Table of contents

A systematic theory of sudden perturbations is derived for quantum systems whose states are described both by wave functions (a pure ensemble) and by a quantum density operator (a mixed ensemble). A perturbation series is written in powers of the parameter ωτ, which is small when the perturbation is "sudden"; ℏω is the typical eigenvalue of the unperturbed system; and τ is the characteristic collision time. When the perturbation (t), taken at different times, commutes with itself, the theory yields a compact analytic expression for the probabilities for stimulated transitions for any value of Vτ /ℏ. The results of many cross-section calculations for atomic collision processes are discussed from a common standpoint: the processes are treated as "jarring" processes which stimulate transitions in the quantum system. If a momentum δ_p is rapidly transferred to the system in a collision, regardless of the physical nature of the "jarring," the probabilities for the stimulated transitions are governed by the parameter N ∼δ_p·δR/ℏ where δR is a measure of the uncertainty in the coordinates which is due to the relatively slow motions in the unperturbed system.

An analysis is made of the results obtained in investigations of dense media by the molecular dynamics method. This method is based on mathematical simulation of the motion of a sufficiently large number of particles with a given interparticle interaction law. The attention is concentrated on new physical ideas about the nature of simple liquids and dense gases which have made their first appearance, have been derived, or confirmed in studies carried out by the molecular dynamics method. The principal laws of particle motion and their influence on the form of the temporal velocity correlation function are considered. Spatial and temporal correlations appearing in dense systems are studied and their role in the propagation of longitudinal and shear waves is discussed. An analysis is made of the results of molecular dynamics investigations of thermodynamic and transport properties of simple liquids and dense gases. The dynamics of a light classical particle in a dense medium of disordered heavy scatterers is discussed. Consideration is given to the close relationship between the behavior of the temporal velocity correlation function of a particle, its spatial velocity correlation function, and "percolation" in a random field of heavy scatterers.

Nonlinear phenomena occurring during interaction between an atom and a strong rf field of resonant or nonresonant frequency are reviewed. The account is given in both semiclassical and consistently quantummechanical languages. The concept of an atom "dressed by the radiation field" in which not only the optical-frequency field but also the radio-frequency field is quantized is presented in detail. The results are summarized of theoretical and experimental studies of multiphoton transitions, radiative shifts of normal magnetic resonance lines, parametric resonance, and coherent resonances under the conditions of optical pumping. The influence of nonresonance rf fields on magnetic properties and the rate of magnetic relaxation of atoms is discussed.

A systematic review is made of the experimental and theoretical investigations of the mechanism and kinetics of mass transfer in a system of islands of substance A deposited on a solid substrate of substance B in which A is insoluble. The analysis is carried out on the assumption that the total amount of matter present jointly in the islands and in a two-dimensional gas of adsorbed atoms is constant. Behavior of systems of islands at rest and in motion is discussed. Coalescence of islands is considered in the case of diffusive mass transfer between islands at rest and also in the case of direct collisions between moving islands. "Dispersion hardening" of the surface by a system of islands, which hinders evaporation and growth of a crystal, is described. Considerable attention is devoted to reporting experimental investigations carried out mainly by electron microscopy. Some new effects are predicted, including a possible phase transition during coalescence of islands, size effect in recrystallization, one-dimensional coalescence, etc.

The advantages of using the 4-dimensional group velocity are demonstrated. After first giving its purely kinematic definition for an arbitrary wave field, the discussion turns to packets of electromagnetic waves in electrically and magnetically anisotropic media which possess space-time dispersion and are smoothly nonuniform in space and slowly varying in time. In particular, a simple expression is obtained for the energy-momentum 4-tensor in terms of the group-velocity 4-vector. Finally, it is shown how the 4-dimensional notation simplifies the derivation of the conditions of orthogonality and conservation of the adiabatic invariant. A note by M. L. Levin which follows this paper contains a brief account of the basis results of W. R. Hamilton's investigations relating to the velocity of wave motion.