in the field, it is an excellent textbook – either as the main text or for supplementary reading – for a variety of graduate courses ranging from a standard class on statistical mechanics or condensed matter physics to more specialised classes such as one on superconductivity.” (Professor K.Tanaka, Department of Physics & Engineering Physics, University of Saskatchewan)

Authors and Affiliations

  • Department of Physics, Hokkaido University, Sapporo, Japan

    Takafumi Kita

About the author

Takafumi Kita is an associate professor at Department of Physics, Hokkaido University, Japan. He obtained a PhD from Department of Applied Physics, the University of Tokyo in 1988. He held positions at Institute of Solid State Physics, the University of Tokyo (1988-1993, research associate), at Department of Physics and Astronomy, University of Illinois at Urbana-Champaign (1991-1993, visiting scientist), and joined Hokkaido University subsequently. He spent a year in Germany (2000-2001) at University of Karlsruhe and at University of Bayreuth (half a year per each) as an overseas research fellow. He has been teaching quantum mechanics, thermodynamics, statistical mechanics, mathematical methods in physics, field theory in statistical mechanics, etc., over 20 years.

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