On the link between Shrodinger and Vlasov Equations

TL;DR

This paper demonstrates a derivation of the Vlasov equation from the Schrödinger equation by introducing hidden degrees of freedom and quantization, revealing a deep connection between quantum and classical kinetic descriptions.

Contribution

It presents a novel derivation of the Vlasov equation from the Schrödinger equation through hidden variables and quantization, bridging quantum and classical kinetic theories.

Findings

Vlasov equation can be derived from Schrödinger equation with hidden degrees of freedom

The derived Schrödinger equation matches the kinetic equation in x-representation

Establishes a link between quantum and classical dynamical systems

Abstract

It is shown that well-known Vlasov equation can be derived by adding "hidden" degrees of freedom and subsequent quantization. The Shrodinger equation obtained in this manner coincides (in x-representation) with the kinetic equation for the original dynamical system