Electronic dynamics under effect of a nonlinear Morse interaction and a static electric field

The problem concerning the time-dependent behavior of an initially localized electronic wave-packet under effect
of nonlinearity and a static electric field has attracted the
interest of scientific community.
It is well known that, at the absence of nonlinearity, a static electric field
applied parallel to a periodic lattice promotes the dynamic localization of a
given initial wave-packet. Furthermore, the presence of static electric field
gives rise to an oscillatory behavior of the electron wave packet (also called "
Bloch oscillations"). The size of the region over which the electron oscillates and the period of
these oscillations are inversely proportional to the magnitude of the static
electric field.
In this work we will make a contribution by going forward on the understanding
of electronic transport in low-dimensional nonlinear systems under effect of
uniform electric field. We study numerically the one-electron dynamics in a
one-dimension alloy in which that the atoms are coupled by a Morse potential. In
addition, we consider a static electric field parallel to chain. Within our
model, the electron transport is treated quantum-mechanically over the alloy in
tight-binding approximation and the longitudinal vibrations of the lattice are
described by using classical formalism. The electron-phonon interaction was
introduced by considering the electron hopping as a function of the
effective distance
between neighboring atoms. By solving numerically dynamic equations for
electron and lattice we can compute the spreading of an initially localized
electronic wave-packet. We
report numerical evidences of the existence of an electron-soliton pair even at
the presence of electric field. We offer a detailed analysis of the dependence
of this electron-soliton pair with the magnitude of the electric field and the electron-phonon interaction.