arXiv subjects

Ramaz Khomeriki

Publications and source records attributed to Ramaz Khomeriki.

48 records · Page 3Linked to original sources

arXiv2004

The Anti-FPU Problem

We present a detailed analysis of the modulational instability of the zone-boundary mode for one and higher-dimensional Fermi-Pasta-Ulam (FPU) lattices. Following this instability, a process of relaxation to equipartition takes place, which we have called the Anti-FPU problem because the energy is initially fed into the highest frequency part of the spectrum, at variance with the original FPU problem (low frequency excitations of the lattice). This process leads to the formation of chaotic breathers in both one and two dimensions. Finally, the system relaxes to energy equipartition on time scales which increase as the energy density is decreased. We show that breathers formed when cooling the lattice at the edges, starting from a random initial state, bear strong qualitative similarities with chaotic breathers.

nlin.PS↗

arXiv2004

Nonlinear supratransmission and bistability in the Fermi-Pasta-Ulam model

The recently discovered phenomenon of nonlinear supratransmission consists in a sudden increase of the amplitude of a transmitted wave triggered by the excitation of nonlinear localized modes of the medium. We examine this process for the Fermi-Pasta-Ulam chain, sinusoidally driven at one edge and damped at the other. The supratransmission regime occurs for driving frequencies above the upper band-edge and originates from direct moving discrete breather creation. We derive approximate analytical estimates of the supratransmission threshold, which are in excellent agreement with numerics. When analysing the long-time behavior, we discover that, below the supratransmission threshold, a conducting stationary state coexists with the insulating one. We explain the bistable nature of the energy flux in terms of the excitation of quasi-harmonic extended waves. This leads to the analytical calculation of a lower-transmission threshold which is also in reasonable agreement with numerical experiments.

cond-mat.stat-mech↗

arXiv2004

Landau-Zener Tunnelling in Waveguide Arrays

Landau-Zener tunnelling is discussed in connection with optical waveguide arrays. Light injected in a specific band of the Bloch spectrum in the propagation constant can be transmitted to another band, changing its physical properties. This is achieved using two waveguide arrays with different refractive indices, which amounts to consider a Schrödinger equation in a periodic potential with a step. The step causes wave "acceleration" and thus induces Landau-Zener tunnelling. The region of physical parameters where this phenomenon can occur is analytically determined and a realistic experimental setup is suggested. Its application could allow the realization of light filters.

cond-mat.other↗

arXiv2004

Self-focusing magnetostatic beams in thin magnetic films

The possibility of generation of stable self-focusing beams in in-plane magnetized thin magnetic films is considered and theoretical conditions for the existence of such localized solutions are discussed. It is shown that for the definite direction between static magnetizing field and preferential direction of radiation from microwave antenna the problem reduces to the one-dimensional nonlinear Schroedinger equation. For such angles it is possible to generate stable self-focusing beams. Particular values of beam width and propagation angles versus magnitude of magnetizing field are calculated in order to suggest the realistic experimental setup for the observation of discovered effect.

cond-mat.other↗

arXiv2004

Ratchet-Like Solitonic Transport in Quantum Hall Bilayers

The pseudo-spin model for double layer quantum Hall system with total landau level filling factor $ν=1$ is discussed. Unlike the "traditional" one where interlayer voltage enters as static magnetic field along pseudo- spin hard axis, in our model we consider applied interlayer voltage as a frequency of precessing pseudo-magnetic field lying into the easy plane. It is shown that a Landau-Lifshitz equation for the considered pseudo magnetic system well describes existing experimental data. Besides that, the mentioned model predicts novel directed intra-layer transport phenomenon in the system: unidirectional intra-layer energy transport is realized due to interlayer voltage induced motion of topological kinks. This effect could be observed experimentally detecting counter-propagating intra-layer inhomogeneous charge currents which are proportional to the interlayer voltage and total topological charge of the pseudo-spin system.

cond-mat.mes-hall↗

arXiv2004

Interaction of spatial solitons in nonlinear optical medium

The effects caused by nonresonant nonlinear interaction between noncollinear self-focusing beams are considered in 2D optical samples using multi-scale analysis. The analytical expression for the beams trajectories shift due to the mutual interaction is derived, and the range of parameters is given beyond which the mentioned consideration fails. We compare our results with the naive geometrical optics model. It is shown that these two approaches give the same results. This justifies the use of geometrical optics approach for description of elastic and almost-elastic collision processes both in Kerr and saturable nonlinear media.

cond-mat.other↗

arXiv2004

Supersonic Discrete Kink-Solitons and Sinusoidal Patterns with "Magic" wavenumber in Anharmonic Lattices

The sharp pulse method is applied to Fermi-Pasta-Ulam (FPU) and Lennard-Jones (LJ) anharmonic lattices. Numerical simulations reveal the presence of high energy strongly localized ``discrete'' kink-solitons (DK), which move with supersonic velocities that are proportional to kink amplitudes. For small amplitudes, the DK's of the FPU lattice reduce to the well-known ``continuous'' kink-soliton solutions of the modified Korteweg-de Vries equation. For high amplitudes, we obtain a consistent description of these DK's in terms of approximate solutions of the lattice equations that are obtained by restricting to a bounded support in space exact solutions with sinusoidal pattern characterized by the ``magic'' wavenumber $k=2π/3$. Relative displacement patterns, velocity versus amplitude, dispersion relation and exponential tails found in numerical simulations are shown to agree very well with analytical predictions, for both FPU and LJ lattices.

cond-mat.stat-mech↗

arXiv2003

Nonlinear Band Gap Transmission in Optical Waveguide Arrays

The effect of nonlinear transmission in coupled optical waveguide arrays is theoretically investigated via numerical simulations on the corresponding model equations. The realistic experimental setup is suggested injecting the beam in a single boundary waveguide, linear refractive index of which ($n_0$) is larger than one ($n$) of other identical waveguides in the array. Particularly, the effect holds if $ω(n_0-n)/c>2Q$, where $Q$ is a linear coupling constant between array waveguides, $ω$ is a carrier wave frequency and $c$ is a light velocity. Making numerical experiments in case of discrete nonlinear Schrödinger equation it is shown that the energy transfers from the boundary waveguide to the waveguide array above certain threshold intensity of the injected beam. This effect is explained by means of the creation and propagation of gap solitons in full analogy with the similar phenomenon of nonlinear supratransmission [F. Geniet, J. Leon, PRL, {\bf 89}, 134102, (2002)] in case of discrete sine-Gordon lattice.

cond-mat↗

arXiv2002

Goldstone mode kink-solitons in double layer quantum Hall systems

It is shown that in charge unbalanced double layer quantum Hall system with zero tunneling pseudospin Goldstone mode excitations form moving kink-soliton in weakly nonlinear limit. This charge-density localization moves with a velocity of gapless linear spin-wave mode and could be easily observed experimentally. We claim that mentioned Goldstone mode kink-solitons define diffusionless charge transport properties in double layer quantum Hall systems.

cond-mat.mes-hall↗

arXiv2002

Excitation of travelling multibreathers in anharmonic chains

We study the dynamics of the "externally" forced and damped Fermi-Pasta-Ulam (FPU) 1D lattice. The forcing has the spatial symmetry of the Fourier mode with wavenumber p and oscillates sinusoidally in time with the frequency omega. When omega is in the phonon band, the p-mode becomes modulationally unstable above a critical forcing, which we determine analytically in terms of the parameters of the system. For omega above the phonon band, the instability of the p-mode leads to the formation of a travelling multibreather, that, in the low-amplitude limit could be described in terms of soliton solutions of a suitable driven-damped nonlinear Schroedinger (NLS) equation. Similar mechanisms of instability could show up in easy-axis magnetic structures, that are governed by such NLS equations.

nlin.PS↗

arXiv2001

Interaction of a Kink-Soliton with a Breather in a Fermi-Pasta-Ulam Chain

Collision process between breather and moving kink-soliton is investigated both analytically and numerically in Fermi-Pasta-Ulam (FPU) chains. As it is shown by both analytical and numerical consideration low amplitude breathers and soft kinks retain their shapes after interaction. Low amplitude breather only changes the location after collision and remains static. As the numerical simulations show, the shift of its position is proportional to the stiffness of the kink-soliton, what is in accordance with the analytical predictions made in this paper. The numerical experiments are also carried out for large amplitude breathers and some interesting effects are observed: The odd parity large amplitude breather does not change position when colliding with widely separated soft kink-antikink pair, whilst in the case of closely placed kink-antikink pair the breather transforms into the moving one. Therefore it is suggested that the "harmless" objects similar to the kink-solitons in FPU chains could be used in order to displace or move the strongly localized structures in realistic physical systems. In particular, the analogies with quasi-one dimensional easy-plane type spin structures are discussed.

cond-mat↗

arXiv2001

Pattern formation and localization in the forced-damped FPU lattice

We study spatial pattern formation and energy localization in the dynamics of an anharmonic chain with quadratic and quartic intersite potential subject to an optical, sinusoidally oscillating field and a weak damping. The zone-boundary mode is stable and locked to the driving field below a critical forcing that we determine analytically using an approximate model which describes mode interactions. Above such a forcing, a standing modulated wave forms for driving frequencies below the band-edge, while a ``multibreather'' state develops at higher frequencies. Of the former, we give an explicit approximate analytical expression which compares well with numerical data. At higher forcing space-time chaotic patterns are observed.

nlin.PS↗