Thermo-quantum diffusion

TL;DR

This paper introduces a novel nonlinear quantum Smoluchowski equation to describe thermo-quantum diffusion, generalizing classical diffusion laws and exploring quantum effects at zero temperature.

Contribution

It derives a new nonlinear quantum diffusion equation and a quantum generalization of Einstein's law, including quantum diffusion at zero temperature.

Findings

Derived a nonlinear quantum Smoluchowski equation.

Established a quantum generalization of Einstein's diffusion law.

Described quantum diffusion behavior at zero temperature.

Abstract

A new approach to thermo-quantum diffusion is proposed and a nonlinear quantum Smoluchowski equation is derived, which describes classical diffusion in the field of the Bohm quantum potential. A nonlinear thermo-quantum expression for the diffusion front is obtained, being a quantum generalization of the classical Einstein law. The quantum diffusion at zero temperature is also described and a new dependence of the position dispersion on time is derived. A stochastic Bohm-Langevin equation is also proposed.