Exciton-Phonon Dynamics with Long-Range Interaction

TL;DR

This paper develops a new theoretical framework for studying exciton-phonon dynamics in 1D lattices with long-range interactions, incorporating fractional derivatives to model nonlocal effects and nonlinear dynamics.

Contribution

It introduces coupled fractional and standard differential equations to describe exciton-phonon interactions with long-range effects, expanding existing models with fractional generalizations of key nonlinear equations.

Findings

Derived a fractional differential equation for excitons

Established a coupled system with phonon equations

Proposed new fractional models for nonlinear dynamics

Abstract

Exciton-phonon dynamics on a 1D lattice with long-range exciton-exciton interaction have been introduced and elaborated. Long-range interaction leads to a nonlocal integral term in the motion equation of the exciton subsystem if we go from discrete to continuous space. In some particular cases for power-law interaction, the integral term can be expressed through a fractional order spatial derivative. A system of two coupled equations has been obtained, one is a fractional differential equation for the exciton subsystem, the other is a standard differential equation for the phonon subsystem. These two equations present a new fundamental framework to study nonlinear dynamics with long-range interaction. New approaches to model the impact of long-range interaction on nonlinear dynamics are: fractional generalization of Zakharov system, Hilbert-Zakharov system, Hilbert-Ginzburg-Landau equation and nonlinear Hilbert-Schrodinger equation. Nonlinear fractional Schrodinger equation and fractional Ginzburg-Landau equation are also part of this framework.