Statistical Mechanics of Superconductivity
by Takafumi Kita

Persian Title: مکانیک آماری ابررسانایی

Summary and Info
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 Cooperpair condensation and the origin of superfluidityThis book provides a theoretical, stepbystep 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 spinstatistics 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 twoparticle correlations of quantum ideal gases, derivation of the Hartree–Fock equations, and Landau’s Fermiliquid theory, among others. With these preliminaries, the fundamental meanfield equations of superconductivity are derived with maximum mathematical clarity based on a coherent state in terms of the Cooperpair 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 Cooperpair condensation can be clearly seen making the superfluidity comprehensible naturally. Subsequently, they are applied to homogeneous cases to describe the BCS theory for classic swave superconductors and its extension to the pwave superfluidity of 3He. Later, the meanfield equations are simplified to the Eilenberger and Ginzburg–Landau equations so as to describe inhomogeneous superconductivity such as Abrikosov’s fluxline lattice concisely and transparently. Chapters provide the latest studies on the quasiclassical theory of superconductivity and a discovery of pwave superfluidity in liquid 3He. The book serves as a standard reference for advanced courses of statistical mechanics with exercises along with detailed answers.Related Subjects: Strongly Correlated Systems, Superconductivity, Statistical Physics, Dynamical Systems and Complexity, Mathematical Physics, Mathematical Methods in Physics
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