Long-wavelength Modes Research Articles

Elastic properties and thermodynamic anomalies of supersolids

We study a supersolid in the context of a Gross-Pitaevskii theory with a nonlocal effective potential. We employ a homogenization technique which allows us to calculate the elastic moduli, supersolid fraction, and other state variables of the system. Our methodology is verified against numerical simulations of elastic deformations. We can also verify that the long-wavelength Goldstone modes that emerge from this technique agree with Bogoliubov theory. We find a thermodynamic anomaly that the supersolid does not obey the thermodynamic relation ∂P/∂V|N=−n(∂P/∂N|V), which we claim is a feature unique to supersolids. Published by the American Physical Society 2024

Reconstructing the long-wavelength matter density fluctuation modes from the scalar-type clustering fossils

Revealing the large-scale structure from the 21cm intensity mapping surveys is only possible after the foreground cleaning. However, most current cleaning techniques relying on the smoothness of the foreground spectrum lead to a severe side effect of removing the large-scale structure signal along the line of sight. On the other hand, the clustering fossil, a coherent variation of the small-scale clustering over large scales, allows us to recover the long-wavelength density modes from the off-diagonal correlation between short-wavelength modes. In this paper, we revisit the reconstruction based on the short-wavelength matter density modes in real space and scrutinize the requirements for an unbiased and optimal clustering-fossil estimator. We show that (A) the estimator is unbiased only when using an accurate bispectrum model for the long-short-short mode coupling and (B) including the connected four-point correlation functions is essential for characterizing the noise power spectrum of the estimated long mode. For matter in real space, the clustering fossil estimator based upon the leading-order bispectrum yields an unbiased estimation of the long-wavelength (k ≲ 0.01 [h/Mpc]) modes with the cross-correlation coefficient of 0.7 at redshifts z = 0 to 3.

Complete analysis of the background and anisotropies of scalar-induced gravitational waves: primordial non-Gaussianity f NL and g NL considered

Investigation of primordial non-Gaussianity holds immense importance in testing the inflation paradigm and shedding light on the physics of the early Universe. In this study, we conduct the complete analysis of scalar-induced gravitational waves (SIGWs) by incorporating the local-type non-Gaussianity f NL and g NL. We develop Feynman-like diagrammatic technique and derive semi-analytic formulas for both the energy-density fraction spectrum and the angular power spectrum. For the energy-density fraction spectrum, we analyze all the relevant Feynman-like diagrams, determining their contributions to the spectrum in an order-by-order fashion. As for the angular power spectrum, our focus lies on the initial inhomogeneities, giving rise to anisotropies in SIGWs, that arise from the coupling between short- and long-wavelength modes due to primordial non-Gaussianity. Our analysis reveals that this spectrum exhibits a typical multipole dependence, characterized by C̃ ℓ ∝ [ℓ(ℓ + 1)]-1, which plays a crucial role in distinguishing between different sources of gravitational waves. Depending on model parameters, significant anisotropies can be achieved. We also show that the degeneracies in model parameters can be broken. The findings of our study underscore the angular power spectrum as a robust probe for investigating primordial non-Gaussianity and the physics of the early Universe. Moreover, our theoretical predictions can be tested using space-borne gravitational-wave detectors and pulsar timing arrays.

Quantum tachyonic preheating, revisited

In certain models of inflation, the postinflationary reheating of the Universe is not primarily due to perturbative decay of the inflaton field into particles, but proceeds through a tachyonic instability. In the process, long-wavelength modes of an unstable field, which is often distinct from the inflaton itself, acquire very large occupation numbers, which are subsequently redistributed into a thermal equilibrium state. We investigate this process numerically through quantum real-time lattice simulations of the Kadanoff-Baym equation, using a 1/N-NLO truncation of the 2PI-effective action. We identify the early-time maximum occupation number, the “classical” momentum range, the validity of the classical approximation and the effective IR temperature, and study the kinetic equilibration of the system and the equation of state.

Anisotropic quasi-static permittivity of rare-earth scandate single crystals measured by terahertz spectroscopy

We report the real-valued static and complex-valued quasi-static anisotropic permittivity parameters of rare-earth scandate orthorhombic single crystal GdScO3 (GSO), TbScO3 (TSO), and DyScO3 (DSO). Employing continuous-wave terahertz spectroscopy (0.2–1 THz), the complex permittivity was extracted using an anisotropic ambient-film-ambient model. Data obtained from multiple samples of the same oxides and different surface cuts were analyzed simultaneously. The zero-frequency limit of the modeled data indicates that at room temperature the real part of the dielectric tensor components for GSO are ɛa = 22.7, ɛb = 19.3, and ɛc = 28.1; for DSO, ɛa = 20.3, ɛb = 17.4, and ɛc = 31.1; and for TSO, ɛa = 21.6, ɛb = 18.1, and ɛc = 30.3, with a, b, and c crystallographic axes constituting the principal directions for the permittivity tensor. These results are in excellent agreement with expectations from theoretical computations and with scarcely available data from previous experimental studies. Furthermore, our results evidence a noticeable attenuation, which increases with frequency, and are very significant especially at the higher frequency end of the measurement and along the c-direction in all samples. We suggest the attenuation is most likely caused by the onset of absorption due to long-wavelength active optical phonon modes. These results are important for electronic and potential sub-terahertz applications (e.g., quarter-wave plate) benefiting from the large index contrast along different directions in these materials.

Effects of the applied fields' strength on the plasma behavior and processes in E × B plasma discharges of various propellants. II. Magnetic field

The effects of magnetic field intensity on the properties of the plasma discharge and on the underlying phenomena are studied for different propellants' ion mass. The plasma setup represents a 2D radial–azimuthal configuration with perpendicular electric and magnetic fields. The electric field is along the axial direction, and the magnetic field is along the radial direction. The magnetic field intensity is changed from 5 to 30 mT, with 5 mT increments. The studied propellant gases are xenon, krypton, and argon. The simulations are carried out using a reduced-order particle-in-cell code. It is shown that, for all the propellants, the change in the magnetic field intensity yields two distinct plasma regimes, where either the modified two-stream instability (MTSI) or the electron cyclotron drift instability (ECDI) are dominant. A third plasma regime is also observed for cases with moderate values of the magnetic field (15 and 20 mT), where the ECDI and the MTSI co-exist with comparable amplitudes. This described variation of plasma regime becomes clearly reflected in the radial distribution of the axial electron current density and the electron temperature anisotropy. At the relatively low-magnetic-field intensities (5 and 10 mT), the MTSI is mitigated. At relatively high magnitudes of the magnetic field (25 and 30 mT), the MTSI becomes strongly present, a long-wavelength wave mode develops, and the ECDI becomes suppressed. An exception to this latter observation was noticed for xenon, for which the ECDI was observed to be detectable with a notable strength up to the magnetic field value of 25 mT.

On covariant perturbations with scalar field in modified Gauss–Bonnet gravity

We investigate cosmological perturbations of f(G) gravity in the presence of a scalar field. Using the 1+3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1+3$$\\end{document} covariant formalism, we present the energy overdensity perturbation equations responsible for large scale structure formation. After applying harmonic decomposition method together with the redshift transformation technique, we obtain the fully perturbed equations in redshift space. The equations are solved to study the growth of matter overdensities contrast with redshift. For both short- and long-wavelength modes, we obtain numerical results for particular functional form f(G) models and scalar field. We find that, for this choice the energy overdensity perturbations decay with increase in redshift. However, for both short- and long-wavelength modes, the perturbations which include amplitude effects due to the f(G) models with a scalar field do differ remarkably from those in Λ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda $$\\end{document}CDM. The results reduce to GR results in the limit of f(G)→G\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$f(G)\\rightarrow G$$\\end{document} and in the absence of scalar field.

Confronting the Chaplygin gas with data: Background and perturbed cosmic dynamics

In this paper, we undertake a unified study of background dynamics and cosmological perturbations in the presence of the Chaplygin gas (CG). This is done by first constraining the background cosmological parameters of different Chaplygin gas models with SNeIa and [Formula: see text] data for detailed statistical analysis of the CG models. Based on the statistical criteria we followed, none of the models has substantial observational support, but we show that the so-called “original” and “extended/generalised” Chaplygin gas models have some observational support and less observational support, respectively, whereas the “modified” and “modified generalised” Chaplygin gas models miss out on the category less observational support, but cannot be ruled out. The so-called “generalised” cosmic Chaplygin gas model, on the other hand, falls under the no observational support category of the statistical criterion and can be ruled out. The models which are statistically accepted are considered for perturbation level in both theoretical and observational aspects. We also apply the [Formula: see text] covariant formalism of perturbation theory and derive the evolution equations of the fluctuations in the matter density contrast of the matter–Chaplygin gas system for the models with some or less statistical support. The solutions to these coupled systems of equations are then computed in both short-wavelength and long-wavelength modes. Then we feed these observationally restricted parameters into the analysis of cosmological perturbations to address the growth of density contrast through redshift. Using the most recent linear growth of the data [Formula: see text], CG models are considered to study the linear growth of the structure.

Squeezed bispectrum and one-loop corrections in transient constant-roll inflation

In canonical single-field inflation, the production of primordial black holes (PBH) requires a transient violation of the slow-roll condition. The transient ultra slow-roll inflation is an example of such scenarios, and more generally, one can consider the transient constant-roll inflation. We investigate the squeezed bispectrum in the transient constant-roll inflation and find that Maldacena's consistency relation holds for a sufficiently long-wavelength mode, whereas it is violated for modes around the peak scale for the non-attractor case. We also demonstrate how the one-loop corrections are modified compared to the case of the transient ultra slow-roll inflation, focusing on representative one-loop terms originating from a time derivative of the second slow-roll parameter in the cubic action. We find that the perturbativity requirement on those terms does not rule out the production of PBH from the transient constant-roll inflation.Therefore, it is a simple counterexample of the recently claimed no-go theorem of PBH production from single-field inflation.

Synchronizing the consistency relation

We study the N-point function of the density contrast to quadratic order in the squeezed limit during the matter-dominated (MD) and radiation-dominated (RD) eras in synchronous gauge. Since synchronous gauge follows the free-fall frame of observers, the equivalence principle dictates that in the gradient approximation for the long-wavelength mode there is only a single, manifestly time-independent consistency relation for the N-point function. This simple form is dictated by the initial mapping between synchronous and local coordinates, unlike Newtonian gauge and its correspondingly separate dilation and Newtonian consistency relations. Dynamical effects only appear at quadratic order in the squeezed limit and are again characterized by a change in the local background, also known as the separate universe approach. We show that for the 3-point function the compatibility between these squeezed-limit relations and second-order perturbation theory requires both the initial and dynamical contributions to match, as they do in single-field inflation. This clarifies the role of evolution or late-time projection effects in establishing the consistency relation for observable bispectra, which is especially important for radiation acoustic oscillations and for establishing consistency below the matter-radiation equality scale in the MD era. Defining an appropriate angle and time average of these oscillations is also important for making separate universe predictions of spatially varying local observables during the RD era, which can be useful for a wider range of cosmological predictions beyond N-point functions.

Global Stability Analysis of Full-Aircraft Transonic Buffet at Flight Reynolds Numbers

Fully three-dimensional (3D) global stability analysis (GSA) is performed on the NASA Common Research Model at turbulent transonic buffet conditions. The framework here proposed is based on a Jacobian-free approach that enables GSA on large 3D grids, making this the first stability study on a full-aircraft at typical flight Reynolds numbers. The Reynolds-averaged Navier–Stokes solutions compare reasonably well with the available experiments and are used as base flows for the stability analyses. GSA is first performed at wind tunnel Reynolds number conditions, and a buffet-cell mode localized in the wing outboard region is found to be responsible for the onset. When the side-of-body (SOB) separation becomes larger at higher angles of attack, two additional modes are detected: a high-frequency mode localized in the SOB region and a low-frequency long-wavelength buffet-cell mode that may represent the link with the shock-oscillation instability found in two-dimensional airfoils. The existence of the buffet-cell mode is confirmed at flight Reynolds numbers. However, due to the presence of large SOB separation at the onset angle of attack, this mode is distributed along the whole wing and an SOB separation mode also appears. As well as characterizing buffet on industry-relevant geometries and flow conditions, this study proves that the proposed GSA framework is feasible for large 3D numerical grids and can represent a useful tool for buffet onset prediction during design and certification phases of commercial aircraft.

On Chaplygin models in f(G) gravity

This work treats cosmological perturbation in a mixture of standard matter, Chaplygin gas as well as Gauss–Bonnet fluids using a 1+3 covariant approach in the context of modified [Formula: see text] gravity. We define the gradient variables to obtain linear perturbation equations. After scalar and redshift transformations, we consider both an original Chaplygin and generalized Chaplygin gas models under Gauss–Bonnet gravity. For pedagogical purposes, the consideration of polynomial [Formula: see text] gravity model was used to solve the perturbation equations for short- and long-wavelength modes and investigate the late-time evolution. The numerical solutions were obtained. The results show that the energy overdensity perturbations decay with an increase in redshift. The treatment recovers GR results under limiting cases.

On 1 + 3 covariant perturbations of the quasi-Newtonian spacetime in modified Gauss–Bonnet gravity

The consideration of a [Formula: see text] covariant approach to cold dark matter universe with no shear cosmological dust model with irrotational flows is developed in the context of [Formula: see text] gravity theory in this study. This approach reveals the existence of integrability conditions which do not appear in noncovariant treatments. We constructed the integrability conditions in modified Gauss–Bonnet [Formula: see text] gravity basing on the constraints and propagation equations. These integrability conditions reveal the linearized silent nature of quasi-Newtonian models in [Formula: see text] gravity. Finally, the linear equations for the overdensity and velocity perturbations of the quasi-Newtonian spacetime were constructed in the context of modified [Formula: see text] gravity. The application of harmonic decomposition and redshift transformation techniques to explore the behavior of the overdensity and velocity perturbations using [Formula: see text] model was made. On the other hand, we applied the quasi-static approximation to study the approximated solutions on small scales which helps to get both analytical and numerical results of the perturbation equations. The analysis of the energy overdensity and velocity perturbations for both short- and long-wavelength modes in a dust-Gauss–Bonnet fluids was done and we see that both energy overdensity and velocity perturbations decay with redshift for both modes. In the limits to [Formula: see text]CDM, it means [Formula: see text] the considered [Formula: see text] model results coincide with [Formula: see text]CDM.

Curvature effect on the instabilities of lid-driven flow in a toroidal square cavity

The effect of curvature on the three-dimensional instabilities of lid-driven flow in a toroidal square cavity is numerically studied using the linear stability analysis based on the spectral element method. The critical stability curves are determined, and four types of instability modes are predicted. For small curvatures (δ ≤ 0.2), the most dangerous mode is a steady short-wavelength mode (λc ≈ 0.4), which is consistent with that in the straight square cavity. In a narrow range of 0.22 ≤ δ ≤ 0.28, the critical mode is oscillatory and of medium wavelength (0.84 < λc < 1.07). For δ ≥ 0.29, two types of steady long-wavelength modes (λc > 1.26) become the critical mode. The disturbance energy analyses show that all the instabilities are caused by the centrifugal instability mechanism.

On erosion transition from the incubation stage to the accumulation stage in liquid impingement erosion

The evolution of surface profiles during erosion caused by the continuous impact of a liquid jet was studied using a water-jet apparatus. In this study, we focused on the erosion transition from the incubation stage to the accumulation stage during liquid impingement erosion, which is important for water-jet cleaning and aging management for nuclear power plants. By computing the local erosion rate distribution and surface roughness parameters, the formations of isolated pits and asperities were investigated. The structure of erosion caused by liquid impingement was extracted by using a dynamic mode decomposition technique. The surface profile changes were primarily caused by the formation of isolated pits and asperities during the incubation stage. The roughness parameters remained unchanged during the incubation stage, with barely measurable erosion depth, whereas the skewness of the surface profile began to increase during this stage. The initial erosion with a small-scale roughness gradually evolved into a large-scale crater. Dynamic mode decomposition analysis showed the presence of a short-wavelength (mode A) surface depression during the incubation stage, followed by a long-wavelength (mode B) erosion crater caused by the merging of mode A surface depressions during the accumulation stage.

Mass renormalization in lattice simulations of false vacuum decay

False vacuum decay, a quantum mechanical first-order phase transition in scalar field theories, is an important phenomenon in early Universe cosmology. Recently, real-time semiclassical techniques based on ensembles of lattice simulations were applied to the problem of false vacuum decay. In this context, or any other lattice simulation, the effective potential experienced by long-wavelength modes is not the same as the bare potential. To make quantitative predictions using the real-time semiclassical techniques, it is therefore necessary to understand the redefinition of model parameters and the corresponding deformation of the vacuum state, as well as stochastic contributions that require modeling of unresolved subgrid modes. In this work, we focus on the former corrections and compute the expected modification of the true and false vacuum effective mass, which manifests as a modified dispersion relationship for linear fluctuations about the vacuum. We compare these theoretical predictions to numerical simulations and find excellent agreement. Motivated by this, we use the effective masses to fix the shape of a parametrized effective potential, and explore the modeling uncertainty associated with nonlinear corrections. We compute the decay rates in both the Euclidean and real-time formalisms, finding qualitative agreement in the dependence on the UV cutoff. These calculations further demonstrate that a quantitative understanding of the rates requires additional corrections.

Effect of spin-orbit coupling on the zero-point renormalization of the electronic band gap in cubic materials: First-principles calculations and generalized Fröhlich model

The electronic structure of semiconductors and insulators is affected by ionic motion through electron-phonon interaction, yielding temperature-dependent band gap energies and zero-point renormalization (ZPR) at absolute zero temperature. For polar materials, the most significant contribution to the band gap ZPR can be understood in terms of the Fr\"ohlich model, which focuses on the nonadiabatic interaction between an electron and the macroscopic electrical polarization created by a long-wavelength optical longitudinal phonon mode. On the other hand, spin-orbit interaction (SOC) modifies the bare electronic structure, which will, in turn, affect the electron-phonon interaction and the ZPR. We present a comparative investigation of the effect of SOC on the band gap ZPR of twenty semiconductors and insulators with cubic symmetry using first-principles calculations. We observe a SOC-induced decrease of the ZPR, up to 30%, driven by the valence band edge, which almost entirely originates from the modification of the bare electronic eigenenergies and the decrease of the hole effective masses near the $\mathrm{\ensuremath{\Gamma}}$ point. We also incorporate SOC into a generalized Fr\"ohlich model, addressing the Dresselhaus splitting which occurs in noncentrosymmetric materials, and confirm that the predominance of nonadiabatic effects on the band gap ZPR of polar materials is unchanged when including SOC. Our generalized Fr\"ohlich model with SOC provides a reliable estimate of the SOC-induced decrease of the polaron formation energy obtained from first principles and brings to light some fundamental subtleties in the numerical evaluation of the effective masses with SOC for noncentrosymmetric materials. We finally warn about a possible breakdown of the parabolic approximation, one of the most fundamental assumptions of the Fr\"ohlich model, within the physically relevant energy range of the Fr\"ohlich interaction for materials with high phonon frequencies treated with SOC.

Parametric investigation of azimuthal instabilities and electron transport in a radial-azimuthal E × B plasma configuration

Partially magnetized low-temperature plasmas (LTP) in an E × B configuration, where the applied magnetic field is perpendicular to the self-consistent electric field, have become increasingly relevant in industrial applications. Hall thrusters, a type of electrostatic plasma propulsion, are one of the main LTP technologies whose advancement is hindered by the not-fully-understood underlying physics of operation, particularly, with respect to the plasma instabilities and the associated electron cross field transport. The development of Hall thrusters with unconventional magnetic field topologies has imposed further questions regarding the instabilities' characteristics and the electrons' dynamics in these modern cross field configurations. Accordingly, we present in this effort a detailed parametric study of the influence of three factors on the plasma processes in the radial-azimuthal coordinates of a Hall thruster, namely, the magnetic field gradient, secondary electron emission, and plasma number density. The studies are carried out using the reduced-order particle-in-cell code developed by the authors. The setup of the radial-azimuthal simulations largely follows a well-defined benchmark case from the literature in which the magnetic field is oriented along the radius, and a constant axial electric field is applied perpendicular to the simulation plane. The salient finding from our investigations is that, in the studied cases corresponding to elevated plasma densities, a long-wavelength azimuthal mode with the frequency of about 1 MHz is developed. Moreover, in the presence of strong magnetic field gradients, this mode results from an inverse energy cascade and induces a significant electron cross field transport as well as a notable heating of the ions.

Nonlocal corrections to dynamical mean-field theory from the two-particle self-consistent method

Theoretical methods that are accurate for both short-distance observables and long-wavelength collective modes are still being developed for the Hubbard model. Here, we benchmark an approach that combines dynamical mean-field theory (DMFT) observables with the two-particle self-consistent theory (TPSC). This offers a way to include non-local correlations in DMFT while also improving TPSC. The benchmarks are published diagrammatic quantum Monte Carlo results for the two-dimensional square lattice Hubbard model with nearest-neighbor hopping. This method (TPSC+DMFT) is relevant for weak to intermediate interaction, satisfies the local Pauli principle and allows us to compute a spin susceptibility that satisfies the Mermin-Wagner theorem. The DMFT double occupancy determines the spin and charge vertices through local spin and charge sum rules. The TPSC self-energy is also improved by replacing its local part with the local DMFT self-energy. With this method, we find improvements for both spin and charge fluctuations and for the self-energy. We also find that the accuracy check developed for TPSC is a good predictor of deviations from benchmarks for this model. TPSC+DMFT can be used in regimes where quantum Monte Carlo is inaccessible. In addition, this method paves the way to multi-band generalizations of TPSC that could be used in advanced electronic structure codes that include DMFT.

Overstable Convective Modes in a Polytropic Stellar Atmosphere

Within the convection zone of a rotating star, the presence of the Coriolis force stabilizes long-wavelength convective modes. These modes, which would have been unstable if the star lacked rotation, are called overstable convective modes or thermal Rossby waves. We demonstrate that the Sun’s rotation rate is sufficiently rapid that the lower half of its convection zone could possess overstable modes. Further, we present an analytic solution for atmospheric waves that reside within a polytropic stratification. We explore in detail the properties of the overstable and unstable wave modes that exist when the polytrope is weakly unstable to convective overturning. Finally, we discuss how the thermal Rossby waves that reside within the convection zone of a star might couple with the prograde branch of the g modes that are trapped within the star’s radiative zone. We suggest that such coupling might enhance the photospheric visibility of a subset of the Sun’s g modes.