Search results for "Nonlinear"

Magnetism in lowdimensional systems

1991

Abstract Magnetism in lowdimensional systems is characterized by the importance of space and time dependent correlations with respect to static long range order which does not exist for finite temperatures in such systems except for the 2D-Ising model. Typical properties of these strongly fluctuating systems will be discussed and compared to the behaviour of normal magnets. Strongly nonlinear effects can be observed, like solitons and new quantum groundstates as in the 1D-Heisenberg antiferromagnet for S=1. As real crystals with quasi-lowdimensional magnetic behaviour can be obtained, experiments in this field have significantly advanced our understanding of collective processes in systems …

Truncated thermalization of incoherent optical waves through supercontinuum generation in photonic crystal fibers

2013

We revisit the process of optical wave thermalization through supercontinuum generation in photonic crystal fibers. We report theoretically and numerically a phenomenon of `truncated thermalization': The incoherent optical wave exhibits an irreversible evolution toward a Rayleigh-Jeans thermodynamic equilibrium state characterized by a compactly supported spectral shape. The theory then reveals the existence of a frequency cut-off which regularizes the ultraviolet catastrophe inherent to ensembles of classical nonlinear waves. This phenomenon sheds new light on the mechanisms underlying the formation of bounded supercontinuum spectra in photonic crystal fibers.

Spectral analysis of two-dimensional Bose-Hubbard models

2016

One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.

Slowdown and speedup of light pulses using the self-compensating photorefractive response

2011

We study theoretically the effects of pulse slowdown and speedup in ferroelectric Sn2P2S6 possessing a self-compensating photorefractive response. It is shown that both these effects can be implemented in one sample for sufficiently large values of the coupling strength. In contrast to other types of the photorefractive response (local and nonlocal), the output pulses do not suffer from strong spatial amplification and broadening.

Surface-directed spinodal decomposition: Lattice model versus Ginzburg-Landau theory

2009

When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long-wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. These boundary conditions can be derived from lattice models by suitable continuum approximations. But the lattice models can also be simulated directly, and thus used to clarify the conditions under which the Ginzburg–Landau type theory is valid. This comparison shows that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations can also be neglecte…

Reservoir Computing with Random Skyrmion Textures

2020

The Reservoir Computing (RC) paradigm posits that sufficiently complex physical systems can be used to massively simplify pattern recognition tasks and nonlinear signal prediction. This work demonstrates how random topological magnetic textures present sufficiently complex resistance responses for the implementation of RC as applied to A/C current pulses. In doing so, we stress how the applicability of this paradigm hinges on very general dynamical properties which are satisfied by a large class of physical systems where complexity can be put to computational use. By harnessing the complex resistance response exhibited by random magnetic skyrmion textures and using it to demonstrate pattern…

Novel prospects in hyperbolic metamaterials: Dyakonov-like surface waves

2014

Real lattices modelled by the nonlinear Schrödinger equation and its generalizations

2006

We present the analysis of two dimerized lattices : a bi-inductance electrical network with macroscopic wave modes, an antiferromagnetic chain whith microscopic spin waves. Using the multiple scale technique of reductive perturbation we show that the original discrete equations of motion can be reduced to a Nonlinear Schrodinger equation with complex coefficients for the first system and two coupled Nonlinear Schrodinger equations for the second system. The possible solutions of these equations are discussed in relation with our numerical simulations and real experiments.

LÉVY FLIGHT SUPERDIFFUSION: AN INTRODUCTION

2008

After a short excursion from discovery of Brownian motion to the Richardson "law of four thirds" in turbulent diffusion, the article introduces the L\'{e}vy flight superdiffusion as a self-similar L\'{e}vy process. The condition of self-similarity converts the infinitely divisible characteristic function of the L\'{e}vy process into a stable characteristic function of the L\'{e}vy motion. The L\'{e}vy motion generalizes the Brownian motion on the base of the $\alpha$-stable distributions theory and fractional order derivatives. The further development of the idea lies on the generalization of the Langevin equation with a non-Gaussian white noise source and the use of functional approach. Th…

Surface tension and interfacial fluctuations in d-dimensional Ising model

2005

The surface tension of rough interfaces between coexisting phases in 2D and 3D Ising models are discussed in view of the known results and some original calculations presented in this paper. The results are summarised in a formula, which allows to interpolate the corrections to finite-size scaling between two and three dimensions. The physical meaning of an analytic continuation to noninteger values of the spatial dimensionality d is discussed. Lattices and interfaces with properly defined fractal dimensions should fulfil certain requirements to possibly have properties of an analytic continuation from d-dimensional hypercubes. Here 2 appears as the marginal value of d below which the (d-1)…