Dispersion Relations Of Modes Research Articles

Model of the dynamics of an interface between a smectic phase and an isotropic phase of different density

Soft modulated phases have been shown to undergo complex morphological transitions, in which layer remodeling induced by mean and Gaussian curvatures plays a major role. This is the case in smectic films under thermal treatment, where focal conics can be reshaped into conical pyramids and concentric ring structures. We build on earlier research on a smectic-isotropic, two phase configuration in which diffusive evolution of the interface was driven by curvature, while mass transport was neglected. Here, we explicitly consider evaporation-condensation processes in a smectic phase with mass transport through a coexisting isotropic fluid phase, as well as the hydrodynamic stresses at the interface and the resulting flows. By employing the Coleman-Noll procedure, we derive a phase-field model that accounts for a varying density field coupled to smectic layering of the order parameter. The resulting equations govern the evolution of an interface between a modulated phase and an isotropic fluid phase with distinct densities, and they capture compressibility effects in the interfacial region and topological transitions. We first verify a numerical implementation of the governing equations by examining the dispersion relation for interfacial transverse modes. The inverse decay rate is shown to scale as $Q^{2}$ ($Q$ is the wavenumber of the perturbation) due to hydrodynamic effects, instead of the $Q^{4}$ expected for diffusive decay. Then, by integrating the equations forward in time, we investigate fluid flow on distorted layers and focal conics, and show how interfacial stresses and density contrast significantly determine the structure of the flow and the evolution of the configuration.

Effect of Differential Rotation of Oscillating Inner Core on Steady Flow Instability in a Rotating Sphere

A comparative analysis of steady flow excited by an oscillating core in a rotating spherical cavity with a liquid is carried out in different cases: when the core is free and performs differential rotation, and when the core differential rotation is absent. In the cavity reference frame the core, whose density is less than the density of the liquid, oscillates near the cavity center under the action of transverse to the rotation axis external force field. In both cases, the oscillations lead to the appearance of almost two-dimensional axisymmetric azimuthal steady flow, with several inflection points in the velocity profile. An increase in the amplitude of core oscillations leads to a loss of stability of the axisymmetric flow. In the supercritical region, there is a series of threshold transitions associated with various instability modes. The instability manifests itself in the development of an azimuthal periodic system of vortices elongated parallel to the rotation axis. The modes differ in an azimuthal wavenumber, the location of the vortices (distance from the axis of rotation), and the azimuthal drift rate of the vortex system relative to the cavity. It is shown that the core differential rotation modifies the azimuthal velocity profile, resulting in a change in the instability thresholds. Due to an additional azimuthal flow, the drift velocity of the same type vortices in the two cases is different. The effect of the core differential rotation on the dispersion relations for various instability modes has been investigated.

Waveguided modes in a planar structure «graphene – thin semiconductor film – graphene»

We investigated optical-range waveguide modes propagating in a semiconductor film sandwiched between two graphene plates. The mode characteristics were shown to depend on the chemical potential of graphene and the film thickness. Based on the numerical analysis, we obtained dispersion relations for the first waveguide modes, frequency dependences of their group and phase velocities, and the distribution of the energy flux density in the structure. We discovered the presence of spectral bands characterized by small phase and negative group velocities of the waveguide modes. The possibility of tuning the waveguide mode by changing the chemical potential of graphene and the thickness of the semiconductor film was established.

Infrared Nanoimaging of Surface Plasmons in Type-II Dirac Semimetal PtTe2 Nanoribbons.

Topological Dirac semimetals made of two-dimensional transition-metal dichalcogenides (TMDCs) have attracted enormous interest for use in electronic and optoelectronic devices because of their electron transport properties. As van der Waals materials with a strong interlayer interaction, these semimetals are expected to support layer-dependent plasmonic polaritons yet to be revealed experimentally. Here, we demonstrate the apparent retardation and attenuation of mid-infrared (MIR) plasmonic waves in type-II Dirac semimetal platinum tellurium (PtTe2) nanoribbons and nanoflakes by near-field nanoimaging. The attenuated dispersion relations for the plasmonic modes in the PtTe2 nanoribbons (15-25 nm thick) extracted from the near-field standing-wave patterns are applied for the fitting of PtTe2 permittivity in the MIR regime, indicating that both free carriers and Dirac fermions are involved in MIR light-matter interaction in PtTe2. The annihilation of plasmonic modes in the ultrathin (<10 nm) PtTe2 is observed and analyzed, which manifests no near-field resonant pattern due to the intrinsic layer-dependent optoelectronic properties of PtTe2. These results could pave a potential wave for MIR photodetection and modulation with TMDC semimetals.

Exciton–polaritons of a 2D semiconductor layer in a cylindrical microcavity

We describe exciton–polariton modes formed by the interaction between excitons in a 2D layer of a transition metal dichalcogenide embedded in a cylindrical microcavity and the microcavity photons. For this, an expression for the excitonic susceptibility of a semiconductor disk placed in the symmetry plane perpendicular to the axis of the microcavity is derived. Semiclassical theory provides dispersion relations for the polariton modes, while the quantum-mechanical treatment of a simplified model yields the Hopfield coefficients, measuring the degree of exciton–photon mixing in the coupled modes. The density of states (DOS) and its projection onto the photonic and the excitonic subspaces are calculated, taking monolayer MoS2 embedded in a Si3N4 cylinder as an example. The calculated results demonstrate a strong enhancement for certain frequencies of the total and local DOS (and, consequently, of the spontaneous emission rate of a nearby point emitter, i.e., the Purcell effect) caused by the presence of the 2D layer.

Horizon constraints on holographic Green\u2019s functions

We explore a new class of general properties of thermal holographic Green’s functions that can be deduced from the near-horizon behaviour of classical perturbations in asymptotically anti-de Sitter spacetimes. We show that at negative imaginary Matsubara frequencies and appropriate complex values of the wavenumber the retarded Green’s functions of generic operators are not uniquely defined, due to the lack of a unique ingoing solution for the bulk perturbations. From a boundary perspective these ‘pole-skipping’ points correspond to locations in the complex frequency and momentum planes at which a line of poles of the retarded Green’s function intersects with a line of zeroes. As a consequence the dispersion relations of collective modes in the boundary theory at energy scales ω ∼ T are directly constrained by the bulk dynamics near the black-brane horizon. For the case of conserved U (1) current and energy-momentum tensor operators we give examples where the dispersion relations of hydrodynamic modes pass through a succession of pole- skipping points as real wavenumber is increased. We discuss implications of our results for transport, hydrodynamics and quantum chaos in holographic systems.

Anisotropy of Isobaric Instability in a Partially Ionized Plasma in a Magnetic Field

Linear equations describing the dynamics of small perturbations in partially ionized heat-releasing plasma in an external magnetic field with an arbitrary induction vector are obtained. Using these equations, a dispersion relation for condensation modes is derived, and their time increments are calculated in the case of isobaric instability in the presence of anisotropy of the plasma thermal conductivity.

Unstable electrostatic surface waves in a turbulent plasma containing streaming ions: transverse truncation approach

The unstable modes of surface waves propagating in a sharply bounded turbulent plasma containing streaming ions are investigated by employing the specular reflection condition and the transverse truncation method. We have found that the bounded turbulent plasma supports damping and growing modes. The damping mode propagates for all values of the ion streaming speed modes and their behavior is similar to the case of surface waves in a turbulent plasma without ion streaming. If the speed of ion streaming is larger than the ion-acoustic speed, growing mode exists for all values of the wave number. However, if the ion stream is slower than the ion acoustic speed, then the growing mode appears under a certain condition. We derive the dispersion relations for such modes of surface waves and investigate the condition for propagation.

Polaritonic contribution to the Casimir energy between two graphene layers

We study the role of surface polaritons in the zero-temperature Casimir effect between two graphene layers that are described by the Dirac model. A parametric approach allows us to accurately calculate the dispersion relations of the relevant modes and to evaluate their contribution to the total Casimir energy. The resulting force features a change of sign from attractive to repulsive as the distance between the layers increases. Contrary to similar calculations that have been performed for metallic plates, our asymptotic analysis demonstrates that at small separations the polaritonic contribution becomes negligible relative to the total energy.

Dispersion relations in non-relativistic two-dimensional materials from quasinormal modes in H\u01d2rava Gravity

We compute dispersion relations of non-hydrodynamic and hydrodynamic modes in a non-relativistic strongly coupled two-dimensional quantum field theory. This is achieved by numerically computing quasinormal modes (QNMs) of a particular analytically known black brane solution to 3+1-dimensional Hǒrava Gravity. Hǒrava Gravity is distinguished from Einstein Gravity by the presence of a scalar field, termed the khronon, defining a preferred time-foliation. Surprisingly, for this black brane solution, the khronon fluctuation numerically decouples from all others, having its own set of purely imaginary eigenfrequencies, for which we provide an analytic expression. All other Hǒrava Gravity QNMs are expressed analytically in terms of QNMs of Einstein Gravity, in units involving the khronon coupling constants and various horizons. Our numerical computation reproduces the analytically known momentum diffusion mode, and extends the analytic expression for the sound modes to a wide range of khronon coupling values. In the eikonal limit (large momentum limit), the analytically known dispersion of QNM frequencies with the momentum is reproduced by our numerics. We provide a parametrization of all QNM frequencies to fourth order in the momentum. We demonstrate perturbative stability in a wide range of coupling constants and momenta.

Longitudinal sound and diffusion in holographic massive gravity

We consider a simple class of holographic massive gravity models for which the dual field theories break translational invariance spontaneously. We study, in detail, the longitudinal sector of the quasi-normal modes at zero charge density. We identify three hydrodynamic modes in this sector: a pair of sound modes and one diffusion mode. We numerically compute the dispersion relations of the hydrodynamic modes. The obtained speed and the attenuation of the sound modes are in agreement with the hydrodynamic predictions. On the contrary, we surprisingly find disagreement in the case of the diffusive mode; its diffusion constant extracted from the quasi-normal mode data does not agree with the expectations from hydrodynamics. We confirm our numerical results using ana- lytic tools in the decoupling limit and we comment on some possible reasons behind the disagreement. Finally, we extend the analysis of the collective longitudinal modes beyond the hydrodynamic limit by displaying the dynamics of the higher quasi-normal modes at large frequencies and momenta.

Linear Analysis of 2-D Sheet Beam Cyclotron Maser With Metallic Grating Structures

Based on a kinetic model, a linear theory of the 2-D sheet beam metallic grating cyclotron maser has been derived and analyzed numerically. The TE mode dispersion relation and the periodicity of the normalized amplitudes of spatial harmonics of the cyclotron maser with rectangular gratings are obtained. Through numerical calculations, the dependence of the growth rate on the gap distance between the metallic grating surface and the beam, the external magnetic field strength, the beam current, the transverse-to-axial velocity ratio, the axial velocity spread, and the beam voltage are analyzed. This article presents an analysis of interaction using the fundamental TE mode in the 2-D metallic grating sheet beam system. The fundamental TE mode in the 2-D metallic rectangular waveguide grating structure is the fundamental TMx mode in the 3-D rectangular waveguide grating structure and this method can be extended to the practical 3-D interaction system that operates at other TMx modes and has a good potential for the study of the combined resonances in cyclotron masers with grating structures.

Fast neutrino flavor conversion: collective motion vs. decoherence

In an interacting neutrino gas, flavor coherence becomes dynamical and can propagate as a collective mode. In particular, tachyonic instabilities can appear, leading to “fast flavor conversion” that is independent of neutrino masses and mixing angles. On the other hand, without neutrino-neutrino interaction, a prepared wave packet of flavor coherence simply dissipates by kinematical decoherence of infinitely many non-collective modes. We reexamine the dispersion relation for fast flavor modes and show that for any wavenumber, there exists a continuum of non-collective modes besides a few discrete collective ones. So for any initial wave packet, both decoherence and collective motion occurs, although the latter typically dominates for a sufficiently dense gas. We derive explicit eigenfunctions for both collective and non-collective modes. If the angular mode distribution of electron-lepton number crosses between positive and negative values, two non-collective modes can merge to become a tachyonic collective mode. We explicitly calculate the interaction strength for this critical point. As a corollary we find that a single crossing always leads to a tachyonic instability. For an even number of crossings, no instability needs to occur.

Bubbly Water as a Natural Metamaterial of Negative Bulk-Modulus

In this study, an oscillator model of bubble-in-water is proposed to analyze the effective modulus of low-concentration bubbly water. We show that in a wide range of wave frequency the bubbly water acquires a negative effective modulus, while the effective density of the medium is still positive. These two properties imply the existence of a wide acoustic gap in which the propagation of acoustic waves in this medium is prohibited. The dispersion relation for the acoustic modes in this medium follows Lorentz type dispersion, which is of the same form as that of the phonon-polariton in an ionic crystal. Numerical results of the gap edge frequencies and the dispersion relation in the long-wavelength regime based on this effective theory are consistent with the sonic band results calculated with the plane-wave expansion method (PWEM). Our theory provides a simple mechanism for explaining the long-wavelength behavior of the bubbly water medium. Therefore, phenomena such as the high attenuation rate of sound or acoustic Anderson localization in bubbly water can be understood more intuitively. The effects of damping are also briefly discussed. This effective modulus theory may be generalized and applied to other bubble-in-soft-medium type sonic systems.

Spin Pinning and Spin-Wave Dispersion in Nanoscopic Ferromagnetic Waveguides

Spin waves are investigated in yttrium iron garnet waveguides with a thickness of 39nm and widths ranging down to 50nm, i.e., with an aspect ratio thickness over width approaching unity, using Brillouin light scattering spectroscopy. The experimental results are verified by a semianalytical theory and micromagnetic simulations. A critical width is found, below which the exchange interaction suppresses the dipolar pinning phenomenon. This changes the quantization criterion for the spin-wave eigenmodes and results in a pronounced modification of the spin-wave characteristics. The presented semianalytical theory allows for the calculation of spin-wave mode profiles and dispersion relations in nanostructures.

Wave dispersion in pulsar plasma. Part 1. Plasma rest frame

Wave dispersion in a pulsar plasma (a one-dimensional, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the low-frequency, non-gyrotropic approximation. For parallel propagation (wave angle$\unicode[STIX]{x1D703}=0$) these are referred to as the X, A and L modes, with the X and A modes having dispersion relation$|z|=z_{\text{A}}\approx 1-1/2\unicode[STIX]{x1D6FD}_{\text{A}}^{2}$, where$z=\unicode[STIX]{x1D714}/k_{\Vert }c$is the phase speed and$\unicode[STIX]{x1D6FD}_{\text{A}}c$is the Alfvén speed. The L mode dispersion relation is determined by a relativistic plasma dispersion function,$z^{2}W(z)$, which is negative for$|z|&lt;z_{0}$and has a sharp maximum at$|z|=z_{\text{m}}$, with$1-z_{\text{m}}&lt;1-z_{0}\ll 1$. We give numerical estimates for the maximum of$z^{2}W(z)$and for$z_{\text{m}}$and$z_{0}$for a one-dimensional Jüttner distribution. The L and A modes reconnect, for$z_{\text{A}}&gt;z_{0}$, to form the O and Alfvén modes for oblique propagation ($\unicode[STIX]{x1D703}\neq 0$). For$z_{\text{A}}&lt;z_{0}$the Alfvén and O mode curves reconnect forming a new mode that exists only for$\tan ^{2}\unicode[STIX]{x1D703}\gtrsim z_{0}^{2}-z_{\text{A}}^{2}$. The L mode is the nearest counterpart to Langmuir waves in a non-relativistic plasma, but we argue that there are no ‘Langmuir-like’ waves in a pulsar plasma, identifying three features of the L mode (dispersion relation, ratio of electric to total energy and group speed) that are not Langmuir like. A beam-driven instability requires a beam speed equal to the phase speed of the wave. This resonance condition can be satisfied for the O mode, but only for an implausibly energetic beam and only for a tiny range of angles for the O mode around$\unicode[STIX]{x1D703}\approx 0$. The resonance is also possible for the Alfvén mode but only near a turnover frequency that has no counterpart for Alfvén waves in a non-relativistic plasma.

Response to “Comment on ‘Symmetry in electron and ion dispersion in 1D Vlasov-Poisson plasma’” [Phys. Plasmas 26, 064701 (2019)

Treating electron and ion kinetics on the same physics footing or in a symmetric framework, dispersion relations (ωr, k) for ion and electron modes in a 1D Vlasov-Poisson (VP) plasma were obtained in the limit of weak flattening of the electron and ion distributions. Using this information of (ωr, k), a nonlinear VP solver with a low amplitude, harmonic external forcing has been solved. A possibility of simultaneous excitation of all the electrostatic normal modes was demonstrated in Trivedi et al. [Phys. Plasmas 25, 112102 (2018)]. The main focus of the paper is on the excitation of normal modes by applying a small amplitude external, monochromatic, electric field drive. In order to drive as well as to identify Phase Space Vortices (i.e., Bernstein-Greene-Kruskal/Cnoidal modes, etc.) formed out of the driven nonlinear VP system, assuming local flattening of electron and ion distributions, the real part of the plasma dispersion function for arbitrary ratios of ion to electron masses and temperatures is solved, which is known to be accurate in the low amplitude, harmonic limit, as pointed out by Schamel [Phys. Plasmas 19, 020501 (2012)].

Interface-phonon–electron interaction potentials and dispersion relations in III-nitride-based structures

In dimensionally confined multilayer heterostructures, phonons that are joint modes of the materials composed of these heterostructures are known to exist over specific frequency ranges. These modes, known as interface phonons, can exhibit phonon-electron interactions that are enhanced as the thicknesses of the layers of the heterostructure are reduced in size to about 10 nm or less. These modes have been shown to be important in phonon engineering and have been applied in optoelectronic and electronic devices, primarily for semiconductor heterostructures with underlying cubic lattices, with few studies existing for heterostructures based on wurtzite III-nitride. Motivated by applications of interface modes in ternary-based nitride structures, such as heat transport, this paper presents generalized expressions for the phonon-electron Fröhlich interactions as well as the dispersion relations for these joint modes for the technologically important case of III-nitride materials. Frequency conditions are found to restrict the existence of interface modes as illustrated through several structures.

Electromagnetic Viscous-Resistive-Drift-Wave Instability in Burning Plasma

Drift wave instabilities (DWI) might be take a part for anomalous transport in modern day tokamaks due to contributions of edge turbulence and zonal flows. Experimentally, it is found that micro-level turbulence (associated with two-fluid dynamics) braced with macro-level (associated with single-fluid dynamics) magnetohydrodynamics-type processes. In this paper, additional two-fluid effect viz. ion viscosity on the electromagnetic (EM) linear resistive drift wave instability is analyzed by using a two-fluid MHD model. A modify dispersion relation for EM drift modes in a nonuniform magnetized plasma is derived, taken into account equilibrium pressure gradients, effect of finite ion-sound gyro-radius associated with electron–ion decoupling and viscous effect due to ions. The dispersion relation is then analyzed both analytically as well as numerically. It is shown, how additional two-fluid effects modify the growth rate for DWI in different regimes. The standard resistive drift-Alfven mode is reproduced in the cold ion case. Moreover, it is estimated that these effects provide the possibility of novel effects on EM instabilities in a nonuniform magnetized plasma. The results should be useful in the interpretation of EM fluctuations in nonuniform magneto-plasmas in which resistivity is a key element in calculations of dissipative drift instabilities.

Electromagnetic wave propagation in a superconducting parallel-plate waveguide filled with an indefinite medium

Abstract The electromagnetic wave propagation is analysed in a superconducting parallel-plate waveguide filled with an indefinite medium. The dispersion relations of transverse electric and transverse magnetic wave modes are derived by using the Meissner boundary conditions. The different cases of these wave modes are discussed by choosing the appropriate signs of the anisotropic parameters of the indefinite medium. In this connection, the regions of propagation/non-propagation are numerically analysed by plotting the phase velocity versus propagation frequency.