Two books on superconductor electronics

Johann Heyen Hinken

В. V. Bondarev

This book contains detailed insights on the calculus of variations that studies the equilibrium density matrix for many-particle Fermi systems. There are two approximations taken into account in the book. The simplest one is the mean field approximation. The second approximation applies not only to the particle distribution pattern but also to the correlation function. The variational principle for electron distribution function among wave vectors has been denoted in the work. The method that makes using the density matrix for finding the valence electron energy in metal has been proposed. It has been proved that the Coulomb interaction of electrons in a crystal lattice results in production of the model Hamiltonian consisting of two components. One component describes attraction of electrons with the equal wave vectors inducing formation of specific electron pairs. The other component describes repulsion of electrons with the wave vectors being equal by size and opposite by direction. This component denotes the anisotropy regarding distribution of electrons among wave vectors thus indicating the superconducting substance ability. The Fermi-Dirac distribution function, as considered together with the model Hamiltonian, explains all the properties exhibited by superconductors. Thus, the effect of a magnetic field on the superconducting states is studied in the book. The book can be interesting for senior schoolchildren, students of higher educational institutions, postgraduates and teachers.

A. S. Alexandrov, Nevill Mott

This book is about a certain class of superfluids, namely the high temperature superconductors. Perhaps the simplest of the superfluids is liquid He4. Since the very early days of quantum mechanics it has been known that the helium atom He4 is a boson; it is built of an even number of particles (two electrons, two neutrons and two protons), so that a wave function ^(ri,F2) must be symmetrical in FI — r? where FI, r-z are the electron's coordinates. This has the result that half the rotational states of the molecule H62 are absent and that the scattering of alpha particles by helium for low energies deviates from the Rutherford scattering law. It also has the remarkable result that this is not so for the light isotope He3, which shows that the number of neutrons in the nucleus affects properties depending otherwise only on the electrons and nuclear charge.

Alexander B Zorin, K. K. Likharev, Vasili K. Semenov

Vladimir N. Gubankov, K. K. Likharev

Monique Combescot, Shiue-Yuan Shiau

Abstract This book bridges the gap between two major fields in condensed matter physics: semiconductors and superconductors. Through an original perspective that their key particles, excitons and Cooper pairs, are composite bosons (cobosons), the book raises fundamental questions: how does the Pauli exclusion principle affect the fermionic components of bosonic particles at the microscopic level, and how does this appear in the coboson many-body physics at the macroscopic level? What insights would the study of Wannier excitons, Frenkel excitons, and Cooper pairs provide about the “bosonic condensation” of composite bosons and how it differs from the Bose-Einstein condensation of elementary bosons? The book starts from a solid mathematical and physical foundation to derive excitons and Cooper pairs and introduces Shiva diagrams as a graphic support to grasp the many-body physics induced by fermion exchange in the absence of fermion-fermion interaction–a mechanism not visualized in standard Feynman diagrams. The book also covers composite bosons related to excitons: trions, biexcitons, and polaritons. The last part of the book is devoted to composite boson condensation, from the prototypical Bose-Einstein condensation of free elementary bosons and the consequence of interaction, to interacting electrons in the dense regime, to electron-hole pairs in the dense and dilute regimes. Advanced undergraduate and graduate students in physics, with no prior background, will benefit from this book, as numerous appendices provide the materials required to follow the various chapters. The concepts and formalism presented should also prove useful in research on ultracold atomic gases, polariton condensation, and quantum information.