Showing papers on "Dispersion relation published in 2012"

One-dimensional quantum liquids: Beyond the Luttinger liquid paradigm

Abstract: For many years, the Luttinger liquid theory has served as a useful paradigm for the description of one-dimensional (1D) quantum fluids in the limit of low energies. This theory is based on a linearization of the dispersion relation of the particles constituting the fluid. Recent progress in understanding 1D quantum fluids beyond the low-energy limit is reviewed, where the nonlinearity of the dispersion relation becomes essential. The novel methods which have been developed to tackle such systems combine phenomenology built on the ideas of the Fermi-edge singularity and the Fermi-liquid theory, perturbation theory in the interaction strength, and new ways of treating finite-size properties of integrable models. These methods can be applied to a wide variety of 1D fluids, from 1D spin liquids to electrons in quantum wires to cold atoms confined by 1D traps. Existing results for various dynamic correlation functions are reviewed, in particular, the dynamic structure factor and the spectral function. Moreover, it is shown how a dispersion nonlinearity leads to finite particle lifetimes and its impact on the transport properties of 1D systems at finite temperatures is discussed. The conventional Luttinger liquid theory is a special limit of the new theory, and the relation between the two is explained.

Synthesis of highly confined surface plasmon modes with doped graphene sheets in the midinfrared and terahertz frequencies

Abstract: We investigate through analytic calculations the surface plasmon dispersion relation for monolayer graphene sheets and a separated parallel pair of graphene monolayers. An approximate form for the dispersion relation for the monolayer case was derived, which was shown to be highly accurate and offers intuition to the properties of the supported plasmon mode. For parallel graphene pairs separated by small gaps, the dispersion relation of the surface plasmon splits into two branches, one with a symmetric and the other with an antisymmetric magnetic field across the gap. For the symmetric (magnetic field) branch, the confinement may be improved at reduced absorption loss over a wide spectrum, unlike conventional surface plasmon modes supported on metallic surfaces that are subjected to the tradeoff between loss and confinement. This symmetric mode becomes strongly suppressed for very small separations, however. On the other hand, its antisymmetric counterpart exhibits reduced absorption loss for very small separations or long wavelengths, serving as a complement to the symmetric branch. Our results suggest that graphene plasmon structures could be promising for waveguiding and sensing applications in the midinfrared and terahertz frequencies.

Directional control of spin-wave emission by spatially shaped light

Abstract: Researchers use spatially shaped light to control the direction of spin-wave emission from the ferrimagnetic insulator Gd4/3Yb2/3BiFe5O12. They capture the essential features of the observations by employing a simple model that maps the spatial profile of the pump pulse onto the dispersion relation of the spin wave.

Constraining Lorentz-violating, modified dispersion relations with gravitational waves

Abstract: Modified gravity theories generically predict a violation of Lorentz invariance, which may lead to a modified dispersion relation for propagating modes of gravitational waves. We construct a parametrized dispersion relation that can reproduce a range of known Lorentz-violating predictions and investigate their impact on the propagation of gravitational waves. A modified dispersion relation forces different wavelengths of the gravitational-wave train to travel at slightly different velocities, leading to a modified phase evolution observed at a gravitational-wave detector. We show how such corrections map to the waveform observable and to the parametrized post-Einsteinian framework, proposed to model a range of deviations from General Relativity. Given a gravitational-wave detection, the lack of evidence for such corrections could then be used to place a constraint on Lorentz violation. The constraints we obtain are tightest for dispersion relations that scale with small power of the graviton's momentum and deteriorate for a steeper scaling.

Acoustic analogue of graphene: observation of Dirac cones in acoustic surface waves.

Abstract: We demonstrate the presence of Dirac cones in the dispersion relation of acoustic waves propagating on the surface of a plate of methyl methacrylate containing a honeycomb lattice of cylindrical boreholes. This structure represents the acoustic analogue of graphene, the cylindrical cavities playing the role of carbon atoms while acoustic surface waves are the equivalent of electronic waves in graphene. Analytical expressions for the Dirac frequency and Dirac velocity in acoustics are given as a function of the radius and depth of boreholes. These parameters have been experimentally determined for a constructed structure and the data are in fairly good agreement with the predicted values.

Negative frequency resonant radiation

Abstract: Soliton resonant radiation emission is predicted to lead to a second mode that originates from the negative frequency branch of the dispersion relation. Measurements in both bulk media and photonic crystal fibres confirm our predictions.

Wave motion and dispersion phenomena: Veering, locking and strong coupling effects

Abstract: The dispersion curves describe wave propagation in a structure, each branch representing a wave mode. As frequency varies the wavenumbers change and a number of dispersion phenomena may occur. This paper characterizes, analyzes, and quantifies these phenomena in general terms and illustrates them with examples. Two classes of phenomena occur. Weak coupling phenomena—veering and locking—arise when branches of the dispersion curves interact. These occur in the vicinity of the frequency at which, for undamped waveguides, the dispersion curves in the uncoupled waveguides would cross: if two dispersion curves (representing either propagating or evanescent waves) come close together as frequency increases then the curves either veer apart or lock together, forming a pair of attenuating oscillatory waves, which may later unlock into a pair of either propagating or evanescent waves. Which phenomenon occurs depends on the product of the gradients of the dispersion curves. The wave mode shapes which describe the deformation of the structure under the passage of a wave change rapidly around this critical frequency. These phenomena also occur in damped systems unless the levels of damping of the uncoupled waveguides are sufficiently different. Other phenomena can be attributed to strong coupling effects, where arbitrarily light stiffness or gyroscopic coupling changes the qualitative nature of the dispersion curves.

Thermal transport in phononic crystals: The role of zone folding effect

Abstract: Recent experiments [Yu et al., Nature Nanotech 5, 718 (2010); Tang et al., Nano Lett. 10, 4279 (2010); Hopkins etal., Nano Lett. 11, 107(2011)] on silicon based nanoscale phononic crystals demonstrated substantially reduced thermal conductivity compared to bulk Si, which cannot be explained by incoherent phonon boundary scattering within the Boltzmann Transport Equation (BTE). In this paper, partial coherent treatment of phonons, where phonons are regarded as either wave or particles depending on their frequencies, was considered. Phonons with mean free path smaller than the characteristic size of phononic crystals are treated as particles and the transport in this regime is modeled by BTE with phonon boundary scattering taken into account. On the other hand, phonons with mean free path longer than the characteristic size are treated as waves. In this regime, phonon dispersion relations are computed using the Finite Difference Time Domain (FDTD) method and are found to be modified due to the zone folding ...

Coexistence of positive and negative refractive index sensitivity in the liquid-core photonic crystal fiber based plasmonic sensor

Abstract: We present and numerically characterize a liquid-core photonic crystal fiber based plasmonic sensor. The coupling properties and sensing performance are investigated by the finite element method. It is found that not only the plasmonic mode dispersion relation but also the fundamental mode dispersion relation is rather sensitive to the analyte refractive index (RI). The positive and negative RI sensitivity coexist in the proposed design. It features a positive RI sensitivity when the increment of the SPP mode effective index is larger than that of the fundamental mode, but the sensor shows a negative RI sensitivity once the increment of the fundamental mode gets larger. A maximum negative RI sensitivity of -5500nm/RIU (Refractive Index Unit) is achieved in the sensing range of 1.50-1.53. The effects of the structural parameters on the plasmonic excitations are also studied, with a view of tuning and optimizing the resonant spectrum.

Phonons in Slow Motion: Dispersion Relations in Ultra-Thin Si Membranes

Abstract: We report the changes in dispersion relations of hypersonic acoustic phonons in free-standing silicon membranes as thin as \sim 8 nm. We observe a reduction of the phase and group velocities of the fundamental flexural mode by more than one order of magnitude compared to bulk values. The modification of the dispersion relation in nanostructures has important consequences for noise control in nano and micro-electromechanical systems (MEMS/NEMS) as well as opto-mechanical devices.

Phonons in slow motion: dispersion relations in ultrathin Si membranes.

Abstract: We report the changes in dispersion relations of hypersonic acoustic phonons in free-standing silicon membranes as thin as ∼8 nm. We observe a reduction of the phase and group velocities of the fundamental flexural mode by more than 1 order of magnitude compared to bulk values. The modification of the dispersion relation in nanostructures has important consequences for noise control in nano- and microelectromechanical systems (MEMS/NEMS) as well as opto-mechanical devices.

Quantum corrections to spinning superstrings in AdS_3 x S^3 x M^4: determining the dressing phase

Abstract: We study the leading quantum string correction to the dressing phase in the asymptotic Bethe Ansatz system for superstring in AdS_3 x S^3 x T^4 supported by RR flux. We find that the phase should be different from the BES phase appearing in the AdS_5 x S^5 case. We use the simplest example of a rigid circular string with two equal spins in S^3 and also consider the general approach based on the algebraic curve description. We also discuss the case of the AdS_3 x S^3 x S^3 x S^1 theory and find the dependence of the 1-loop correction to the effective string tension function h(\lambda) (expected to enter the magnon dispersion relation) on the parameters alpha related to the ratio of the two 3-sphere radii. This correction vanishes in the AdS_3 x S^3 x T^4 case.

Magnetic Dispersion and Anisotropy in Multiferroic BiFeO3

Abstract: We have determined the full magnetic dispersion relations of multiferroic BiFeO3. In particular, two excitation gaps originating from magnetic anisotropies have been clearly observed. The direct observation of the gaps enables us to accurately determine the Dzyaloshinskii-Moriya (DM) interaction and the single ion anisotropy. The DM interaction supports a sizable magnetoelectric coupling in this compound.

Double Dirac cones in triangular-lattice metamaterials

Abstract: It is shown by tight-binding approximation and group theory that a double Dirac cone, or a pair of two identical Dirac cones, of the electromagnetic dispersion relation can be created in the Brillouin zone center by accidental degeneracy of E1 and E2 modes in triangular-lattice metamaterials of C6v symmetry. The Dirac point thus obtained is equivalent to a zero-index system, so we can expect unique optical propagation phenomena such as constant-phase waveguides and lenses of arbitrary shapes. Zitterbewegung is also expected without disturbance due to an auxiliary quadratic dispersion surface, which is present for other combinations of mode symmetries to materialize the Dirac cones. To the best of the author’s knowledge, this is the first prediction of the presence of a double Dirac cone in metamaterials.

Broadband directional acoustic waveguide with high efficiency

Abstract: We have realized both theoretically and experimentally a directional acoustic transmission in a bended waveguide. For acoustic plane waves that incident from the two openings of the waveguide, an efficient partial band gap of dispersion relations is yielded by employing a linear two-dimensional phononic crystal properly designed according to the structural parameters of waveguide. As a result, a highly efficient directional transmission of acoustic waves can be achieved within a broad frequency range. The numerical predictions agree well with the experimental results. This should be potentially significant in various areas such as medical ultrasound and duct acoustics.

Fully kinetic description of the linear excitation and nonlinear saturation of fast-ion-driven geodesic acoustic mode instability

Abstract: We show in this paper that geodesic acoustic modes (GAMs) can be efficiently excited by a population of fast ions even when Landau damping on thermal ions is accounted for. We report in particular fully kinetic calculations of the GAM dispersion relation and its complete solution. Written under a variational form, the quasi-neutrality condition, together with the kinetic Vlasov equation, leads to the density of exchanged energy between particles and the mode. In particular, a linear threshold for the GAMs excitation is derived. Two examples of fast ion distribution have been discussed analytically. It turns out that particles with high perpendicular energy compared to the parallel resonance energy are most responsible for the excitation of the mode. Subsequent numerical simulations of circular plasmas using gysela code have been carried out. In particular, the linear kinetic threshold has been reproduced during the excitation phase, and a nonlinear saturation has been observed. Analysis in the phase space of the evolution of the equilibrium distribution function is presented and the saturation level quantified.

Properties of neutral mesons in a hot and magnetized quark matter

Abstract: The properties of non-interacting $\sigma$ and $\pi^{0}$ mesons are studied at finite temperature, chemical potential and in the presence of a constant magnetic field. To do this, the energy dispersion relations of these particles, including nontrivial form factors, are derived using a derivative expansion of the effective action of a two-flavor, hot and magnetized Nambu--Jona-Lasinio (NJL) model up to second order. The temperature dependence of the pole and screening masses as well as the directional refraction indices of magnetized neutral mesons are explored for fixed magnetic fields and chemical potentials. It is shown that, because of the explicit breaking of the Lorentz invariance by the magnetic field, the refraction index and the screening mass of neutral mesons exhibit a certain anisotropy in the transverse and longitudinal directions with respect to the direction of the external magnetic field. In contrast to their longitudinal refraction indices, the transverse indices of the neutral mesons are larger than unity.

Nonlinear Waves in Shallow Honeycomb Lattices

Abstract: The linear spectrum and corresponding Bloch modes of shallow honeycomb lattices near Dirac points are investigated. Via perturbation theory, the dispersion relation is found to have threefold degeneracy at leading order with eigenvalue splitting at the following two orders; i.e., the threefold eigenvalue splits into single and double values. Multiscale perturbation methods are employed to describe the nonlinear dynamics of the associated wave envelopes. The dynamics of the envelope depends on different asymptotic balances whereupon a three-level nonlinear Dirac-type equation or a two-level nonlinear Dirac equation is derived. The analysis agrees well with direct numerical simulations.

Engineering the hypersonic phononic band gap of hybrid Bragg stacks.

Abstract: We report on the full control of phononic band diagrams for periodic stacks of alternating layers of poly(methyl methacrylate) and porous silica combining Brillouin light scattering spectroscopy and theoretical calculations. These structures exhibit large and robust on-axis band gaps determined by the longitudinal sound velocities, densities, and spacing ratio. A facile tuning of the gap width is realized at oblique incidence utilizing the vector nature of the elastic wave propagation. Off-axis propagation involves sagittal waves in the individual layers, allowing access to shear moduli at nanoscale. The full theoretical description discerns the most important features of the hypersonic one-dimensional crystals forward to a detailed understanding, a precondition to engineer dispersion relations in such structures.

Effect of point source and heterogeneity on the propagation of SH-Waves in a viscoelastic layer over a viscoelastic half space

Abstract: The present paper is concerned with the propagation of shear waves in a homogeneous viscoelastic isotropic layer lying over a semi-infinite heterogeneous viscoelastic isotropic half-space due to point source. The inhomogeneity parameters associated to rigidity, internal friction and density are assumed to be functions of depth. The dispersion equation of shear waves has been obtained using Green’s function technique. The dimensionless angular frequency has been plotted against dimensionless wave number for different values of inhomogeneity parameters. The effects of inhomogeneity have been shown in the dispersion curves. graphical user interface (GUI) software in MATLAB has been developed to show the effect of various inhomogeneity parameters on angular frequency. The topic can be of interest for geophysical applications in propagation of shear waves on the Earth’s crust.

Direct probe of linearly dispersing 2D interband plasmons in a free-standing graphene monolayer

Abstract: In low-dimensional systems, a detailed understanding of plasmons and their dispersion relation is crucial for applying their optical response in the field of plasmonics. Electron energy-loss spectroscopy is a direct probe of these excitations. Here we report on electron energy-loss spectroscopy results on the dispersion of the ? plasmons in free-standing graphene monolayers at the momentum range of 0?|q|?0.5???1 and parallel to the ?-M direction of the graphene Brillouin zone. In contrast to the parabolic dispersion in graphite and in good agreement with theoretical predictions of a 2D electron gas of Dirac electrons, linear ? plasmon dispersion is observed. As with previous EELS results obtained from single-wall carbon nanotubes, this can be explained by local-field effects in the anisotropic 2D system yielding a significant contribution of the low-energy band structure on the high-energy ? plasmon response.

Transverse wave propagation in elastically confined single-walled carbon nanotubes subjected to longitudinal magnetic fields using nonlocal elasticity models

Abstract: Lateral wave propagation in an elastically confined single-walled carbon nanotube (SWCNT) experiences a longitudinal magnetic field is examined using nonlocal Rayleigh, Timoshenko, and higher-order beam theories. The SWCNT is modeled via an equivalent continuum structure (ECS) and its interaction with the surrounding elastic medium is simulated via lateral and rotational continuous springs along its length. For the proposed models, the dimensionless governing equations describing transverse vibration of the SWCNT are constructed. Assuming harmonic solutions for the propagated sound waves, the dispersion equation associated with each model is obtained. Subsequently, the explicit expressions of the frequencies as well as the corresponding phase and group velocities, called characteristics of the waves, are derived for the proposed models. The influences of the slenderness ratio, the mean radius of the ECS, the small-scale parameter, the longitudinal magnetic field, the lateral and rotational stiffness of the surrounding matrix on the characteristics of flexural and shear waves are explored and discussed.

Scale dependence of the variance anisotropy near the proton gyroradius scale: Additional evidence for kinetic Alfvén waves in the solar wind at 1 AU

Abstract: [1] The kinetic Alfven wave (KAW) has the property that for βp ∼ 1 the ratio (δB∥)2/(δB⊥)2 approaches zero in the small wave number limit k⊥ρp ≪ 1 and increases monotonically to values of order unity when k⊥ρp ∼ 1, where ρp is the thermal proton gyroradius In this study, the wave number dependence of the ratio (δB∥)2/(δB⊥)2 is used to investigate the existence of KAWs in the solar wind near the proton gyroradius scale k⊥ρp = 1 To facilitate comparisons between theory and observations, solar wind measurements of (δB∥)2/(δB⊥)2 are restricted to times when the local mean magnetic field B0 is nearly perpendicular to the local flow velocity of the solar wind V The quantity (δB∥)2 is the average magnetic power in the B0 direction and (δB⊥)2 is the average magnetic power in the V × B0 direction The analysis of 20 high speed streams in the ecliptic plane near 1 AU from 2007 through 2011 consistently yield quantitatively similar results which all show a steady increase in the ratio (δB∥)2/(δB⊥)2 in the neighborhood of k⊥ρp= 1 that is in reasonable agreement with the theory of KAWs derived from the Vlasov-Maxwell dispersion relation These results are interpreted as evidence for the existence of an axisymmetric spectrum of KAWs in the fast solar wind at wave numbers neark⊥ρp = 1 where the energy spectrum of solar wind fluctuations steepens and kinetic physics becomes important

Torsional Alfv\'en waves in solar partially ionized plasma: effects of neutral helium and stratification

Abstract: Ion-neutral collisions may lead to the damping of Alfven waves in chromospheric and prominence plasmas. Neutral helium atoms enhance the damping in certain temperature interval, where the ratio of neutral helium and neutral hydrogen atoms is increased. Therefore, the height-dependence of ionization degrees of hydrogen and helium may influence the damping rate of Alfven waves. We aim to study the effect of neutral helium in the damping of Alfven waves in stratified partially ionized plasma of the solar chromosphere. We consider a magnetic flux tube, which is expanded up to 1000 km height and then becomes vertical due to merging with neighboring tubes, and study the dynamics of linear torsional Alfven waves in the presence of neutral hydrogen and neutral helium atoms. We start with three-fluid description of plasma and consequently derive single-fluid magnetohydrodynamic (MHD) equations for torsional Alfven waves. Thin flux tube approximation allows to obtain the dispersion relation of the waves in the lower part of tubes, while the spatial dependence of steady-state Alfven waves is governed by Bessel type equation in the upper part of tubes. Consecutive derivation of single-fluid MHD equations results in a new Cowling diffusion coefficient in the presence of neutral helium which is different from previously used one. We found that shorter-period ( 5 s) waves do not reach the transition region as they become evanescent at lower heights in the network cores. Propagation of torsional Alfven waves through the chromosphere into the solar corona should be considered with caution: low-frequency waves are evanescent due to the stratification, while high-frequency waves are damped due to ion neutral collisions.

Spontaneous inertia-gravity-wave generation by surface-intensified turbulence

Abstract: The spontaneous generation of inertia-gravity waves (IGWs) by surface-intensified, nearly balanced motion is examined using a high-resolution simulation of the primitive equations in an idealized oceanic configuration. At large scale and mesoscale, the dynamics, which is driven by baroclinic instability near the surface, is balanced and qualitatively well described by the surface quasi-geostrophic model. This however predicts an increase of the Rossby number with decreasing spatial scales and, hence, a breakdown of balance at small scale; the generation of IGWs is a consequence of this breakdown. The wave field is analysed away from the surface, at depths where the associated vertical velocities are of the same order as those associated with the balanced motion. Quasi-geostrophic relations, the omega equation in particular, prove sufficient to separate the IGWs from the balanced contribution to the motion. A spectral analysis indicates that the wave energy is localized around dispersion relation for free IGWs, and decays only slowly as the frequency and horizontal wavenumber increase. The IGW generation is highly intermittent in time and space: localized wavepackets are emitted when thin filaments in the surface density are formed by straining, leading to large vertical vorticity and correspondingly large Rossby numbers. At depth, the IGW field is the result of a number of generation events; away from the generation sites it takes the form of a relatively homogeneous, apparently random wave field. The energy of the IGW field generated spontaneously is estimated and found to be several orders of magnitude smaller than the typical IGW energy in the ocean.

Chorus wave-normal statistics in the Earth's radiation belts from ray tracing technique

Abstract: . Discrete ELF/VLF (Extremely Low Frequency/Very Low Frequency) chorus emissions are one of the most intense electromagnetic plasma waves observed in radiation belts and in the outer terrestrial magnetosphere. These waves play a crucial role in the dynamics of radiation belts, and are responsible for the loss and the acceleration of energetic electrons. The objective of our study is to reconstruct the realistic distribution of chorus wave-normals in radiation belts for all magnetic latitudes. To achieve this aim, the data from the electric and magnetic field measurements onboard Cluster satellite are used to determine the wave-vector distribution of the chorus signal around the equator region. Then the propagation of such a wave packet is modeled using three-dimensional ray tracing technique, which employs K. Ronnmark's WHAMP to solve hot plasma dispersion relation along the wave packet trajectory. The observed chorus wave distributions close to waves source are first fitted to form the initial conditions which then propagate numerically through the inner magnetosphere in the frame of the WKB approximation. Ray tracing technique allows one to reconstruct wave packet properties (electric and magnetic fields, width of the wave packet in k-space, etc.) along the propagation path. The calculations show the spatial spreading of the signal energy due to propagation in the inhomogeneous and anisotropic magnetized plasma. Comparison of wave-normal distribution obtained from ray tracing technique with Cluster observations up to 40° latitude demonstrates the reliability of our approach and applied numerical schemes.

Propagation of magnetoelastic shear waves in an irregular self-reinforced layer

Abstract: The propagation of horizontally polarised shear waves in an internal irregular magnetoelastic self-reinforced stratum which is sandwiched between two semi-infinite magnetoelastic self-reinforced media is studied. Two shapes of irregularities on the interface of layer and lower semi-infinite media are considered, namely rectangular and parabolic. The dispersion equation is obtained in closed form. The combined effects of reinforcement, magnetic field and irregularity are also studied. Some important features of the results are highlighted. It is also observed that the dispersion equation is in agreement with the classical Love-type wave equation for an isotropic layer sandwiched between two isotropic half-spaces in the absence of reinforcement, magnetic field and irregularity.