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

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)

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

Solitons in Triangular and Honeycomb Dynamical Lattices with the Cubic Nonlinearity

We study the existence and stability of localized states in the discrete nonlinear Schr{\"o}dinger equation (DNLS) on two-dimensional non-square lattices. The model includes both the nearest-neighbor and long-range interactions. For the fundamental strongly localized soliton, the results depend on the coordination number, i.e., on the particular type of the lattice. The long-range interactions additionally destabilize the discrete soliton, or make it more stable, if the sign of the interaction is, respectively, the same as or opposite to the sign of the short-range interaction. We also explore more complicated solutions, such as twisted localized modes (TLM's) and solutions carrying multiple topological charge (vortices) that are specific to the triangular and honeycomb lattices. In the cases when such vortices are unstable, direct simulations demonstrate that they turn into zero-vorticity fundamental solitons.Comment: 17 pages, 13 figures, Phys. Rev.

Re-localization due to finite response times in a nonlinear Anderson chain

We study a disordered nonlinear Schr\"odinger equation with an additional relaxation process having a finite response time $\tau$. Without the relaxation term, $\tau=0$, this model has been widely studied in the past and numerical simulations showed subdiffusive spreading of initially localized excitations. However, recently Caetano et al.\ (EPJ. B \textbf{80}, 2011) found that by introducing a response time $\tau > 0$, spreading is suppressed and any initially localized excitation will remain localized. Here, we explain the lack of subdiffusive spreading for $\tau>0$ by numerically analyzing the energy evolution. We find that in the presence of a relaxation process the energy drifts towards the band edge, which enforces the population of fewer and fewer localized modes and hence leads to re-localization. The explanation presented here is based on previous findings by the authors et al.\ (PRE \textbf{80}, 2009) on the energy dependence of thermalized states.Comment: 3 pages, 4 figure

Asymptotic Dynamics of Breathers in Fermi-Pasta-Ulam Chains

We study the asymptotic dynamics of breathers in finite Fermi-Pasta-Ulam chains at zero and non-zero temperatures. While such breathers are essentially stationary and very long-lived at zero temperature, thermal fluctuations tend to lead to breather motion and more rapid decay

Spreading, Nonergodicity, and Selftrapping: a puzzle of interacting disordered lattice waves

Localization of waves by disorder is a fundamental physical problem encompassing a diverse spectrum of theoretical, experimental and numerical studies in the context of metal-insulator transitions, the quantum Hall effect, light propagation in photonic crystals, and dynamics of ultra-cold atoms in optical arrays, to name just a few examples. Large intensity light can induce nonlinear response, ultracold atomic gases can be tuned into an interacting regime, which leads again to nonlinear wave equations on a mean field level. The interplay between disorder and nonlinearity, their localizing and delocalizing effects is currently an intriguing and challenging issue in the field of lattice waves. In particular it leads to the prediction and observation of two different regimes of destruction of Anderson localization - asymptotic weak chaos, and intermediate strong chaos, separated by a crossover condition on densities. On the other side approximate full quantum interacting many body treatments were recently used to predict and obtain a novel many body localization transition, and two distinct phases - a localization phase, and a delocalization phase, both again separated by some typical density scale. We will discuss selftrapping, nonergodicity and nonGibbsean phases which are typical for such discrete models with particle number conservation and their relation to the above crossover and transition physics. We will also discuss potential connections to quantum many body theories.Comment: 13 pages in Springer International Publishing Switzerland 2016 1 M. Tlidi and M. G. Clerc (eds.), Nonlinear Dynamics: Materials, Theory and Experiment, Springer Proceedings in Physics 173. arXiv admin note: text overlap with arXiv:1405.112

Structure, stability and stress properties of amorphous and nanostructured carbon films

Structural and mechanical properties of amorphous and nanocomposite carbon are investigated using tight-binding molecular dynamics and Monte Carlo simulations. In the case of amorphous carbon, we show that the variation of sp^3 fraction as a function of density is linear over the whole range of possible densities, and that the bulk moduli follow closely the power-law variation suggested by Thorpe. We also review earlier work pertained to the intrinsic stress state of tetrahedral amorphous carbon. In the case of nanocomposites, we show that the diamond inclusions are stable only in dense amorphous tetrahedral matrices. Their hardness is considerably higher than that of pure amorphous carbon films. Fully relaxed diamond nanocomposites possess zero average intrinsic stress.Comment: 10 pages, 6 figure

Photoionization of hydrogen in atmospheres of magnetic neutron stars

The strong magnetic fields (B ~ 10^{12} - 10^{13} G) characteristic of neutron stars make all the properties of an atom strongly dependent on the transverse component K_\perp of its generalized momentum. In particular, the photoionization process is modified substantially: (i) threshold energies are decreased as compared with those for an atom at rest, (ii) cross section values are changed significantly, and (iii) selection rules valid for atoms at rest are violated by the motion so that new photoionization channels become allowed. To calculate the photoionization cross sections, we, for the first time, employ exact numerical treatment of both initial and final atomic states. This enables us to take into account the quasi-bound (autoionizing) atomic states as well as coupling of different ionization channels. We extend the previous consideration, restricted to the so-called centered states corresponding to relatively small values of K_\perp, to arbitrary states of atomic motion. We fold the cross sections with the thermal distribution of atoms over K. For typical temperatures of neutron star atmospheres, the averaged cross sections differ substantially from those of atoms at rest. In particular, the photoionization edges are strongly broadened by the thermal motion of atoms; this "magnetic broadening" exceeds the usual Doppler broadening by orders of magnitude. The decentered states of the atoms give rise to the low-energy component of the photoionization cross section. This new component grows significantly with increasing temperature above 10^{5.5} K and decreasing density below 1 g/cm^3, i.e., for the conditions expected in atmospheres of middle-aged neutron stars.Comment: 19 pages including 8 figures, LaTeX (using aas2pp4.sty and epsf.sty). Accepted for publication in ApJ. PostScript available also at http://www.ioffe.rssi.ru/dtastrop.htm