637 research outputs found
A Nonlinear Dynamical Model for Ultrafast Catalytic Transfer of Electrons at Zero Temperature
The complex amplitudes of the electronic wavefunctions on different sites are
used as Kramers variables for describing Electron Transfer. The strong coupling
of the electronic charge to the many nuclei, ions, dipoles, etc, of the
environment, is modeled as a thermal bath better considered classically. After
elimination of the bath variables, the electron dynamics is described by a
discrete nonlinear Schrodinger equation with norm preserving dissipative terms
and Langevin random noises (at finite temperature). The standard Marcus results
are recovered far from the inversion point, where atomic thermal fluctuations
adiabatically induce the electron transfer. Close to the inversion point, in
the non-adiabatic regime, electron transfer may become ultrafast (and
selective) at low temperature essentially because of the nonlinearities, when
these are appropriately tuned. We demonstrate and illustrate numerically that a
weak coupling of the donor site with an extra appropriately tuned (catalytic)
site, can trigger an ultrafast electron transfer to the acceptor site at zero
degree Kelvin, while in the absence of this catalytic site no transfer would
occur at all (the new concept of Targeted Transfer initially developed for
discrete breathers is applied to polarons in our theory). Among other
applications, this theory should be relevant for describing the ultrafast
electron transfer observed in the photosynthetic reaction centers of living
cells.Comment: submitted to the Proceedings of "Dynamics Days Asia-Pacific: Second
International Conference on Nonlinear Science", HangZhou, China, August 8-12,
200
Discrete breathers in polyethylene chain
The existence of discrete breathers (DBs), or intrinsic localized modes
(localized periodic oscillations of transzigzag) is shown. In the localization
region periodic contraction-extension of valence C-C bonds occurs which is
accompanied by decrease-increase of valence angles. It is shown that the
breathers present in thermalized chain and their contribution dependent on
temperature has been revealed.Comment: 5 pages, 6 figure
Dynamical studies of periodic and disordered systems
The time evolution of two classes of systems is studied with real time molecular dynamics simulations. The first consists of a coupled electron-lattice system. For a periodic system, we present results for the time evolution of a one-dimensional system consisting of an electron, described by a tight-binding Hamiltonian, and a harmonic lattice, coupled by a deformation-type potential. We solve numerically the nonlinear system of equations of motion for this model in order to study the effects of varying the electronic effective mass for several initial conditions and coupling strengths. A large effective mass favors localized polaron formation for initially localized electrons. For initially extended electronic states, increasing the effective mass of an electron initially close to the bottom of the band makes localization more difficult, while for an initially highly excited electron, localized polaron formation is possible only when the electronic effective mass and the atomic masses of the lattice become of the same order. For a small parameter range, we find an impressive recurrence, a periodic and a complete exchange between the electronic and vibrational degrees of freedom of a small part of the initial electronic energy. The disordered case, described by a tight-binding model exhibiting metal-insulator transition (the diagonal matrix elements having a spatial variation incommensurate with the lattice), demonstrates the combined effects of disorder and electron-phonon interaction. The el-ph interaction has profound effects, especially on one-electron extended states just above the mobility edge, where the electronic states change from extended to localized. Polaron formation is facilitated close to the mobility edge and, in most cases, the localization length (lc) decreases upon increasing the disorder or el-ph coupling, as expected. However, for strongly localized states due to disorder or el-ph interaction, increase of el-ph coupling or disorder, respectively, results in an increase of lc. This increase is due to phonon assisted hopping. The second class of systems studied consists of carbon and hydrogen. We calculate phonon anharmonic effects in diamond and graphite using a tight-binding molecular dynamics scheme. Using one-phonon spectral intensities that have been calculated through the Fourier transform of the velocity-velocity correlation function, we study the temperature dependence of the phonon frequency shift and phonon linewidth. In the case of the zone-center optical mode of diamond where experimental data are available, our results are in good agreement with experiment. A tight-binding model for carbon-hydrogen interaction is developed and used in molecular dynamics simulations. The parameters are obtained by fitting to the electronic and vibrational properties of methane. The results obtained for hydrocarbon molecules are in good agreement with experimental data and first-principles results. Interstitial hydrogen in diamond is also studied with this model and the results are compared with available experimental and ab initio results. The case of hydrogenated amorphous carbon is considered as well
Anomalous Thermostat and Intraband Discrete Breathers
We investigate the dynamics of a macroscopic system which consists of an
anharmonic subsystem embedded in an arbitrary harmonic lattice, including
quenched disorder. Elimination of the harmonic degrees of freedom leads to a
nonlinear Langevin equation for the anharmonic coordinates. For zero
temperature, we prove that the support of the Fourier transform of the memory
kernel and of the time averaged velocity-velocity correlations functions of the
anharmonic system can not overlap. As a consequence, the asymptotic solutions
can be constant, periodic,quasiperiodic or almost periodic, and possibly weakly
chaotic. For a sinusoidal trajectory with frequency we find that the
energy transferred to the harmonic system up to time is proportional
to . If equals one of the phonon frequencies ,
it is . We prove that there is a full measure set such that for
in this set it is , i.e. there is no energy dissipation.
Under certain conditions there exists a zero measure set such that for (0 \leq
\alpha < 1)(1 <\alpha \leq 2)\Omega\Omega\mathcal{C}(k)\Omega\in\mathcal{C}(k)t$.Comment: Physica D in prin
Stationary localized states due to nonlinear impurities described by the modified discrete nonlinear Schr\"odinger equation
The modified discrete nonlinear Schr\"odinger equation is used to study the
formation of stationary localized states in a one-dimensional lattice with a
single impurity and an asymmetric dimer impurity. A periodically modulated and
a perfectly nonlinear chain is also considered. Phase diagrams of localized
states for all systems are presented. From the mean square displacement
calculation, it is found that all states are not localized even though the
system comprises random nonlinear site energies. Stability of the states is
discussed.Comment: Six pages including five figure
Absence of Wavepacket Diffusion in Disordered Nonlinear Systems
We study the spreading of an initially localized wavepacket in two nonlinear
chains (discrete nonlinear Schroedinger and quartic Klein-Gordon) with
disorder. Previous studies suggest that there are many initial conditions such
that the second moment of the norm and energy density distributions diverge as
a function of time. We find that the participation number of a wavepacket does
not diverge simultaneously. We prove this result analytically for
norm-conserving models and strong enough nonlinearity. After long times the
dynamical state consists of a distribution of nondecaying yet interacting
normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this
result holds for any initially localized wavepacket, a limit profile for the
norm/energy distribution with infinite second moment should exist in all cases
which rules out the possibility of slow energy diffusion (subdiffusion). This
limit profile could be a quasiperiodic solution (KAM torus)
Extreme events in two dimensional disordered nonlinear lattices
Spatiotemporal complexity is induced in a two dimensional nonlinear
disordered lattice through the modulational instability of an initially weakly
perturbed excitation. In the course of evolution we observe the formation of
transient as well as persistent localized structures, some of which have
extreme magnitude. We analyze the statistics of occurrence of these extreme
collective events and find that the appearance of transient extreme events is
more likely in the weakly nonlinear regime. We observe a transition in the
extreme events recurrence time probability from exponential, in the
nonlinearity dominated regime, to power law for the disordered one.Comment: 5 figures, 5 page
Aspects of Discrete Breathers and New Directions
We describe results concerning the existence proofs of Discrete Breathers
(DBs) in the two classes of dynamical systems with optical linear phonons and
with acoustic linear phonons. A standard approach is by continuation of DBs
from an anticontinuous limit. A new approach, which is purely variational, is
presented. We also review some numerical results on intraband DBs in random
nonlinear systems. Some non-conventional physical applications of DBs are
suggested. One of them is understanding slow relaxation properties of glassy
materials. Another one concerns energy focusing and transport in biomolecules
by targeted energy transfer of DBs. A similar theory could be used for
describing targeted charge transfer of nonlinear electrons (polarons) and, more
generally, for targeted transfer of several excitations (e.g. Davydov soliton).Comment: to appear in the Proceedings of NATO Advanced Research Workshop
"Nonlinearity and Disorder: Theory and Applications",
Tashkent,Uzbekistan,October 1-6, 200
Hydrogen dynamics and light-induced structural changes in hydrogenated amorphous silicon
We use accurate first principles methods to study the network dynamics of
hydrogenated amorphous silicon, including the motion of hydrogen. In addition
to studies of atomic dynamics in the electronic ground state, we also adopt a
simple procedure to track the H dynamics in light-excited states. Consistent
with recent experiments and computer simulations, we find that dihydride
structures are formed for dynamics in the light-excited states, and we give
explicit examples of pathways to these states. Our simulations appear to be
consistent with aspects of the Staebler-Wronski effect, such as the
light-induced creation of well separated dangling bonds.Comment: 9 pages, 8 figures, submitted to PR
Softening of ultra-nanocrystalline diamond at low grain sizes
Ultra-nanocrystalline diamond is a polycrystalline material, having
crystalline diamond grains of sizes in the nanometer regime. We study the
structure and mechanical properties of this material as a function of the
average grain size, employing atomistic simulations. From the calculated
elastic constants and the estimated hardness, we observe softening of the
material as the size of its grains decreases. We attribute the observed
softening to the enhanced fraction of interfacial atoms as the average grain
size becomes smaller. We provide a fitting formula for the scaling of the
cohesive energy and bulk modulus with respect to the average grain size. We
find that they both scale as quadratic polynomials of the inverse grain size.
Our formulae yield correct values for bulk diamond in the limit of large grain
sizes.Comment: 5 pages, 3 figures, to be published in Acta Materiali
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