Formation of Cluster Systems in Chaotic Condensed Media

Purpose. The study of cluster formation in a system of chaotically moving and interacting particles taking into account the Efimov effect and the "golden" section.
Methods. Methods of mathematical modeling, quantum mechanics, a model of solid spheres, and a cluster model were used.
Results. Within the framework of the proposed work, it is noted that in a three-particle system of particles, it is possible to form their spatial configuration in the form of a "golden" triangle, and in the case of an excited state of two particles, the third particle is far enough away from the other two, it is this configuration that corresponds to the conditions for the occurrence of the Efimov effect in a three-particle system.
Based on the mathematical formalism of the description of self-organization processes in the work, it is shown that in chaotic environments within the framework of the Efimov model, with the involvement of the "golden" section in the mutual arrangement of three interacting particles, it is possible to form disk-shaped clusters containing a "magic" number of particles. In the structure of these clusters, the formation of quantum-dimensional regions in the form of a torus is possible. The parameters of such areas are defined.
Conclusion. The described model of the formation and decay of disk-shaped clusters, taking into account the Efimov effect and the "golden" section rule, allows us, without resorting to a complex solution of equations in the three-body problem, to obtain important relations following from strict theories. The proposed approach implies the possibility of self-organization of clusters and the formation of quantum-dimensional regions in their structure, for example, in the form of a torus with a potential well, capable of capturing charged particles and determining their energy spectrum, as well as explaining the appearance of spectral bands in the IR spectra of substances.
The proposed approach may be of practical importance, for example, for predicting the IR spectra of liquids, the presence of quantum dots in liquids with a wide spectrum of excitation from UV to IR radiation.

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