Showing papers on "Dispersion relation published in 2021"

Crossing Symmetric Dispersion Relations in Quantum Field Theories.

Abstract: For 2-2 scattering in quantum field theories, the usual fixed t dispersion relation exhibits only two-channel symmetry. This Letter considers a crossing symmetric dispersion relation, reviving certain old ideas from the 1970s. Rather than the fixed t dispersion relation, this needs a dispersion relation in a different variable z, which is related to the Mandelstam invariants s, t, u via a parametric cubic relation making the crossing symmetry in the complex z plane a geometric rotation. The resulting dispersion is manifestly three-channel crossing symmetric. We give simple derivations of certain known positivity conditions for effective field theories, including the null constraints, which lead to two sided bounds and derive a general set of new nonperturbative inequalities. We show how these inequalities enable us to locate the first massive string state from a low energy expansion of the four dilaton amplitude in type II string theory. We also show how a generalized (numerical) Froissart bound, valid for all energies, is obtained from this approach.

First-principles modeling of plasmons in aluminum under ambient and extreme conditions

Abstract: The theoretical understanding of plasmon behavior is crucial for an accurate interpretation of inelastic scattering diagnostics in many experiments. We highlight the utility of linear response time-dependent density functional theory (LR-TDDFT) as a first-principles framework for consistently modeling plasmon properties. We provide a comprehensive analysis of plasmons in aluminum from ambient to warm dense matter conditions and assess typical properties such as the dynamical structure factor, the plasmon dispersion, and the plasmon lifetime. We compare our results with scattering measurements and with other TDDFT results as well as models such as the random phase approximation, the Mermin approach, and the dielectric function obtained using static local field corrections of the uniform electron gas parametrized from path-integral Monte Carlo simulations. We conclude that results for the plasmon dispersion and lifetime are inconsistent between experiment and theories and that the common practice of extracting and studying plasmon dispersion relations is an insufficient procedure to capture the complicated physics contained in the dynamic structure factor in its full breadth.

Hydrodynamic gradient expansion in linear response theory

Abstract: A foundational question in relativistic fluid mechanics concerns the properties of the hydrodynamic gradient expansion at large orders. We establish the precise conditions under which this gradient expansion diverges for a broad class of microscopic theories admitting a relativistic hydrodynamic limit, in the linear regime. Our result does not rely on highly symmetric fluid flows utilized by previous studies of heavy-ion collisions and cosmology. The hydrodynamic gradient expansion diverges whenever energy density or velocity fields have support in momentum space exceeding a critical momentum and converges otherwise. This critical momentum is an intrinsic property of the microscopic theory and is set by branch point singularities of hydrodynamic dispersion relations.

Crossing Symmetric Dispersion Relations for Mellin Amplitudes.

Abstract: We consider manifestly crossing symmetric dispersion relations for Mellin amplitudes of scalar four point correlators in conformal field theories. This allows us to set up the nonperturbative Polyakov bootstrap for the conformal field theories in Mellin space on a firm foundation, thereby fixing the contact term ambiguities in the crossing symmetric blocks. Our new approach employs certain "locality"constraints replacing the requirement of crossing symmetry in the usual fixed-t dispersion relation. Using these constraints, we show that the sum rules based on the two channel dispersion relations and the present dispersion relations are identical. Our framework allows us to connect with the conceptually rich picture of the Polyakov blocks being identified with Witten diagrams in anti-de Sitter space. We also give two sided bounds for Wilson coefficients for effective field theories in anti-de Sitter space. © 2021 authors.

New $$(3+1)$$ ( 3 + 1 ) -dimensional Painlevé integrable fifth-order equation with third-order temporal dispersion

Abstract: This work deals with a new $$(3+1)$$ -dimensional Painleve integrable fifth-order equation characterized by third-order temporal and spatial dispersions. The Painleve test is carried out to demonstrate the complete integrability of this model. A rule that governs the dispersion relation with the spatial variables coefficients is reported. We employ the simplified Hirota’s method to obtain multiple soliton solutions. We examine specific cases of the dispersion relations along with their respective coefficients. It is hoped that the results reported in this work can enrich applications in solitary waves theory, and more specifically, in models with third-order temporal dispersion.

Spatiotemporal imaging of 2D polariton wave packet dynamics using free electrons.

Abstract: Coherent optical excitations in two-dimensional (2D) materials, 2D polaritons, can generate a plethora of optical phenomena that arise from the extraordinary dispersion relations that do not exist in regular materials. Probing of the dynamical phenomena of 2D polaritons requires simultaneous spatial and temporal imaging capabilities and could reveal unknown coherent optical phenomena in 2D materials. Here, we present a spatiotemporal measurement of 2D wave packet dynamics, from its formation to its decay, using an ultrafast transmission electron microscope driven by femtosecond midinfrared pulses. The ability to coherently excite phonon-polariton wave packets and probe their evolution in a nondestructive manner reveals intriguing dispersion-dependent dynamics that includes splitting of multibranch wave packets and, unexpectedly, wave packet deceleration and acceleration. Having access to the full spatiotemporal dynamics of 2D wave packets can be used to illuminate puzzles in topological polaritons and discover exotic nonlinear optical phenomena in 2D materials.

Electron-phonon hydrodynamics

Abstract: We developed the theory of hydrodynamics of an isotropic Fermi liquid of electrons coupled to isotropic acoustic phonons, assuming that umklapp processes may be neglected. At low temperatures, the fluid is approximately Galilean invariant; at high temperatures, the fluid is nearly relativistic; at intermediate temperatures, there are seven additional temperature regimes with unconventional thermodynamic properties and hydrodynamic transport coefficients in a three-dimensional system. We predict qualitative signatures of electron-phonon fluids in incoherent transport coefficients, shear and Hall viscosity, and plasmon dispersion relations. Our theory may be relevant for numerous quantum materials where strong electron-phonon scattering has been proposed to underlie a hydrodynamic regime, including ${\mathrm{WTe}}_{2}, {\mathrm{WP}}_{2}$, and ${\mathrm{PtSn}}_{4}$.

Tunable ultralow frequency wave attenuations in one-dimensional quasi-zero-stiffness metamaterial

Abstract: Metamaterials are artificially structured materials that enable wave attenuation in band gaps. However, opening an ultralow-frequency band gap is still a challenge, since it is hard to realize near-zero stiffness in a traditional way. In this paper, a one-dimensional tunable quasi-zero-stiffness (QZS) metamaterial is engineered for ultralow-frequency (about a few tens Hertz) wave attenuation. Design optimization on the configuration of this new metamaterial is conducted to achieve quasi-zero stiffness. The dispersion relation is derived theoretically based on a lumped diatomic chain model, and then the band structure is revealed. The characteristics of longitudinal wave propagation in the metamaterial are studied by both numerical analyses and FE simulations, which are also validated by experimental tests. The results indicate that the stiffness is deformation-related, and the band gap can be tuned substantially by just changing the pre-compression. Therefore, the quasi-zero stiffness and then the ultralow-frequency band gap can be fulfilled by pre-compressing the metamaterial properly.

Roton-like acoustical dispersion relations in 3D metamaterials

Abstract: Roton dispersion relations have been restricted to correlated quantum systems at low temperatures, such as liquid Helium-4, thin films of Helium-3, and Bose–Einstein condensates. This unusual kind of dispersion relation provides broadband acoustical backward waves, connected to energy flow vortices due to a “return flow”, in the words of Feynman, and three different coexisting acoustical modes with the same polarization at one frequency. By building mechanisms into the unit cells of artificial materials, metamaterials allow for molding the flow of waves. So far, researchers have exploited mechanisms based on various types of local resonances, Bragg resonances, spatial and temporal symmetry breaking, topology, and nonlinearities. Here, we introduce beyond-nearest-neighbor interactions as a mechanism in elastic and airborne acoustical metamaterials. For a third-nearest-neighbor interaction that is sufficiently strong compared to the nearest-neighbor interaction, this mechanism allows us to engineer roton-like acoustical dispersion relations under ambient conditions. Here, the authors introduce beyond-nearest-neighbour interactions as a mechanism for molding the flow of waves in acoustic metamaterials. They find that for strong third-nearest-neighbour interactions, this mechanism allows for engineering roton-like acoustical dispersion relations under ambient conditions.

Engineering the Spectral and Spatial Dispersion of Thermal Emission via Polariton–Phonon Strong Coupling

Abstract: Strong coupling between optical modes can be implemented into nanophotonic design to modify the energy-momentum dispersion relation. This approach offers potential avenues for tuning the thermal emission frequency, line width, polarization, and spatial coherence. Here, we employ three-mode strong coupling between propagating and localized surface phonon polaritons, with zone-folded longitudinal optic phonons within periodic arrays of 4H-SiC nanopillars. Energy exchange, mode evolution, and coupling strength between the three polariton branches are explored experimentally and theoretically. The influence of strong coupling upon the angle-dependent thermal emission was directly measured, providing excellent agreement with theory. We demonstrate a 5-fold improvement in the spatial coherence and 3-fold enhancement of the quality factor of the polaritonic modes, with these hybrid modes also exhibiting a mixed character that could enable opportunities to realize electrically driven emission. Our results show that polariton-phonon strong coupling enables thermal emitters, which meet the requirements for a host of IR applications in a simple, lightweight, narrow-band, and yet bright emitter.

An integral four-variable hyperbolic HSDT for the wave propagation investigation of a ceramic-metal FGM plate with various porosity distributions resting on a viscoelastic foundation

Abstract: This work studies the dispersion relations of wave propagation in infinite advanced functionally graded (FG) ceramic-metal plates. A simple integral hyperbolic higher-order shear deformation theory...

Near-field radiative heat transfer between uniaxial hyperbolic media: Role of volume and surface phonon polaritons

Abstract: It has been found that near-field radiative heat transfer (NFRHT) between hyperbolic media, such as hexagonal boron nitride (hBN), can be significantly enhanced due to excitation of hyperbolic volume phonon polaritons (HVPPs) and hyperbolic surface phonon polaritons (HSPPs). However, the role of HVPPs and HSPPs in type I and type II hyperbolic bands has rarely been discussed in depth. In this paper, we investigate the NFRHT between two hBN slabs considering the role of HVPPs and HSPPs. The theoretical analysis and numerical results show that when the optical axis is perpendicular to the material surface, the enhanced NFRHT is attributed to the excitation of HVPPs in both type I and type II hyperbolic bands, while HSPPs cannot be excited in this case. When the optical axis is parallel to the material surface, only HVPPs can be excited in type I hyperbolic band, while both HVPPs and HSPPs can be excited in type II hyperbolic band. In addition, the effect of the slab thickness on the dispersion relations of HVPPs and HSPPs, and on the enhancement of NFRHT is also studied. We believe the results in this paper could help to elucidate the mechanisms and manipulation of enhanced NFRHT between uniaxial hyperbolic materials.

Dispersion relation of Landau elementary excitations and thermodynamic properties of superfluid He 4

Abstract: The dispersion relation $\epsilon(k)$ of the elementary excitations of superfluid $^4$He has been measured at very low temperatures, from saturated vapor pressure up to solidification, using a high flux time-of-flight neutron scattering spectrometer equipped with a high spatial resolution detector (10$^5$ 'pixels'). A complete determination of $\epsilon(k)$ is achieved, from very low wave-vectors up to the end of Pitaeskii's plateau. The results compare favorably in the whole the wave-vector range with the predictions of the dynamic many-body theory (DMBT). At low wave-vectors, bridging the gap between ultrasonic data and former neutron measurements, the evolution with the pressure from anomalous to normal dispersion, as well as the peculiar wave-vector dependence of the phase and group velocities, are accurately characterized. The thermodynamic properties have been calculated analytically, developing Landau's model, using the measured dispersion curve. A good agreement is found below 0.85 K between direct heat capacity measurements and the calculated specific heat, if thermodynamically consistent power series expansions are used. The thermodynamic properties have also been calculated numerically; in this case, the results are applicable with excellent accuracy up to 1.3 K, a temperature above which the dispersion relation itself becomes temperature dependent.

Measuring phonon dispersion at an interface.

Abstract: The breakdown of translational symmetry at heterointerfaces leads to the emergence of new phonon modes localized at the interface1. These modes have an essential role in thermal and electrical transport properties in devices, especially in miniature ones wherein the interface may dominate the entire response of the device2. Although related theoretical work began decades ago1,3–5, experimental research is totally absent owing to challenges in achieving the combined spatial, momentum and spectral resolutions required to probe localized modes. Here, using the four-dimensional electron energy-loss spectroscopy technique, we directly measure both the local vibrational spectra and the interface phonon dispersion relation for an epitaxial cubic boron nitride/diamond heterointerface. In addition to bulk phonon modes, we observe modes localized at the interface and modes isolated from the interface. These features appear only within approximately one nanometre around the interface. The localized modes observed here are predicted to substantially affect the interface thermal conductance and electron mobility. Our findings provide insights into lattice dynamics at heterointerfaces, and the demonstrated experimental technique should be useful in thermal management, electrical engineering and topological phononics. Four-dimensional electron energy-loss spectroscopy measurements of the vibrational spectra and the phonon dispersion at a heterointerface show localized modes that are predicted to affect the thermal conductance and electron mobility.

Hydrodynamic collective modes in graphene

Abstract: Collective behavior is one of the most intriguing aspects of the hydrodynamic approach to electronic transport. Here we provide a consistent, unified calculation of the dispersion relations of the hydrodynamic collective modes in graphene. Taking into account viscous effects, we show that the hydrodynamic sound mode in graphene becomes overdamped at sufficiently large momentum scales. Extending the linearized theory beyond the hydrodynamic regime, we connect the diffusive hydrodynamic charge density fluctuations with plasmons.

Experimental observation of roton-like dispersion relations in metamaterials

Abstract: Previously, rotons were observed in correlated quantum systems at low temperatures, including superfluid helium and Bose-Einstein condensates. Here, following a recent theoretical proposal, we repo...

Reaching the Planck scale with muon lifetime measurements

Abstract: Planck scale modified dispersion relations are one way how to capture the influence of quantum gravity on the propagation of fundamental point particles effectively. We derive the time dilation between an observer's or particle's proper time, given by a Finslerian length measure induced from a modified dispersion relation, and a reference laboratory time. To do so, the Finsler length measure for general first order perturbations of the general relativistic dispersion relation is constructed explicitly. From this we then derive the time dilation formula for the $\kappa$-Poincar\'e dispersion relation in several momentum space bases, as well as for modified dispersion relations considered in the context of loop quantum gravity and Ho\v{r}ava-Lifshitz gravity. Most interestingly we find that the momentum Lorentz factor in the present and future colliders can, in principle, become large enough to constrain the $\kappa$-Poincar\'e dispersion relation in the bicrossproduct basis with Planck scale sensitivity with help of the muon's lifetime.

An optical lattice with sound

Abstract: Quantised sound waves -- phonons -- govern the elastic response of crystalline materials, and also play an integral part in determining their thermodynamic properties and electrical response (e.g., by binding electrons into superconducting Cooper pairs). The physics of lattice phonons and elasticity is absent in simulators of quantum solids constructed of neutral atoms in periodic light potentials: unlike real solids, traditional optical lattices are silent because they are infinitely stiff. Optical-lattice realisations of crystals therefore lack some of the central dynamical degrees of freedom that determine the low-temperature properties of real materials. Here, we create an optical lattice with phonon modes using a Bose-Einstein condensate (BEC) coupled to a confocal optical resonator. Playing the role of an active quantum gas microscope, the multimode cavity QED system both images the phonons and induces the crystallisation that supports phonons via short-range, photon-mediated atom-atom interactions. Dynamical susceptibility measurements reveal the phonon dispersion relation, showing that these collective excitations exhibit a sound speed dependent on the BEC-photon coupling strength. Our results pave the way for exploring the rich physics of elasticity in quantum solids, ranging from quantum melting transitions to exotic "fractonic" topological defects in the quantum regime.

The effect of the magnetic field on the damping of slow waves in the solar corona

Abstract: Context. Slow magnetoacoustic waves are routinely observed in astrophysical plasma systems such as the solar corona, and they are usually seen to damp rapidly. As a slow wave propagates through a plasma, it modifies the equilibrium quantities of density, temperature, and the magnetic field. In the corona and other plasma systems, the thermal equilibrium is comprised of a balance between continuous heating and cooling processes, the magnitudes of which vary with density, temperature and the magnetic field. Thus the wave may induce a misbalance between these competing processes. Its back reaction on the wave has been shown to lead to dispersion, and amplification or damping, of the wave.Aims. This effect of heating and cooling misbalance has previously been studied in the infinite magnetic field approximation in a plasma whose thermal equilibrium is comprised of optically thin radiative losses and field-aligned thermal conduction, balanced by an (unspecified) heating process. In this work we extend this analysis by considering a non-zero β plasma. The importance of the effect of the magnetic field in the rapid damping of slow waves in the solar corona is evaluated and compared to the effects of thermal conduction.Methods. A linear perturbation under the thin flux tube approximation is considered, and a dispersion relation describing the slow magnetoacoustic modes is found. The dispersion relation’s limits of strong non-adiabaticity and weak non-adiabaticity are studied. The characteristic timescales were calculated for plasma systems with a range of typical coronal densities, temperatures, and magnetic field strengths.Results. The number of timescales characterising the effect of the misbalance is found to remain at two, as with the infinite magnetic field case. In the non-zero β case, these two timescales correspond to the partial derivatives of the combined heating and cooling function with respect to constant gas pressure and with respect to constant magnetic pressure. The predicted damping times of slow waves from thermal misbalance in the solar corona are found to be of the order of 10–100 min, coinciding with the wave periods and damping times observed. Moreover, the slow wave damping by thermal misbalance is found to be comparable to the damping by field-aligned thermal conduction. The change in damping with plasma-β is complex and depends on the coronal heating function’s dependence on the magnetic field in particular. Nonetheless, we show that in the infinite field limit, the wave dynamics is insensitive to the dependence of the heating function on the magnetic field, and this approximation is found to be valid in the corona so long as the magnetic field strength is greater than approximately 10 G for quiescent loops and plumes, and 100 G for hot and dense loops.Conclusions. A thermal misbalance may damp slow magnetoacoustic waves rapidly in much of the corona, and its inclusion in our understanding of slow mode damping may resolve discrepancies between the observations and theory relying on compressive viscosity and thermal conduction alone.

Polariton topological transition effects on radiative heat transfer

Abstract: Twisted two-dimensional bilayer anisotropy materials exhibit many exotic physical phenomena. Manipulating the “twist angle” between the two layers enables the hybridization phenomenon of polaritons, resulting in fine control of the dispersion engineering of the polaritons in these structures. Here, combined with the hybridization phenomenon of anisotropy polaritons, we study theoretically the near-field radiative heat transfer (NFRHT) between two twisted hyperbolic systems. These two twisted hyperbolic systems are mirror images of each other. Each twisted hyperbolic system is composed of two graphene gratings, where there is an angle φ between these two graphene gratings. By analyzing the photonic transmission coefficient as well as the plasmon dispersion relation of the twisted hyperbolic system, we prove the enhancement effect of the topological transitions of the surface state at a special angle [from open (hyperbolic) to closed (elliptical) contours] on radiative heat transfer. Meanwhile the role of the thickness of dielectric spacer and vacuum gap on the manipulating the topological transitions of the surface state and the NFRHT are also discussed. We predict the hysteresis effect of topological transitions at a larger vacuum gap, and demonstrate that as the thickness of the dielectric spacer increases, the transition from the enhancement effect of heat transfer caused by the twisted hyperbolic system to a suppression.

Hydrodynamic dispersion relations at finite coupling

Abstract: By using holographic methods, the radii of convergence of the hydrodynamic shear and sound dispersion relations were previously computed in the ${\cal N} = 4$ supersymmetric Yang-Mills theory at infinite 't Hooft coupling and infinite number of colours. Here, we extend this analysis to the domain of large but finite 't Hooft coupling. To leading order in the perturbative expansion, we find that the radii grow with increasing inverse coupling, contrary to naive expectations. However, when the equations of motion are solved using a qualitative non-perturbative resummation, the dependence on the coupling becomes piecewise continuous and the initial growth is followed by a decrease. The piecewise nature of the dependence is related to the dynamics of branch point singularities of the energy-momentum tensor finite-temperature two-point functions in the complex plane of spatial momentum squared. We repeat the study using the Einstein-Gauss-Bonnet gravity as a model where the equations can be solved fully non-perturbatively, and find the expected decrease of the radii of convergence with the effective inverse coupling which is also piecewise continuous. Finally, we provide arguments in favour of the non-perturbative approach and show that the presence of non-perturbative modes in the quasinormal spectrum can be indirectly inferred from the analysis of perturbative critical points.

Dispersion properties of slab waveguides with a linear graded-index film and a nonlinear substrate

Abstract: Three-layer slab waveguide with a graded-index film and a nonlinear substrate is investigated. The nonlinear substrate is considered of Kerr-type and the film index is assumed to change linearly as we move from the film-clad to the film-substrate interfaces. The solutions of the fields in the guiding film contains Airy functions which can be written as Bessel functions of order 1/3. The dispersion relation is derived in terms of three well-known normalized parameters V, a and b and the dispersion properties are plotted and studied. Many interesting features are obtained such as the nonexistence of cut-off thickness due to the nonlinear substrate and the value of the normalized guide index does not exceed unity which means they correspond to guided modes.

On Pollard's wave solution at the Equator

Abstract: In this paper we present a dynamical study of the exact nonlinear Pollard wave solution to the geophysical water-wave problem in the f-plane approximation. We deduce an exact dispersion relation and we discuss some properties of this solution.

Dispersion relation analysis of the radiative corrections to gA in the neutron β-decay

Abstract: We present the first and complete dispersion relation analysis of the inner radiative corrections to the axial coupling constant gA in the neutron β-decay. Using experimental inputs from the elastic form factors and the spin-dependent structure function g1, we determine the contribution from the γW-box diagram to a precision better than 10−4. Our calculation indicates that the inner radiative corrections to the Fermi and the Gamow-Teller matrix element in the neutron β-decay are almost identical, i.e. the ratio λ = gA/gV is almost unrenormalized. With this result, we predict the bare axial coupling constant to be $$ {\overset{\circ }{g}}_A=-1.2754{(13)}_{\mathrm{exp}}{(2)}_{\mathrm{RC}} $$ based on the PDG average λ = −1.2756(13).