Georgios Kopidakis

Absence of wave packet diffusion in disordered nonlinear systems

We study the spreading of an initially localized wave packet in two nonlinear chains (discrete nonlinear Schrödinger 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 diverges with time. We find that the participation number of a wave packet does not diverge simultaneously. We prove this result analytically for norm-conserving models and strong enough nonlinearity. After long times we find a distribution of nondecaying yet interacting normal modes. The Fourier spectrum shows quasiperiodic dynamics. Assuming this result holds for any initially localized wave packet, we rule out the possibility of slow energy diffusion. The dynamical state could approach a quasiperiodic solution (Kolmogorov-Arnold-Moser torus) in the long time limit.

Standing wave instabilities in a chain of nonlinear coupled oscillators

We consider existence and stability properties of nonlinear spatially periodic or quasiperiodic standing waves (SWs) in one-dimensional lattices of coupled anharmonic oscillators. Specifically, we consider Klein-Gordon (KG) chains with either soft (e.g., Morse) or hard (e.g., quartic) on-site potentials, as well as discrete nonlinear Schrodinger (DNLS) chains approximating the small-amplitude dynamics of KG chains with weak inter-site coupling. The SWs are constructed as exact time-periodic multibreather solutions from the anticontinuous limit of uncoupled oscillators. In the validity regime of the DNLS approximation these solutions can be continued into the linear phonon band, where they merge into standard harmonic SWs. For SWs with incommensurate wave vectors, this continuation is associated with an inverse transition by breaking of analyticity. When the DNLS approximation is not valid, the continuation may be interrupted by bifurcations associated with resonances with higher harmonics of the SW. Concerning the stability, we identify one class of SWs which are always linearly stable close to the anticontinuous limit. However, approaching the linear limit all SWs with non-trivial wave vectors become unstable through oscillatory instabilities, persisting for arbitrarily small amplitudes in infinite lattices. Investigating the dynamics resulting from these instabilities, we find two qualitatively different regimes for wave vectors smaller than or larger than π/2, respectively. In one regime persisting breathers are found, while in the other regime the system rapidly thermalizes.

KAM tori in 1D random discrete nonlinear Schrödinger model

We suggest that KAM theory could be extended for certain infinite-dimensional systems with purely discrete linear spectrum. We provide empirical arguments for the existence of square summable infinite-dimensional invariant tori in the random discrete nonlinear Schrodinger equation, appearing with a finite probability for a given initial condition with sufficiently small norm. Numerical support for the existence of a fat Cantor set of initial conditions generating almost periodic oscillations is obtained by analyzing i) sets of recurrent trajectories over successively larger time scales, and ii) finite-time Lyapunov exponents. The norm region where such KAM-like tori may exist shrinks to zero when the disorder strength goes to zero and the localization length diverges.

Analytic conditions for targeted energy transfer between nonlinear oscillators or discrete breathers

It is well known that any amount of energy injected in a harmonic oscillator which is resonant and weakly coupled with a second harmonic oscillator, tunnels back and forth between these two oscillators. When the two oscillators are anharmonic, the amplitude dependence of their frequencies breaks, in general, any eventual initial resonance so that no substantial energy transfer occurs unless, exceptionally, an almost perfect resonance persists. This paper considers this interesting situation more generally between two discrete breathers belonging to two weakly coupled nonlinear systems, finite or infinite. A specific amount of energy injected as a discrete breather in a nonlinear system (donor) which is weakly coupled to another nonlinear system (acceptor) sustaining another discrete breather, might be totally transferred and oscillate back and forth between these donor and acceptor breathers. The condition is that a certain well-defined detuning function is bounded from above and below by two coupling functions. This targeted energy transfer is selective, i.e., it only occurs for an initial energy close to a specific value. The explicit calculation of these functions in complex models with numerical techniques developed earlier for discrete breathers, allows one to detect the existence of possible targeted energy transfer, between which breathers, and at which energy. It should also help for designing models having desired targeted energy transfer properties at will. We also show how extra linear resonances could make the energy transfer incomplete and irreversible. Future developments of the theory will be able to describe more spectacular effects, such as targeted energy transfer cascades and avalanches, and energy funnels. Besides rather short-term applications for artificially built devices, this theory might provide an essential clue for understanding puzzling problems of energy kinetics in real materials, chemistry, and bioenergetics.

Discrete breathers in realistic models: hydrocarbon structures

Discrete breathers (DBs), or intrinsic localized modes, are time-periodic spatially localized solutions that exist generically in nonlinear discrete models and persist as long-lived robust solutions when they are not resonant with linear excitations. Without using the powerful but rather technical self-consistent methods of calculation already developed and applied to DBs in relatively simple models, we study DBs with tight-binding molecular dynamics simulations using a realistic model for carbon}hydrogen systems. We focus here on the carbon}hydrogen stretch vibrations, whose frequencies are well separated from the rest of the vibrational modes. We show that in the anharmonic region of the interaction potential these spatially localized solutions persist for time scales which are orders of magnitude longer than the period of the atomic vibrations and with frequencies that are di!erent from the normal-mode frequencies. The conditions under which these DB solutions are created, the implications on energy relaxation, and experimental evidence of their existence are discussed. 2001 Elsevier Science B.V. All rights reserved.

Transmission thresholds in time-periodically driven nonlinear disordered systems

We study energy propagation in locally time-periodically driven disordered nonlinear chains. For frequencies inside the band of linear Anderson modes, three different regimes are observed with increasing driver amplitude: 1) below threshold, localized quasiperiodic oscillations and no spreading; 2) three different regimes in time close to threshold, with almost regular oscillations initially, weak chaos and slow spreading for intermediate times and finally strong diffusion; 3) immediate spreading for strong driving. The thresholds are due to simple bifurcations, obtained analytically for a single oscillator, and numerically as turning points of the nonlinear response manifold for a full chain. Generically, the threshold is nonzero also for infinite chains.

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.

All-Optical Header Processing in a 42.6 Gb/s Optoelectronic Firewall

A novel architecture to enable future network security systems to provide effective protection in the context of continued traffic growth and the need to minimize energy consumption is proposed. It makes use of an all-optical prefiltering stage operating at the line rate under software control to distribute incoming packets to specialized electronic processors. An experimental system that integrates software controls and electronic interfaces with an all-optical pattern recognition system has demonstrated the key functions required by the new architecture. As an example, the ability to sort packets arriving in a 42.6 Gb/s data stream according to their service type was shown experimentally.

A tight-binding molecular dynamics study of phonon anharmonic effects in diamond and graphite

We study the temperature dependence of phonon frequency shifts and phonon linewidths in diamond and graphite using tight-binding molecular dynamics simulations. The calculation of one-phonon spectral intensities of several modes through velocity-velocity correlation functions allows a quantitative and nonperturbative study of these anharmonic effects. Our results for the zone-centre optical mode of diamond, for which experimental data are available, agree very well with first-order Raman-scattering measurements.

Shape-Dependent Single-Electron Levels for Au Nanoparticles

The shape of metal nanoparticles has a crucial role in their performance in heterogeneous catalysis as well as photocatalysis. We propose a method of determining the shape of nanoparticles based on measurements of single-electron quantum levels. We first consider nanoparticles in two shapes of high symmetry: cube and sphere. We then focus on Au nanoparticles in three characteristic shapes that can be found in metal/inorganic or metal/organic compounds routinely used in catalysis and photocatalysis. We describe the methodology we use to solve the Schrödinger equation for arbitrary nanoparticle shape. The method gives results that agree well with analytical solutions for the high-symmetry shapes. When we apply our method in realistic gold nanoparticle models, which are obtained from Wulff construction based on first principles calculations, the single-electron levels and their density of states exhibit distinct shape-dependent features. Results for clean-surface nanoparticles are closer to those for cubic particles, while CO-covered nanoparticles have energy levels close to those of a sphere. Thiolate-covered nanoparticles with multifaceted polyhedral shape have distinct levels that are in between those for sphere and cube. We discuss how shape-dependent electronic structure features could be identified in experiments and thus guide catalyst design.