Conformal quantum mechanics and Fick-Jacobs equation

TL;DR

This paper establishes a connection between conformal quantum mechanics and the Fick-Jacobs equation, providing exact solutions for diffusion in channels with varying geometries and linking conformal Hamiltonians to different channel configurations.

Contribution

It introduces a novel relation between conformal quantum mechanics and diffusion in channels, offering exact solutions and linking Hamiltonians to channel geometries.

Findings

Relation between conformal Hamiltonians and channel geometries

Exact solutions for Fick-Jacobs equation in specific channels

Conformal quantum mechanics applied to diffusion problems

Abstract

It is found a relation between conformal quantum mechanics and Fick-Jacobs equation, which describes diffusion in channels. This relation is given between a family of channels and a family of conformal Hamiltonians. In addition, it is shown that a conformal Hamiltonian is associated with two channels with different geometry. Furthermore exact solutions for Fick-Jacobs equation are given for this family of channels.