Fractional Liouville Equation on Lattice Phase-Space

TL;DR

This paper introduces a lattice-based fractional Liouville equation that models nonlocal media, transforming into a continuum form with Riesz fractional derivatives, applicable to plasma-like systems.

Contribution

It proposes a novel lattice fractional Liouville equation and demonstrates its continuum limit involving Riesz fractional derivatives, extending phase-space dynamics modeling.

Findings

Lattice fractional Liouville equation derived for systems with long-range jumps.

Continuum limit yields Liouville equation with Riesz fractional derivatives.

Application to plasma-like nonlocal media demonstrates model relevance.

Abstract

In this paper we propose a lattice analog of phase-space fractional Liouville equation. The Liouville equation for phase-space lattice with long-range jumps of power-law types is suggested. We prove that the continuum limit transforms this lattice equation into Liouville equation with conjugate Riesz fractional derivatives of non-integer orders with respect to coordinates of continuum phase-space. An application of the fractional Liouville equation with these Riesz fractional derivatives to describe properties of plasma-like nonlocal media is considered.