Multiquantum states derived from Davydov'sansatz: II. An exact special case solution for the Su-Schrieffer-Heeger Hamiltonian and its relation to the state

Abstract

We present the derivation of an exact special case solution (for a classical lattice) for the Su-Schrieffer-Heeger model for the calculation of soliton dynamics in trans-polyacetylene. Our solution is exact, in the sense that the ansatz state yields an exact solution provided that the equations of motion for its parameters are obeyed. However, these equations can be solved only numerically (in principle to any desired accuracy), not analytically. The model is applied to time simulations of neutral solitons as a function of temperature. We find agreement of the results of our time simulations with experimental data on the mobility of neutral solitons in the system. Comparative calculations using the completely adiabatic model indicate that the results of this model are at variance both with experiment and with those of our model. A simple consideration of the potential barriers for soliton displacement leads to an overestimation of the soliton mobility for low temperatures and an underestimation for higher ones. In an appendix we discuss in some detail the relationship of this exact solution with the | 2 state ansatz as presented in our previous paper. We find that the ansatz state and the exact solution yield identical results for lattice momenta, displacements and site occupancies, but differ in a time dependent phase factor. Thus spectra computed with the dynamics resulting from the exact solution for the classical lattice on one hand and from the ansatz state on the other would differ from each other.

Spectra of charged solitons and temperature dependence of the mobility of neutral solitons intrans-polyacetylene

“…[94] is derived in detail in the Appendix of Ref. [95]. The comparison in Appendix B shows that it yields the same time evolution of the lattice and of the electron distribution as the exact classical solution, however, with different phases.…”

“…These terms as well as the norm N j are constant in time as can be shown [95]. After a lengthy derivation given in detail in Ref.…”

“…[94] and [95] for more details) for the lattice as in the previous section. Since Langevin equations are strictly correct only for classical systems, our results for very low temperature (T = 10 K) are approximative.…”

“…After a lengthy derivation given in detail in Ref. [95], we arrive at the FÖRNER equations of motion: p n = K(q n+1 − 2q n + q n−1 ) + 2α Re[P n,n+1 − P n,n−1 ] + R n (t) − p n (B13) and ihċ nj = (β + E n )c n+1,j + (β + E n−1 )c n−1,j ,…”

Influences of Quantum and Disorder Effects on Solitons Excited in Protein Molecules in Improved Model

“…The results of Careri et al [17] appear to indicate that even relatively small amounts of disorder in amorphous film of acetanilide, a protein-like crystal, is enough to destroy the spectral signature of a "soliton". Recently, Forner, [18] Zolotaryuk et al, [19] Henning, [20] Ivic et al, [21] Cruzeiro-Hansson, [22] and Svirschevski [23] studied serious influences of disorder and nonuniformrity of structures of the protein molecules on the soliton in the Davydov and Davydov-Scott models, especially, Forner [10,18] studied fully the influences of different types of disorder and different thermalization schemes on the Davydov soliton by different wave functions and different associated dynamics and Runge-Kutta way. These studies result in a very complicated picture for the Davydov model, and show that the Davydov soliton is not robust against the influences of the structure disorders, but do not completely rule out the Dovydov theory.…”