This review is devoted to describing nonequilibrium carrier systems and relaxational and kinetic phenomena in three-dimensional point-contacts. Attention is focused on describing a phonon system which becomes substantially modified under conditions of ballistic transport. In such systems the energy fluxes are limited by the presence of weakly coupled layers of impurity atoms, planar defects, or microscopic-size contacts. The small size of point-contacts, ranging from several to 1000 nm, makes it possible to investigate low-temperature heat and charge transfer on scales less than the characteristic inelastic scattering lengths. A mechanism of phonon transport in the presence of an interface is analyzed, and various models of a planar defect are examined. The special features of interfacial phonon transport, where the transport coefficients are determined not by scattering processes in the volume of a bulk crystal but rather by the properties of the intercrystalline boundary, are studied. The quantum phonon thermal conductivity of point-contacts is studied in detail.

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The degree of ordering of the structure of technologically important materials formed as a result of the evolution of complex physicochemical systems determines their physical properties, in particular optical. In this regard, the primary task for the theoretical study of methods for obtaining materials with predetermined physical properties is to develop approaches to describe the evolution of fractal (scale-invariant) objects in the formation of self-similar structures in systems exhibiting chaotic behavior. The paper forms an idea of the processes of evolution in materials formed as a result of stochastic processes. It is established that the conduct of ultrametrics in time space allows to characterize the time of the evolutionary process of fractal dimension, which is calculated either theoretically or model. The description of evolutionary processes in a condensed medium, accompanied by topological transformations, is significantly supplemented by the method of describing the stages of evolution of structures, which makes it possible to analyze a wide range of materials and can control their properties, primarily optical. It is shown that the most large-scale invariant structures, due to the investigated properties, can be used as information carriers. It is demonstrated that the presence in physical systems of fractal temporal dimension and generates a self-similar (consisting of parts in a sense similar to the whole object) evolutionary tree, which, in turn, generates spatial objects of non-integer dimension, observed in real situations. On the other hand, temporal fractality provides analysis of systems with dynamic chaos, leading to universal relaxation functions. In particular, in systems with a large-scale invariant distribution of relaxation characteristics, an algebraic law of relaxation is manifested, which leads to rheological models and equations of states, which are characterized by fractional derivatives. It is argued that the fractal dimension of time hierarchies stores information that determines the process of self-organization. Developed in the paper ideas about the processes of building the structure of materials, which lead to the fractal geometry of objects, can be used to predict their properties, in particular, optical.

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