Abstract
An asymptotic method has been developed for investigation of kinetics of formation of compact objects with strong internal bonds. The method is based on the uncertainty relation for a coordinate and a momentum in space of sizes of objects (clusters) with strongly pronounced collective quantum properties resulted from exchange interactions of various physical nature determined by spatial scales of the processes under consideration. The proposed phenomenological approach has been developed by analogy with the all-known ideas about coherent states of quantum mechanical oscillator systems for which a product of coordinate and momentum uncertainties (dispersions) accepts the value, which is minimally possible within uncertainty relations. With such an approach the leading processes are oscillations of components that make up objects, mainly: collective nucleon oscillations in a nucleus and phonon excitations in a mesostructure crystal lattice. This allows us to consider formation and growth of subatomic and mesoscopic objects in the context of a single formalism. The proposed models adequately describe characteristics of formation processes of nuclear matter clusters as well as mesoscopic crystals having covalent and quasi-covalent bonds between atoms.
Highlights
In works [1]-[6] various physical objects and their environment are described
Object sizes “intermediate” between atoms and solid bodies in mesoscopic crystal structures can reach considerable values, at which the lower complexity limit of a macroscopic crystal is reached
Fundamental considerations and assessments of quantum representation feasibility show that the “coordinate-momentum” uncertainty relation can fit for bodies with the sizes about 10–7 m, i.e., at a level of nanometer scales [2]
Summary
In works [1]-[6] various physical objects and their environment are described. They are of interest in. Mechanical behavior of nanostructured objects is described using molecular dynamics methods and using statistic models allowing for both thermodynamic and kinetic aspects of problems under consideration These problems cover incompleteness of classical description of process running in mesoscopic scales, necessity of developing new models including phenomenological ones that take into account formation of quantum systems and determine growth regularities and nanostructure consolidation, and determination of phase transformation size dependencies, in particular, ascertainment of the effect of polymorphic transformations on synergy of crystal structures. In this connection it is important in principle to determine general features of dynamics of object growth both in microcosm and in “mesocosm”. It is reasonable to present the expanded fields of application for the proposed asymptotic models
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