Abstract
We present a one-parameter family of mathematical models describing the dynamics of polarons in periodic structures, such as linear polypeptides, which, by tuning the model parameter, can be reduced to the Davydov or the Scott model. We describe the physical significance of this parameter and, in the continuum limit, we derive analytical solutions which represent stationary polarons. On a discrete lattice, we compute stationary polaron solutions numerically. We investigate polaron propagation induced by several external forcing mechanisms. We show that an electric field consisting of a constant and a periodic component can induce polaron motion with minimal energy loss. We also show that thermal fluctuations can facilitate the onset of polaron motion. Finally, we discuss the bio-physical implications of our results.
Highlights
The polaron, a quasi-particle formed by the coupling of an electron to a vibrating lattice, was first theorised by Landau in 1933 [1]
We propose a generalisation to the Davydov-Scott model, and use it to explore the properties of polarons in a linear peptide chain
We derive a set of coupled dynamical equations which govern the electron and phonon parts of the polaron, as well as how they interact
Summary
The polaron, a quasi-particle formed by the coupling of an electron to a vibrating lattice, was first theorised by Landau in 1933 [1]. We derive a set of coupled dynamical equations which govern the electron and phonon parts of the polaron, as well as how they interact. We use only numerical methods to obtain our results, as well as those, where we consider how the polaron’s motion is affected by temperature of the environment. We briefly discuss the generalisability of our model to studying electron transport by polarons in α-helices
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