Table of contents

Thermoelectric effects in superconductors began to be studied about 50 years ago, but until recently the opinion was widespread that they completely vanish in the superconducting state. Yet as far back as 1944 attention was called to the fact that distinctive thermoelectric effects should arise within the framework of the two-fluid concept (allowing for the possible existence in a superconductor of a normal current as well as a superconducting current). Concretely, in an isotropic but inhomogeneous superconductor, or else in a homogeneous but anisotropic one, a thermocurrent and a magnetic field associated with it should arise in the presence of a temperature gradient. Generally these effects are small, yet in recent years they have become accessible to measurement, and a number of pertinent experimental studies have appeared. On the other hand, progress has also been made in the field of theory, in particular, in understanding the nature and various features of thermoelectric phenomena in superconductors. This article is devoted to a general physical and more detailed theoretical analysis of the problem of thermoelectric effects in superconductors. The content of the article in greater detail is evident from the table of contents.

The review deals with the problem of selective interaction of laser radiation with atoms and molecules. Objects of selective interaction (chemical elements and compounds, isotopes, molecular bonds, etc.) are considered first. Next, possible elementary selective processes (photoionization of atoms and molecules, photodissociation and photoisomerization of molecules, photodeflection of particles, photochemical reactivity, etc.) are discussed and the available techniques are classified into photophysical and photochemical methods, atomic and molecular methods, and so on. The review is concerned mainly with the photophysical and photochemical methods of selective interaction in the specific case of laser isotope separation. The last sections of the review deal with other applications which are in the course of development, such as preparation of pure substances, selective laser biochemistry, selective detection of nuclei, atoms, and molecules, and spatial localization of molecular bonds.

The definition of turbulence and the differences between turbulence and random wave motions of liquids or gases are discussed. The Landau scheme of the generation of turbulence with increasing Reynolds number as a result of a sequence of normal bifurcations that creates a quasiperiodic motion is considered; several examples are discussed, including flow between rotating cylinders, convection at small Prandtl numbers, and the boundary layer at a flat plate. Results obtained in recent years from the ergodic theory and associated with the discovery of strange attractors in the phase spaces of typical dynamic systems are described. Flows with inverse bifurcations are considered, including the plane Poiseuille flow and Lorenz's example with idealized three-mode convection at large Prandtl numbers. In the latter case, the results of numerical calculations are analyzed and point to the existence of a strange attractor with the structure of a Cantor discontinuum; other examples of systems with strange attractors are also considered. It becomes clear that strange attractors in the phase spaces of systems with few modes may explain their nonperiodic behavior, but cannot explain why turbulence has a continuous spatial spectrum.

Until quite recently, it was thought that turbulence, i.e., stochastic self-oscillations of a continuous medium, was related exclusively to the excitation of an exceedingly large number of degrees of freedom. This review is devoted to the discussion of new ideas on the nature of the unpredictable turbulent motions in dissipative media connected with the discovery of strange attractors, i.e., attractive regions in phase space within which all paths are unstable and behave in a very complex fashion (motions on an attractor of this kind are characterized by a continuous spectrum). Turbulence represented by a strange attractor is described by a finite number of degrees of freedom, i.e., modes whose physical nature may be different. The example of a simple electronic noise generator is used to illustrate how the instability (divergence) of such paths leads to stochastic behavior. The analysis is based on the introduction of a nonreciprocally single-valued Poincare mapping onto itself, which is then used to describe the strange attractors encountered in different physical problems. An example of this mapping is used to demonstrate the discrete, symbolic, description of dynamic systems. The properties of such systems which indicate their stochastic nature, for example, positive topologic entropy and hyperbolicity are discussed. Specific physical mechanisms leading to the appearance of stochastic behavior and characterized by a continuous time spectrum are discussed. Strange attractors that appear in the case of parametric instability of waves in plasmas, laser locking by an external field, and so on, are demonstrated. "Attractor models" of hydrodynamic turbulence are reviewed, and in particular, finite-dimensional hydrodynamic models of convection in a layer and of Couette flow between rotating cylinders are constructed and found to exhibit stochastic behavior.

The article contains a brief historical review of the mutual influences on one another of elementary-particle theory and many-body theory. The main attention is devoted to the idea of spontaneous symmetry breaking and the unified theory of particles based on it. The intimate and far reaching analogy between unified theory and the theory of superconductivity is traced. Some consequences of this analogy for particle physics and cosmology are considered.