Quantum Vibrational Impurity Embedded in a One-dimensional Chain

We perform a fully quantum mechanical numerical calculation for the problem of a single electron (or excitation) propagating in a N-site one-dimensional chain in the presence of a single Holstein impurity. We compute the long-time averaged probability for finding the electron on the impurity site as a function of the nonlinearity parameter, defined in terms of the electron-phonon coupling strength and the oscillator frequency. The results, in the intermediate nonlinearity parameter range, differ substantially from the ones obtained through the use of the discrete nonlinear Schroedinger equation, even in the high-frequency regime.Comment: 8 pages, 4 figure

Cooperative surmounting of bottlenecks

The physics of activated escape of objects out of a metastable state plays a key role in diverse scientific areas involving chemical kinetics, diffusion and dislocation motion in solids, nucleation, electrical transport, motion of flux lines superconductors, charge density waves, and transport processes of macromolecules, to name but a few. The underlying activated processes present the multidimensional extension of the Kramers problem of a single Brownian particle. In comparison to the latter case, however, the dynamics ensuing from the interactions of many coupled units can lead to intriguing novel phenomena that are not present when only a single degree of freedom is involved. In this review we report on a variety of such phenomena that are exhibited by systems consisting of chains of interacting units in the presence of potential barriers. In the first part we consider recent developments in the case of a deterministic dynamics driving cooperative escape processes of coupled nonlinear units out of metastable states. The ability of chains of coupled units to undergo spontaneous conformational transitions can lead to a self-organised escape. The mechanism at work is that the energies of the units become re-arranged, while keeping the total energy conserved, in forming localised energy modes that in turn trigger the cooperative escape. We present scenarios of significantly enhanced noise-free escape rates if compared to the noise-assisted case. The second part deals with the collective directed transport of systems of interacting particles overcoming energetic barriers in periodic potential landscapes. Escape processes in both time-homogeneous and time-dependent driven systems are considered for the emergence of directed motion. It is shown that ballistic channels immersed in the associated high-dimensional phase space are the source for the directed long-range transport

Dynamical symmetry breaking through AI: the dimer self-trapping transition

The nonlinear dimer obtained through the nonlinear Schrödinger equation has been a workhorse for the discovery the role nonlinearity plays in strongly interacting systems. While the analysis of the stationary states demonstrates the onset of a symmetry broken state for some degree of nonlinearity, the full dynamics maps the system into an effective [Formula: see text] model. In this later context, the self-trapping transition is an initial condition-dependent transfer of a classical particle over a barrier set by the nonlinear term. This transition that has been investigated analytically and mathematically is expressed through the hyperbolic limit of Jacobian elliptic functions. The aim of this work is to recapture this transition through the use of methods of Artificial Intelligence (AI). Specifically, we used a physics motivated machine learning model that is shown to be able to capture the original dynamic self-trapping transition and its dependence on initial conditions. Exploitation of this result in the case of the nondegenerate nonlinear dimer gives additional information on the more general dynamics and helps delineate linear from nonlinear localization. This work shows how AI methods may be embedded in physics and provide useful tools for discovery.Boston UniversityFirst author draf

Driven linear modes: Analytical solutions for finite discrete systems

We have obtained exact analytical expressions in closed form, for the linear modes excited in finite and discrete systems that are driven by a spatially homogeneous alternating field. Those modes are extended for frequencies within the linear frequency band while they are either end-localized or end-avoided for frequencies outside the linear frequency band. The analytical solutions are resonant at particular frequencies, which compose the frequency dispersion relation of the finite system.Comment: 4 pages, 3 figures, submitted to Phys. Rev.

Self-trapping transition for nonlinear impurities embedded in a Cayley tree

The self-trapping transition due to a single and a dimer nonlinear impurity embedded in a Cayley tree is studied. In particular, the effect of a perfectly nonlinear Cayley tree is considered. A sharp self-trapping transition is observed in each case. It is also observed that the transition is much sharper compared to the case of one-dimensional lattices. For each system, the critical values of $\chi$ for the self-trapping transitions are found to obey a power-law behavior as a function of the connectivity $K$ of the Cayley tree.Comment: 6 pages, 7 fig

Fractal entropy of a chain of nonlinear oscillators

We study the time evolution of a chain of nonlinear oscillators. We focus on the fractal features of the spectral entropy and analyze its characteristic intermediate timescales as a function of the nonlinear coupling. A Brownian motion is recognized, with an analytic power-law dependence of its diffusion coefficient on the coupling.Comment: 6 pages, 3 figures, revised version to appear in Phys. Rev.

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

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

Heat conduction in 1D lattices with on-site potential

The process of heat conduction in one-dimensional lattice with on-site potential is studied by means of numerical simulation. Using discrete Frenkel-Kontorova, $\phi$--4 and sinh-Gordon we demonstrate that contrary to previously expressed opinions the sole anharmonicity of the on-site potential is insufficient to ensure the normal heat conductivity in these systems. The character of the heat conduction is determined by the spectrum of nonlinear excitations peculiar for every given model and therefore depends on the concrete potential shape and temperature of the lattice. The reason is that the peculiarities of the nonlinear excitations and their interactions prescribe the energy scattering mechanism in each model. For models sin-Gordon and $\phi$--4 phonons are scattered at thermalized lattice of topological solitons; for sinh-Gordon and $\phi$--4 - models the phonons are scattered at localized high-frequency breathers (in the case of $\phi$--4 the scattering mechanism switches with the growth of the temperature).Comment: 26 pages, 18 figure

Resonance Effects in the Nonadiabatic Nonlinear Quantum Dimer

The quantum nonlinear dimer consisting of an electron shuttling between the two sites and in weak interaction with vibrations, is studied numerically under the application of a DC electric field. A field-induced resonance phenomenon between the vibrations and the electronic oscillations is found to influence the electronic transport greatly. For initially delocalization of the electron, the resonance has the effect of a dramatic increase in the transport. Nonlinear frequency mixing is identified as the main mechanism that influences transport. A characterization of the frequency spectrum is also presented.Comment: 7 pages, 6 figure