Geometrical Resonances Research Articles

Observation of commensurability oscillations of thermopower in an antidot lattice

Commensurability oscillations of thermopower in a square antidot lattice are observed. The oscillations are attributed to the geometrical resonances of the classical electron motion in a magnetic field and are much more pronounced than the corresponding magnetoresistance oscillations. The off-diagonal component of the thermopower tensor (the Nernst-Ettingshausen effect) changes sign at resonances. Additional measurements of magnetoresistance verify the correctness of the method used for thermopower measurements and provide information on the temperature distribution in the sample.

Unusually Strong Optical Interactions between Particles in Quasi-One-Dimensional Geometries

A theoretical analysis of the optically induced interaction between small particles in a quasi-one-dimensional system is presented. The total reflection of light modes near a geometric resonance leads to strong radiation pressure on a single particle. The presence of the two particles splits the resonance leading to a nontrivial oscillating interaction. The existence of stable, optically bound dimers under two counterpropagating (noncorrelated) light modes is also discussed.

Exactly solvable model of the BCS-BEC crossover.

We discuss an integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin 1/2 fermions to the Lieb-Liniger model of repulsive bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from -infinity to +infinity while the system evolves from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.

Pattern control and suppression of spatiotemporal chaos using geometrical resonance

Abstract We generalize the concept of geometrical resonance to perturbed sine-Gordon, Nonlinear Schrodinger, ϕ4, and Complex Ginzburg–Landau equations. Using this theory we can control different dynamical patterns. For instance, we can stabilize breathers and oscillatory patterns of large amplitudes successfully avoiding chaos. On the other hand, this method can be used to suppress spatiotemporal chaos and turbulence in systems where these phenomena are already present. This method can be generalized to even more general spatiotemporal systems. A short report of some of our results has been published in [Europhys. Lett. 64 (2003) 743].

Extended molecules and geometric scattering resonances in optical lattices.

We develop a theory describing neutral atom scattering at low energies in an optical lattice. We show that, for a repulsive interaction, as the microscopic scattering length increases the effective scattering amplitude approaches a limiting value which depends only on the lattice parameters. In the case of attractive interaction a geometric resonance occurs before reaching this limit. Close to the resonance, the effective interaction becomes repulsive and supports a weakly bound state, which can extend over several lattice sites.

Geometric resonance in a periodic waveguide

The geometric resonance has been predicted in a planar periodically corrugated waveguide. It is shown that for a change in thickness of the waveguide, at some of its values, one of the cutoff frequencies splits into two, separated by the forbidden gap, while other cutoff frequencies experience only slight shifts due to the periodicity. This resonant splitting causes the creation of an additional mode in the electromagnetic spectrum of the waveguide with the negative group velocity.

Infrared passbands from fractal slit patterns on a metal plate

We show that a fractal pattern of submicron wide slits, etched on a 0.1-μm-thick gold film, exhibit multiple pass and stop bands in the wavelength regime of 2–200 μm. In the midinfrared regime, the passbands show ∼36% transmission (three orders of magnitude higher than the reference), and the stop bands exhibit ∼80% reflection. In the far infrared regime, the passband transmittances are 25%, 29%, and 14%, respectively, at wavelengths of 34, 62, and 111 μm. These transmittances are rather high in view of the fact that supporting substrate is itself only about 40% transmitting, and a control pattern of holes with similar void-to-metal ratio is 3000 times less transmitting in all frequencies. We attribute the high transmittance from subwavelength slits to geometric resonances.

On the theory of magnetotransport in a periodically modulated two-dimensional electron gas

A semiclassical theory based on the Boltzmann transport equation for a two-dimensional electron gas modulated along one direction with weak electrostatic or magnetic modulations is proposed. It is shown that oscillations of the magnetoresistivity ρ ∥ corresponding to the current driven along the modulation lines observed at moderately low magnetic fields, can be explained as classical geometric resonances reflecting the commensurability of the period of spatial modulations and the cyclotron radius of electrons.

Resonance Phenomena in Bistable Systems

It is shown through the example of a bistable stochastic system driven by oscillating fields that stochastic resonance is associated with the appearance of a maximum Lyapunov exponent, for an equivalent autonomous stochastic system, induced when the purely deterministic system is at geometrical resonance. The nature of the generic mechanism of the asymmetric purely deterministic case is also explained in terms of geometrical resonance.

Geometric and morphological changes of the intervertebral disc under fatigue testing

Objective. To understand the injury mechanism of the intervertebral disc at different loading rates and to explore the anatomic and histological changes of intervertebral discs. Design. Fresh porcine lumbar spines were used for fatigue testing to study the morphological changes of the intervertebral disc. Background. Intervertebral disc problem is one of the most common causes that lead to low back pain. Slow repetitive loading was considered to be the critical factor of spine and disc injuries. Methods. Twenty-four lumbar functional units were subjected to cyclic loading at three different loading rates. The geometric measurements and magnetic resonance image observations were conducted for the comprehension of morphological changes. The detail observation was taken through a stereomicroscope. Results. There was no significance in geometric changes between different loading rates. For magnetic resonance imagings, morphological changes included the changes of nucleus pulposus shape, bulge of anterior and posterior longitudinal ligaments, and dehydration in annulus fibrosus. Conclusion. The morphological changes of intervertebral disc were revealed in certain kinds of lesions. The results imply that fatigue failure and degeneration or instability are strongly linked. The correlation of magnetic resonance imaging and anatomic observation showed a high correspondence in the comparison of shape and position of the nucleus pulpasus. Relevance The changes of geometric measurements and relationship between anatomic observation and magnetic resonance imaging finding had been analyzed. It could help in understanding the mechanism of triggering cause in the early stage of disc degeneration.

Coherent electronic transport through a superconducting film

We study coherent quantum transport through a superconducting film connected to normal-metal electrodes. Simple expressions for the differential conductance and the local density of states are obtained in the clean limit and for transparent interfaces. Quasiparticle interference causes periodic vanishing of the Andreev reflection at the energies of geometrical resonances, subgap transport, and gapless superconductivity near the interfaces. Application of the results to spectroscopic measurements of the superconducting gap and the Fermi velocity is analyzed.

Geometric resonance in the optical properties of microinhomogeneous PdMnxFe1−x alloys

The optical properties of PdMnxFe1−x ternary alloys in the homogeneous ferromagnetic (F1, for x ∼ 0) and antiferromagnetic (A, for x ∼ 1) states, as well as in the microinhomogeneous state (at x=0.7), are discussed. In the x=0.7 alloy, the presence of nuclei of the low-resistivity, PdFe-type F1 phase in the high-resistivity, PdMn-type A matrix was shown to produce a narrow maximum on the optical-conductivity σ(ω) curve at E ∼ 0.1 eV, which is due to a geometric resonance associated with light scattering from phase inhomogeneities of the sample. The behavior of σ(ω) in the interband transition region is dominated by parameters of the electronic spectrum of both the A and F1 phases.

Quantum size effect in conductivity of multilayer metal films

Conductivity of quantized multilayer metal films is analyzed with an emphasis on scattering by rough interlayer interfaces. Three different types of quantum size effect (QSE) in conductivity are predicted. Two of these QSE's are similar to those in films with scattering by rough walls. The third type of QSE is unique and is observed only for certain positions of the interface. The corresponding peaks in conductivity are very narrow and high with a finite cutoff which is due only to some other scattering mechanism or the smearing of the interface. There are two classes of these geometric resonances. Some of the resonance positions of the interface are universal and do not depend on the strength of the interface potential while the others are sensitive to this potential. This geometric QSE gradually disappears with an increase in the width of the interlayer potential barrier.

Commensurability oscillations in the antidot lattice in a quasi-three-dimensional electron gas

A three-dimensional electron billiard system is obtained by patterning a rectangular array of cylindrical voids in $\mathrm{GaAs}/{\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ parabolic quantum wells containing a high mobility quasi-three-dimensional electron gas. Resistivity ${(R}_{\mathrm{xx}})$ measurements reveal anomalous broadened peaks in the low-field magnetoresistance, in a similar way as measurements in two-dimensional antidot systems. ${R}_{\mathrm{xx}}$ in a tilted magnetic field show that commensurability peaks transform continuously to different kinds of peaks that we attribute to geometrical resonances between the cyclotron radius ${(R}_{c})$ and the well width $(W).$

Electronic structure and phase separation in LaxMnO3 films (0.83≤x≤1.10): Optical and magnetooptical data

The variations in the electronic structure and the evolution of phase separation as a result of creation of vacancies or excess of lanthanum in lanthanum manganites are studied on the basis of analysis of optical and magnetic properties of LaxMnO3 epitaxial films (0.83≤x≤1.10) in the fundamental absorption range. The Kerr effect, the temperature dependences of resistivity, optical density, and magnetoabsorption of light indicate the charge and magnetic phase separation in the films. The fine structure observed in the spectrum is attributed to spectral overlapping of electron transitions with charge transfer and geometrical resonances reflecting an inhomogeneous nanoscopic structure of the films, which strongly depends on stoichiometry and stresses emerging during film deposition. It is shown that, in contrast to bulk polycrystals, the gradient of stresses over the film thickness significantly affects the phase separation in the films.

TWO-SCALE GEOMETRICAL RESONANCE: FROM PARAMETRIC RESONANCE IN AN OSCILLATOR TO THERMODYNAMIC CYCLES

The paper deals with influence of two-scale variations of parameters on the behavior of different dynamical systems. By two-scale we mean parameter oscillations occur in an alternating manner with large and small temporal gradient, on a typical period intervals. The shape of such parameter dependence resembles relaxation oscillations. Parametric instability is revealed under these conditions. We call it two-scale geometric resonance (TGR). TGR can be described with the help of certain geometric structures on the extended phase space. TGR possesses similar properties and can be described in similar ways in seemingly different systems. The article presents general models for the TGR description and considers a few specific examples: classical oscillator, Van-der-Pol oscillator and thermodynamic system with ideal gas.

Field probe for low-pressure capacitively coupled radio-frequency dischargeplasmas

A field probe has been developed to measure the radio-frequency (RF) fields inlow-pressure capacitively coupled RF discharges at frequencies up to 50 MHz. Theprobe consists of a pair of parallel insulated wires that are connected through aresistor-matching network to an oscilloscope with a fast Fourier transformfunction to separate out harmonics. An insulated single wire potential probe isused to obtain the corresponding potential profiles. The probes are calibrated bydirect measurement of the RF content of the plasma up to the third harmonicusing an active Langmuir probe that also gives the plasma parametersne,Te.Two types of plasmas are investigated—electropositive Ar plasmas andelectronegative air plasmas that have much lower electron densitiesfor the same fill pressure. It is found that for fill pressures p > 10−3mbar most of the voltage drop is across the sheaths with only asmall field in the plasma. For lower fill pressures, p < 5 × 10−4mbar of air, then geometric resonance effects are observed with strong fieldreversal in the plasma. A higher-pressure Ar plasma driven simultaneously at13.56 and 27.12 MHz shows a small non-resonant field at the fundamental withthe second harmonic near to geometric resonance.

Coherent effects in double-barrier ferromagnet/superconductor/ferromagnet junctions

Coherent quantum transport in ferromagnet/superconductor/ferromagnet (FSF) double-barrier junctions is studied. Analytic expressions for charge and spin conductance spectra are derived for the general case of insulating interfaces (from metallic to tunnel limit), the Fermi velocity mismatch, and for parallel and antiparallel (AP) alignment of the electrode magnetizations. We focus on two characteristic features of finite size and coherency: subgap electronic transport and oscillations of the differential conductance. Periodic vanishing of the Andreev reflection at the energies of geometrical resonances above the superconducting gap is a striking consequence of the quasiparticle interference. In contrast with the case of incoherent transport, a nontrivial spin polarization without the excess spin accumulation is found for the AP alignment.

Nanoscale inhomogeneities and optical properties of doped cuprates

We propose a new approach to theoretical description of doped cuprate like $La_{2-x}Sr_{x}CuO_4$ and $YBa_2Cu_3O_{6+x}$, assuming phase separation and treating it as inhomogeneous composite material, containing the dielectric and metallic stripe-like nanoparticles. The formalism of effective medium theory is then applied for calculation of dielectric permittivity, optical and EELS spectra of $La_{2-x}Sr_{x}CuO_4$ with $x$ varying in a wide range. Reasonable semi-quantitative agreement with experiment has been obtained even for the simplest version of the theory. The model was found able to reproduce all essential features of optical conductivity $\sigma(\omega)$ and transmittance both for thin films (M. Suzuki, Phys. Rev. B 39, 2321 (1989)) and bulk single-crystalline samples (S. Uchida {\it et al.} Phys. Rev. B 43, 7942 (1991)). Substantial difference in spectral and doping dependence of optical absorption for the thin-film and bulk samples is easily explained if only to assume different shape of metallic and dielectric regions in both materials. New peaks in optical conductivity and absorption spectra, that emerge in the midinfrared range near 0.5 and 1.5 eV upon doping are attributed to geometrical (Mie's) resonances. Overall, we point out that all main peculiarities of the doping effect on optical and EELS spectra for cuprates including the spectral changes accompanying the insulator-to-metal transition can be explained rather prosaically by recognizing that the doping results in emergence of nanoscopic metallic stripe-like droplets.

Methods/Data Testing for Advanced LWR Fuel Designs and Operational Modes in the PROTEUS Facility

In the framework of the LWR-PROTEUS programme, integral experiments are being performed for the validation of reactor physics methods/data applied to the analysis of modem light water reactor (LWR) fuel assembly designs. One of the important aspects pertaining to this programme is the investigation of the sensitivity of integral quantities, such as reaction rate spatial distributions, local reaction rate ratios and reactivity effects, to different nuclear data sets, e.g. ENDF/B-V, ENDF/B-VI and JEF-2.2. Data sensitivity studies are currently reported, largely based on continuous-energy Monte Carlo calculations at PROTEUS-core, BWR fuel assembly and pin-cell levels. Data effects could thus be investigated systematically, independent of the inherent limitations of deterministic codes such as geometrical simplification and resonance shielding approximations. The results show a significant sensitivity of system reactivity to the data set employed, calculated values being larger by several hundreds of pcm with JEF-2.2 than with ENDF/B-V or B-VI. As regards detailed reaction rate distributions in BWR assemblies (investigated in LWR-PROTEUS Phase I), there appears to be only a weak dependence on the data library used. In the context of the investigations planned with highly burnt fuel rod segments in the Phase II experiments, certain studies made at pincell level have indicated that the effects of basic data differences are likely to be much lower than uncertainties in fuel composition predictions.