2016/10/03 by E. M. Beniaminov, Beniaminov, E. M.
Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #math-ph #math.MP #quant-ph #stochastic dynamics and bifurcation
paper · pdf · doi:10.48550/arxiv.1610.00536
17 pages
arxiv created 2016/10/03 · openalex publication_date 2016/10/03 · arxiv updated 2016/10/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of computing energy distribution of inner harmonic oscillations of a nanoparticle in its phase space, when the particle moves in a medium in heat equilibrium under certain temperature. It is assumed that the particle obeys the Brownian motion under the action of the medium and the force field given by a potential function. In the present paper we provide and study an equation describing the problem, generalizing the Klein--Kramers equation. It is shown that for large value of medium resistance, the process of energy distribution of inner harmonic oscillations of the nanoparticle is represented as the composition of a rapid transition process and a slow process. After the rapid transition process, the system goes to a quasi-stationary state. The slow process is approximately described by the standard Schrodinger equation used for description ofquantum processes. Thus, the process being studied can serve as a model of quantum processes.