TY - JOUR
T1 - Charge and energy transport by Holstein solitons in anharmonic one-dimensional systems
AU - Cisneros-Ake, Luis A.
AU - Brizhik, L.
N1 - Publisher Copyright:
© 2019 Elsevier Ltd
PY - 2019/2
Y1 - 2019/2
N2 - We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.
AB - We consider the problem of electron transport and energy transfer in a one-dimensional molecular chain with non-dipole optical phonon mode. We take into account the dispersion of optical phonons, anharmonicity of the lattice on-site potential and electron-lattice interaction. In the lowest order linear approximation such a system admits solutions in the form of the Holstein polaron. Here, within the traveling wave formalism for the corresponding non-linear equations of motion in the long-wave limit, we show the existence of three particular types of exact analytical localized solutions. Two of them, here referred to as Holstein solitons of the first and second kind, respectively, describe a one-hump localized electron wave functions, while the third one displays two humps in the envelope of the wave function. We use the variational approach to reproduce the exact analytical profiles in the three cases of the particular normalized solutions and to variationally predict the existence of branches of normalized solutions for the three types of profiles. We confirm our findings by numerically continuing, in the parameter of velocity of propagation, the analytically exact particular solutions.
KW - Holstein polaron
KW - Lattice anharmonicity
KW - Low-dimensional system
KW - Optical phonons
KW - Soliton
KW - Variational approach
UR - http://www.scopus.com/inward/record.url?scp=85060339100&partnerID=8YFLogxK
U2 - 10.1016/j.chaos.2018.12.025
DO - 10.1016/j.chaos.2018.12.025
M3 - Artículo
SN - 0960-0779
VL - 119
SP - 343
EP - 354
JO - Chaos, Solitons and Fractals
JF - Chaos, Solitons and Fractals
ER -