Dynamics of a self‐trapped quasiparticle in a one‐dimensional molecular lattice with two phonon modes

Abstract

AbstractIn this work we study numerically the dynamics of a self‐trapped quasiparticle (electron, hole or excitation) in a one‐dimensional molecular chain with two phonon modes, one acoustical and one optical. This model generalizes the model of Davydov solitons and Holstein polaron model: Davydov solitons are formed by a quasiparticle interacting with acoustical phonons, and Holstein polarons are formed due the interaction with optical phonons. Our model describes soliton‐like (large polaron) states in soft quasi‐one‐dimensional systems, such as conducting polymers, alpha‐helical polypeptide macromolecules, DNA etc. For the purpose of modelling self‐trapping of quasiparticles without any influence of chain boundaries, we consider a molecular chain with periodic boundary conditions. Then, to study the dynamics of quasiparticles in such states, we use the adiabatic acceleration method. We show that soliton velocity is an oscillating function of time. These oscillations are caused by the presence of optical vibrations and by the Peierls–Nabarro barrier formed by discrete lattice. We also show that self‐trapping of a quasiparticle takes place at random dynamical lattice potential induced by some random initial conditions for acoustical and optical phonons, provided the random range constant, i.e., the amplitude of random field, is not too big. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)