TY - JOUR
T1 - Self-localized states for electron transfer in nonlocal continuum deformable media
AU - Cisneros-Ake, Luis A.
N1 - Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2016/8/19
Y1 - 2016/8/19
N2 - We consider the problem of electron transport in a deformable continuum medium subjected to an external harmonic substrate potential. We then consider the quasi-stationary state of the full problem to find a Gross–Pitaevskii type equation with a nonlocal external potential, which is solved by variational and numerical means (considered as the exact solution) to find the parameter conditions for the existence of self-localized solutions. The variational approach predicts a threshold on the on-site or nonlocality parameter where localized solutions cease to exist from the Non-Linear Schrödinger soliton limit. A numerical continuation of stationary state solutions in the corresponding discrete system is used to confirm the prediction of the turning value in the on-site term. We finally study the full stationary state and make use of an approximation, proposed by Briedis et al. [17], for the nonlocal term, corresponding to strong nonlocalities, to find analytic expressions for self-localized states in terms of the series solutions of a nonlinear modified Bessel equation.
AB - We consider the problem of electron transport in a deformable continuum medium subjected to an external harmonic substrate potential. We then consider the quasi-stationary state of the full problem to find a Gross–Pitaevskii type equation with a nonlocal external potential, which is solved by variational and numerical means (considered as the exact solution) to find the parameter conditions for the existence of self-localized solutions. The variational approach predicts a threshold on the on-site or nonlocality parameter where localized solutions cease to exist from the Non-Linear Schrödinger soliton limit. A numerical continuation of stationary state solutions in the corresponding discrete system is used to confirm the prediction of the turning value in the on-site term. We finally study the full stationary state and make use of an approximation, proposed by Briedis et al. [17], for the nonlocal term, corresponding to strong nonlocalities, to find analytic expressions for self-localized states in terms of the series solutions of a nonlinear modified Bessel equation.
KW - Davydov's equations
KW - Gross–Pitaevskii equation
KW - NLS soliton
KW - On-site interactions
KW - Variational approximation
UR - http://www.scopus.com/inward/record.url?scp=84980012075&partnerID=8YFLogxK
U2 - 10.1016/j.physleta.2016.06.052
DO - 10.1016/j.physleta.2016.06.052
M3 - Artículo
SN - 0375-9601
VL - 380
SP - 2828
EP - 2835
JO - Physics Letters, Section A: General, Atomic and Solid State Physics
JF - Physics Letters, Section A: General, Atomic and Solid State Physics
IS - 36
ER -