Polarons with a twist

We consider a polaron model where molecular \emph{rotations} are important. Here, the usual hopping between neighboring sites is affected directly by the electron-phonon interaction via a {\em twist-dependent} hopping amplitude. This model may be of relevance for electronic transport in complex molecules and polymers with torsional degrees of freedom, such as DNA, as well as in molecular electronics experiments where molecular twist motion is significant. We use a tight-binding representation and find that very different polaronic properties are already exhibited by a two-site model -- these are due to the nonlinearity of the restoring force of the twist excitations, and of the electron-phonon interaction in the model. In the adiabatic regime, where electrons move in a {\em low}-frequency field of twisting-phonons, the effective splitting of the energy levels increases with coupling strength. The bandwidth in a long chain shows a power-law suppression with coupling, unlike the typical exponential dependence due to linear phonons.Comment: revtex4 source and one eps figur

The problem of integrable discretization: Hamiltonian approach A skeleton of the book

SIGLEAvailable from TIB Hannover: RR 1596(479) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekDEGerman

Miura transformations for Toda-type integrable systems, with applications to the problem of integrable discretizations

We study lattice Miura transformations for the Toda and Volterra lattices, relativistic Toda and Volterra lattices, and their modifications. In particular, we give three successive modifications for the Toda lattice, two for the Volterra lattice and for the relativistic Toda lattice, and one for the relativistic Volterra lattice. We discuss Poisson properties of the Miura transformations, their permutability properties, and their role as localizing changes of variables in the theory of integrable discretizations. (orig.)Available from TIB Hannover: RR 1596(367) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman

Discrete Lagrangian reduction, discrete Euler-Poincare equations, and semidirect products

A discrete version of Lagrangian reduction is developed in the context of discrete time Lagrangian systems on G x G, where G is a Lie group. We consider the case when the Lagrange function is invariant with respect to the action of an isotropy subgroup of a fixed element in the representation space of G. In this context the reduction of the discrete Euler-Lagrange equations is shown to lead to the so called discrete Euler-Poincare equations. A constrained variational principle is derived. The Legendre transformation of the discrete Euler-Poincare equations leads to discrete Hamiltonian (Lie-Poisson) systems on a dual space to a semiproduct Lie algebra. (orig.)Available from TIB Hannover: RR 1596(398) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekSIGLEDEGerman