Table of contents

An attempt is made to present an instanton "calculus" in a relatively simple form. The physical meaning of instantons is explained by the example of the quantum-mechanical problem of energy levels in a two-humped potential. The nonstandard solution to this problem based on instantons is analyzed, and the reader is acquainted with the main technical elements used in this approach. Instantons in quantum chromodynamics are then considered. The Euclidean formulation of the theory is described. Classical solutions of the field equations (the Belavin–Polyakov–Shvarts–Tyapkin instantons) are obtained explicitly and their properties are studied. The calculation of the instanton density is described and the complete result is given for an arbitrary number of colors. The effects associated with fermion fields are briefly described.

This review gives a systematic exposition of the qualitative problems of nonlinear laser resonance spectroscopy, taking into account the effect of the light field on the dynamics of the broadening collision and, correspondingly, on the rate of phase relaxation. The results of experiments, in which these nonlinear optocollisional effects, predicted earlier theoretically, were observed, are presented briefly.

The properties of magnetic insulators containing orbitally degenerate transition metal ions (Jahn-Teller ions) are discussed. The Jahn-Teller effect in these insulators causes structural phase transitions, lowers the lattice symmetry, and gives rise to an orbital ordering. Various interactions responsible for these effects are discussed: the electron-lattice, quadrupole-quadrupole, and exchange interactions. The mutual effects of the orbital ordering and the magnetic properties of corresponding compounds are discussed. The exchange interaction in the cases of twofold and threefold orbital degeneracy is discussed. The effect of a magnetic field on the orbital and magnetic structure and the temperature dependence of the exchange interaction are studied. The properties of several representative compounds containing Jahn-Teller ions are discussed.

This article reviews the theoretical and experimental studies on a number of the thermodynamic aspects of superionic conduction, the intensive study of which began in the past decade. We discuss the relation of superionic conductivity to the disordering of one of the sublattices of the crystal, disordering phase transitions caused by the interaction of point defects, and the mechanism of polymorphic transitions associated with partial disordering. We analyze the effect of jumpwise variation of the ionic conductivity induced by an external electric field, the thermodynamics of domain states in superionic conductors, and the effect of pressure on the phase transitions and the ionic conductivity.