Quantum Effects on the Mesoscale

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In different areas of mechanics, highly non-equilibrium processes are accompanied by
self-organization of various type turbulent structures and localized inhomogeneities at intermediate
scale between macro and micro levels. In order to describe the self-organization of the new dynamic
structures on the mesoscale, a new problem formulation based on the results of non-equilibrium
statistical mechanics, control theory of adaptive systems, and theory of a special type nonlinear
operator sets is proposed. Determination of the turbulent structure parameters through constraints
imposed on the system in the form of nonlinear functionals is an inverse problem similar to problems
on spectra in quantum mechanics. Like in quantum mechanics, the bounded system in response
to impact forms a discrete spectrum of the turbulent structure sizes and lifetimes which goes into
continuous spectrum close-to-equilibrium. The proposed description of the structure evolution on the
intermediate scale level which is valid far from thermodynamic equilibrium bridges the gap between
macroscopic theories and quantum mechanics and affirms the unity of the physical laws of nature.
Original languageEnglish
Pages (from-to)562-575
Number of pages14
Issue number3
StatePublished - 27 Jul 2020

Scopus subject areas

  • Physics and Astronomy(all)


  • mesoscale, turbulent structure, wave packet, size spectrum, inverse problem, nonlinear functional


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