Modelling Quantum Mechanical Processes by Processes Energy Distribution of Inner Oscillations of a Nanoparticle in the Phase Space

TL;DR

This paper models quantum processes by analyzing the energy distribution of nanoparticle oscillations in phase space, revealing a connection between classical Brownian motion and quantum behavior through a generalized equation.

Contribution

It introduces a generalized Klein-Kramers equation that links classical stochastic dynamics with quantum mechanics in nanoparticle systems.

Findings

Energy distribution described by a generalized equation.

System reaches a quasi-stationary state after rapid transition.

Slow process approximates the Schrödinger equation.

Abstract

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.