Comments on the davydov hamiltonian for quasi‐one‐dimensional molecular chains

Abstract

The almost lossless transfer of energy and electronic charge along quasi-one-dimensional molecular substances such as peptide chains (H-N-C=O),found an explanation in a model proposed by Davydov. The Davydov model is based on the dipole-dipole interactions between neighboring peptide groups and on the fact that the internal C=O vibrations are coupled to the elastic deformations of the chain. The Davydov Hamiltonian is written in the position-space representation and, on making a continuum transformation, leads to a nonlinear Schrodinger equation whose solutions are sol8ons. A Davydov soliton is a coupled pair of an exciton and a lattice deformation. In this paper, the Davydov Hamiltonian is transformed to the reciprocal lattice and its equivalent, second-quantized Hamiltonian is investigated. Some important obsemations are made about the coupling constants, their dispersion relations, and the equation of motion for the ladder operators. Our procedure is free of semiclassical approximations but, instead, assumes the onset of Bose condensation. The resultant nonlinear Schrodinger equation is similar to that of Davydov, but a more complete set of solutions is found.

Plausibility of quantum coherent states in biological systems

“…The hypothesis invoking long-range coherence in biological systems was proposed by H. Fröhlich's [5][6][7] and followed by detailed investigations by Tuszynski et al [8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], Pokorny [23][24][25], Mesquita et al [26][27][28] and others for over three decades. The possible role played by coherent states manifested outside low temperature physics has attracted considerable interest in both the physics and biology communities.…”