Exciton-Phonon Dynamics with Long-Range Interaction

Details Exciton-Phonon Dynamics with Long-Range Interaction Exciton-Phonon Dynamics with Long-Range Interaction

2011-04-07

arxiv.org/abs/1104.1310v1

Physics

Mathematical Physics

Scientific paper

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.

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