2,362 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
Energy thresholds for discrete breathers
Discrete breathers are time-periodic, spatially localized solutions of the
equations of motion for a system of classical degrees of freedom interacting on
a lattice. An important issue, not only from a theoretical point of view but
also for their experimental detection, are their energy properties. We
considerably enlarge the scenario of possible energy properties presented by
Flach, Kladko, and MacKay [Phys. Rev. Lett. 78, 1207 (1997)]. Breather energies
have a positive lower bound if the lattice dimension is greater than or equal
to a certain critical value d_c. We show that d_c can generically be greater
than two for a large class of Hamiltonian systems. Furthermore, examples are
provided for systems where discrete breathers exist but do not emerge from the
bifurcation of a band edge plane wave. Some of these systems support breathers
of arbitrarily low energy in any spatial dimension.Comment: 4 pages, 4 figure
Discrete Nonlinear Schr{\"o}dinger Breathers in a Phonon Bath
We study the dynamics of the discrete nonlinear Schr{\"o}dinger lattice
initialized such that a very long transitory period of time in which standard
Boltzmann statistics is insufficient is reached. Our study of the nonlinear
system locked in this {\em non-Gibbsian} state focuses on the dynamics of
discrete breathers (also called intrinsic localized modes). It is found that
part of the energy spontaneously condenses into several discrete breathers.
Although these discrete breathers are extremely long lived, their total number
is found to decrease as the evolution progresses. Even though the total number
of discrete breathers decreases we report the surprising observation that the
energy content in the discrete breather population increases. We interpret
these observations in the perspective of discrete breather creation and
annihilation and find that the death of a discrete breather cause effective
energy transfer to a spatially nearby discrete breather. It is found that the
concepts of a multi-frequency discrete breather and of internal modes is
crucial for this process. Finally, we find that the existence of a discrete
breather tends to soften the lattice in its immediate neighborhood, resulting
in high amplitude thermal fluctuation close to an existing discrete breather.
This in turn nucleates discrete breather creation close to a already existing
discrete breather
On inward motion of the magnetopause preceding a substorm
Magnetopause inward motion preceding magnetic storms observed by means of OGO-E magnetomete
Transition to Chaos in a Shell Model of Turbulence
We study a shell model for the energy cascade in three dimensional turbulence
at varying the coefficients of the non-linear terms in such a way that the
fundamental symmetries of Navier-Stokes are conserved. When a control parameter
related to the strength of backward energy transfer is enough small,
the dynamical system has a stable fixed point corresponding to the Kolmogorov
scaling. This point becomes unstable at where a stable
limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal
decomposition, the transition to chaos is shown to follow the Ruelle-Takens
scenario. For the dynamical evolution is intermittent
with a positive Lyapunov exponent. In this regime, there exists a strange
attractor which remains close to the Kolmogorov (now unstable) fixed point, and
a local scaling invariance which can be described via a intermittent
one-dimensional map.Comment: 16 pages, Tex, 20 figures available as hard cop
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)
Multi-peaked localized states of DNLS in one and two dimensions
Multi-peaked localized stationary solutions of the discrete nonlinear
Schrodinger (DNLS) equation are presented in one (1D) and two (2D) dimensions.
These are excited states of the discrete spectrum and correspond to
multi-breather solutions. A simple, very fast, and efficient numerical method,
suggested by Aubry, has been used for their calculation. The method involves no
diagonalization, but just iterations of a map, starting from trivial solutions
of the anti-continuous limit. Approximate analytical expressions are presented
and compared with the numerical results. The linear stability of the calculated
stationary states is discussed and the structure of the linear stability
spectrum is analytically obtained for relatively large values of nonlinearity.Comment: 34 pages, 12 figure
The Exact Ground State of the Frenkel-Kontorova Model with Repeated Parabolic Potential: I. Basic Results
The problem of finding the exact energies and configurations for the
Frenkel-Kontorova model consisting of particles in one dimension connected to
their nearest-neighbors by springs and placed in a periodic potential
consisting of segments from parabolas of identical (positive) curvature but
arbitrary height and spacing, is reduced to that of minimizing a certain convex
function defined on a finite simplex.Comment: 12 RevTeX pages, using AMS-Fonts (amssym.tex,amssym.def), 6
Postscript figures, accepted by Phys. Rev.
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