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.
