Localized vibrations in three-dimensional lattices with defects

The method used in previous papers [1], [2]to calculate the frequency of localized vibrations of a diatomic linear chain with defects is generalized to an arbitrary type of crystal lattice.     

Localized optical structures in the scheme of a nonlinear layer with a feedback mirror

An analysis is made of the dynamics of the transverse structure of the field in the scheme of a layer of a medium with nonlinear amplitude-phase transmittance and a feedback mirror separated from it by a linear spacing. For the case of small field changes in a single passage, an approximate equation is derived, which is close in form to the equation used in the average-field approximation for nonlinear interferometers excited with external emission. For the nonlinearity of threshold type, an analytical form is presented for the field distribution corresponding to localized dissipative structures (dissitons).     

Vortex structures in planar lattices of magnetic dipoles in the presence of exchange coupling

Vortex equilibrium states of planar square lattices of magnetic dipoles in the presence of the exchange interaction have been studied. It has been shown that the vortex equilibrium configurations differ in the position of the vortex center and, correspondingly, in the magnitude and direction of the total magnetic moment of the system. In the case of the position of the vortex center in the center of the array, the total magnetic moment of the system is zero. The vortex center moves in the direction perpendicular to the field under the action of the external planar magnetic field on the system. Thus, the transitions between different equilibrium vortex configurations are implemented and the magnetic moment of the system of dipoles is controlled.     

Optical solitons supported by finite waveguide lattices with diffusive nonlocal nonlinearity

We investigate the properties of fundamental, multi-peak, and multi-peaked twisted solitons in three types of finite waveguide lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Two opposite soliton self-bending signals are considered for different families of solitons. Power thresholdless fundamental and multi-peaked solitons are stable in the low power region. The existence domain of two-peaked twisted solitons can be changed by the soliton self-bending signals. When solitons tend to self-bend toward the waveguide lattice, stable two-peaked twisted solitons can be found in a larger region in the middle of their existence region. Three-peaked twisted solitons are stable in the lower (upper) cutoff region for a shallow (deep) lattice depth. Our results provide an effective guidance for revealing the soliton characteristics supported by a finite waveguide lattice with diffusive nonlocal nonlinearity.     

Addressing individual atoms in optical lattices with standing-wave driving fields

A scheme for addressing individual atoms in one- or two-dimensional optical lattices loaded with one atom per site is proposed. The scheme is based on position-dependent atomic population transfer induced by several standing-wave driving fields. This allows various operations important in quantum-information processing, such as manipulation and measurement of any single-atom, two-qubit operations between any pair of adjacent atoms, and patterned loading of the lattice with one atom per every nth site for arbitrary n. The proposed scheme is robust against considerable imperfections and actually within reach of current technology.     

Resonance effects in nonlinear lattices

We study a class of one-dimensional nonlinear lattices with nearest-neighbour interactions described by a potential of the binomial type. This potential contains a free parameter which can be chosen to reproduce a variety of models, such as the Toda, the Fermi-Pasta-Ulam and the Coulomb-like lattices. Carrying out essentially numerical experiments, the effects of soliton propagation on a lattice with defects are investigated. In particular, the properties of the localized mode, generated by the propagation of the soliton through the defect, are discussed with respect to the defect mass and the potential parameter, in the light of a simple theoretical model. Furthermore, an interesting phenomenon is observed: the amplitude of the speed of the mass defect shows a sequel of resonance peaks in terms of the mass defect. The positions of these peaks appear to be independent of the potential parameter. Received 16 August 1999 and Received in final form 3 February 2000     

First-order diffusive effects in nonlinear rate processes

It is shown that first-order diffusive effects can be incorporated immediately into the general initial-value problem solution to a system of nonlinear rate equations.     

Surface lattice solitons in diffusive nonlinear media

We address the properties of surface solitons supported by optical lattices imprinted in photorefractive media with asymmetrical diffusion nonlinearity. Such solitons exist only in finite gaps of the lattice spectrum. In contrast to latticeless geometries, where surface waves exist only when nonlinearity deflects light toward the material surface, the surface lattice solitons exist in settings where diffusion would cause beam bending against the surface.     

Localized nonlinear waves in systems with time- and space-modulated nonlinearities

Using similarity transformations we construct explicit nontrivial solutions of nonlinear Schr?dinger equations with potentials and nonlinearities depending both on time and on the spatial coordinates. We present the general theory and use it to calculate explicitly nontrivial solutions such as periodic (breathers), resonant, or quasiperiodically oscillating solitons. Some implications to the field of matter waves are also discussed.     

Localized vibrations of point defects in body-centred cubic lattices

The paper gives an exact calculation of the localized frequencies of substitutional defects in a body-centred cubic lattice by the method of Green's functions and compares it with the approximate calculation carried out after [14]. The exact calculation is based on newly computed Green's functions of a b.c.c. lattice [18]. It is shown how by means of group theory the symmetry of the system can be used both in an approximate and in the exact calculation. Some symmetry relations between Green's functions, which limit the number of functions necessary for numerical calculations, are derived.     

Localized structures in convective experiments

In this work we review localized structures appearing in thermo-convective experiments performed in extended (large “aspect ratio”) fluid layers. After a brief general review (not exhaustive), we focus on some results obtained in pure fluids in a Bénard-Marangoni system with non-homogeneous heating where some structures of this kind appear. The experimental results are compared in reference to the most classical observed in binary mixtures experiments or simulations. In the Bénard-Marangoni experiment we present the stability diagram where localized structures appear and the typical situations where these local mechanisms have been studied experimentally. Some new experimental results are also included. The authors want to honor Prof. H. Brand in his 60th. birthday and to thank him for helpful discussions.     

Asymmetric dark solitons in nonlinear lattices

New types of stable discrete solitons are discovered. They represent the first example of asymmetric dark solitons and shock waves with a nonzero background. Both types of solutions exhibit a strong intrinsic phase dynamics. Their domains of existence and criteria of stability are identified. Numerical experiments support the analytical findings.     

Non-nearest-neighbor interactions in nonlinear dynamical lattices

We revisit the theme of non-nearest-neighbor interactions in nonlinear dynamical lattices, in the prototypical setting of the discrete nonlinear Schrödinger equation. Our approach offers a systematic way of analyzing the existence and stability of solutions of the system near the so-called anti-continuum limit of zero coupling. This affords us a number of analytical insights such as the fact that, for instance, next-nearest-neighbor interactions allow for solutions with nontrivial phase structure in infinite one-dimensional lattices; in the case of purely nearest-neighbor interactions, such phase structure is disallowed. On the other hand, such non-nearest-neighbor interactions can critically affect the stability of unstable structures, such as topological charge S=2 discrete vortices. These analytical predictions are corroborated by numerical bifurcation and stability computations.     

Multiple Andreev reflections in diffusive SNS structures

We report new measurements on subgap energy structures originating from multiple Andreev reflections in mesoscopic SNS junctions. The junctions were fabricated in a planar geometry with high-transparency superconducting contacts of Al deposited on highly diffusive and surface δ -dopedn ^{+ +} -GaAs. For samples with a normal GaAs region of active length 0.3μ m, the Josephson effect with a maximal supercurrent I_c = 3μ A at T = 237 mK was observed. The subgap structure was observed as a series of local minima in the differential resistance at dc bias voltages V = ± 2Δ / (ne) with n = 1, 2, 4, i.e. only the even subgap positions. While at V = ± 2Δ / e(n = 1) only one dip is observed, then = 2 and the n = 4 subgap structures each consists of two separate dips in the differential resistance. The mutual spacing of these two dips is independent of temperature, and the mutual spacing of the n = 4 dips is half the spacing of the n = 2 dips. The voltage bias positions of the subgap differential resistance minima coincide with the maxima in the oscillation amplitude when a magnetic field is applied in an interferometer configuration, where one of the superconducting electrodes has been replaced by a flux-sensitive open loop.     

Asymmetric heat conduction in nonlinear lattices

In this Letter, we conduct an extensive study of the two-segment Frenkel-Kontorova model. We show that the rectification effect of the heat flux reported in recent literature is possible only in the weak interfacial coupling limit. The rectification effect will be reversed when the properties of the interface and the system size change. These two types of asymmetric heat conduction are governed by different mechanisms though both are induced by nonlinearity. An intuitive physical picture is proposed to interpret the reversal of the rectification effect. Since asymmetric heat conduction depends critically on the properties of the interface and the system size, it is probably not an easy task to fabricate a thermal rectifier or thermal diode in practice.     

Random-phase solitons in nonlinear periodic lattices

We predict the existence of random phase solitons in nonlinear periodic lattices. These solitons exist when the nonlinear response time is much longer than the characteristic time of random phase fluctuations. The intensity profiles, power spectra, and statistical (coherence) properties of these stationary waves conform to the periodicity of the lattice. The general phenomenon of such solitons is analyzed in the context of nonlinear photonic lattices.