Mobile localized solutions for an electron in lattices with dispersive and non-dispersive phonons

Cisneros-Ake, Luis A.; Cruzeiro, Leonor; Velarde, Manuel G.

doi:10.1016/j.physd.2015.05.008

Cited by 12 publications

(6 citation statements)

References 16 publications

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“…Proceeding now as in Ref. 38, let us transform the equations of motion (7) and (11) into non-dimensional equations by rescaling the time t and the displacement variables u n to dimensionless variables as follows:…”

Section: The Mixed Quantum-classical Davydov Modelmentioning

confidence: 99%

Knowns and unknowns in the Davydov model for energy transfer in proteins

Cruzeiro

2022

Low Temperature Physics

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The Davydov model for amide I propagation in hydrogen-bonded chains of proteins is revisited. The many similarities between the mixed quantum-classical dynamical equations and those that are derived from the full quantum Davydov model while applying the so-called D2 ansatz are highlighted. The transition from a minimum energy localized amide I state to a fully delocalized state is shown to operate in four phases, one of which is abrupt and the last of which is a fast but smooth change from a very broad yet localized state to a completely delocalized one. Exploration of the dynamical phase space at zero temperature includes the well-known soliton propagation as well as double and triple discrete breathers, and dispersion of initially localized states. The uncertainties related to the question of the thermal stability of the Davydov soliton are illustrated. A solution to the seemingly endless problem of the short radiative lifetime of the amide I excitations is proposed.

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Section: The Mixed Quantum-classical Davydov Modelmentioning

confidence: 99%

Knowns and unknowns in the Davydov model for energy transfer in proteins

Cruzeiro

2022

Low Temperature Physics

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“…For the initial data we use polaron (the amplitudes of probability b n and displacements (7) corresponds to the lowest energy for T = 0), Gaussian random variables are added to these displacements, and the velocities of the sites un are determined by Gaussian random variables with a relevant distribution.…”

Section: Setting Up a Computational Experimentsmentioning

confidence: 99%

“…Discrete nonlinear systems have appeared in the various fields of physics, chemistry and biology [1,2,3,4,5,6,7,8,9] and have attracted considerable attention recently. The problem of charge transfer in quasi-one-dimensional molecules, such as DNA or proteins, is of interest to biophysics.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Holstein polaron in a chain with thermal fluctuations

Fialko¹,

Лахно²

2020

Preprint

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Numerical modeling is used to investigate the dynamics of a polaron in a chain with small random Langevin-like perturbations which imitate the environmental temperature T and under the influence of a constant electric field. In the semiclassical Holstein model the region of existence of polarons in the thermodynamic equilibrium state depends not only on temperature but also on the chain length. Therefore when we compute dynamics from initial polaron data, the mean displacement of the charge mass center differs for different-length chains at the same temperature. For a large radius polaron, it is shown numerically that the "mean polaron displacement" (which takes account only of the polaron peak and its position) behaves similarly for different-length chains during the time when the polaron persists. A similar slope of the polaron displacement enables one to find the polaron mean velocity and, by analogy with the charge mobility, assess the "polaron mobility". The calculated values of the polaron mobility for T ≈ 0 are close to the value at T = 0, which is small but not zero. For the parameters corresponding to the small radius polaron, simulations of dynamics demonstrate switching mode between immobile polaron and delocalized state. The position of the new polaron is not related to the position of the previous one; charge transfer occurs in the delocalized state.

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“…Discrete breathers could be mobile (subsonic or otherwise), pinned, or even impossible depending indeed on parameter values, whereas solitons would always be supersonically moving [15,16]. Coupling the inter-site Morse potential to the on-site Morse potential offers a variety of possibilities as the latter favours the onset of DB (for the case of on-site harmonic oscillations coupled to inter-site harmonic oscillations see [17] and references therein).…”

Section: Introductionmentioning

confidence: 99%

Wave motions along lattices with nonlinear on-site and inter-site potentials. Cooperation and/or competition leading to lattice solitons and/or discrete breathers

Velarde¹,

Chetverikov²,

Ébeling³

et al. 2015

Proc. Estonian Acad. Sci.

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We consider the wave dynamics of a one-dimensional lattice where both on-site and inter-site vibrations, coupled together, are governed by Morse interactions. We focus attention on the onset of lattice solitons and discrete breathers (DBs, aka intrinsic localized modes, ILM). We show how varying the relative strength of the on-site potential to that of the inter-site potential permits transition from one mode of (travelling or otherwise) localized excitation to the other.

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Mobile localized solutions for an electron in lattices with dispersive and non-dispersive phonons

Cited by 12 publications

References 16 publications

Knowns and unknowns in the Davydov model for energy transfer in proteins

Knowns and unknowns in the Davydov model for energy transfer in proteins

Dynamics of Holstein polaron in a chain with thermal fluctuations

Wave motions along lattices with nonlinear on-site and inter-site potentials. Cooperation and/or competition leading to lattice solitons and/or discrete breathers

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