Statistical Mechanics of Superconductivity

  • Takafumi Kita

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Takafumi Kita
    Pages 1-12
  3. Takafumi Kita
    Pages 25-41
  4. Takafumi Kita
    Pages 43-60
  5. Takafumi Kita
    Pages 91-99
  6. Takafumi Kita
    Pages 101-123
  7. Takafumi Kita
    Pages 125-141
  8. Takafumi Kita
    Pages 159-174
  9. Takafumi Kita
    Pages 189-200
  10. Takafumi Kita
    Pages 229-246
  11. Takafumi Kita
    Pages 247-263
  12. Takafumi Kita
    Pages 265-286
  13. Back Matter
    Pages 287-289

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 mathematical clarity 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 with exercises along with detailed answers.


Abrikosov’s Flux-line Lattice Bogoliubov-de Gennes Equations Coherence of the Cooper-pair Condensation Cooper-pair Condensation and BCS Theory Eilenberger Equations Ginzburg-Landau Theory Landau Theory of Fermi Liquids Origin of Superfluidity Second Quantization Spin-statistics Theorem

Authors and affiliations

  • Takafumi Kita
    • 1
  1. 1.Department of PhysicsHokkaido UniversitySapporoJapan

Bibliographic information