Nonlinear Self-interaction Research Articles

Foundry manufacturing of octave-spanning microcombs.

Soliton microcombs provide a chip-based, octave-spanning source for self-referencing and optical metrology. We use a silicon nitride integrated photonics foundry to manufacture 280 single-chip solutions of octave-spanning microcombs on a wafer. By group-velocity dispersion (GVD) engineering with the waveguide cross section, we shape the soliton spectrum for dispersive-wave spectral enhancements at the frequencies for f-2f self-referencing. Moreover, we demonstrate the other considerations, including models for soliton spectrum design, ultra-broadband resonator external coupling, low-loss edge couplers, and the nonlinear self-interactions of few-cycle solitons. To cover the fabrication tolerance, we systematically scan 336 parameter sets of resonator width and radius, ensuring at least one device on each chip can yield an octave-spanning comb with an electronically detectable carrier-envelope offset frequency, which has been supported by our experiment. Our design and testing process permit highly repeatable creation of single-chip solutions of soliton microcombs optimized for pump operation ∼100 mW and high comb mode power for f-2f detection, which is the central component of a compact microsystem for optical metrology.

Nonlinear self-interaction induced black hole bomb

Nonlinear self-interaction induced black hole bomb

Relativistic description of dense matter equation of state and neutron star observables constrained by recent astrophysical observations

In the present work, we investigate the bulk properties of nuclear matter and neutron stars with the newly proposed relativistic interaction NL-RS which provides an opportunity to readjust the coupling constants keeping in view the properties of finite nuclei, nuclear matter, PREX-II results for neutron skin thickness in 208Pb and astrophysical observations. The NL-RS model interaction has been proposed by fitting the ground state properties (binding energies and charge radii) of finite nuclei, bulk nuclear matter properties, and PREX-II results for neutron skin thickness of 208Pb. The relativistic interaction has been generated by including nonlinear self-interactions of σ and ω μ -mesons and mixed interactions of ω μ , and ρ μ -meson up to the quartic order. The proposed interaction harmonizes with the finite nuclei, bulk nuclear matter, and neutron star properties. A covariance analysis is performed to assess the statistical uncertainties on the model parameters and nuclear observables of interest along with correlations amongst them. The equation of state (EoS) composed of nucleons and leptons in β-equilibrium is computed with the proposed parameter set and used to study the neutron star structure. The maximum mass of the neutron star by employing the EoS computed with the NL-RS parameter set is 2.04 ± 0.03M ⊙ and the radius of a canonical mass neutron star (R 1.4) comes out to be equal to 13.06 ± 0.16 Km. The value of dimensionless tidal deformability, for canonical mass, is 602.23 ± 33.13 which satisfies the constraints of waveform models analysis of GW170817 within 90% confidence level.

Theory of Nonlinear Diffusion with a Physical Gapped Mode.

In a system with one conserved charge the charge diffusion is modified by nonlinear self-interactions within an effective field theory (EFT) of diffusive fluctuations. We include the slowest ultraviolet (UV) mode, constructing a UV-regulated EFT. The relaxation time of this UV mode is protected from renormalization, as supported by experimental data in a bad metal system. Furthermore, the retarded density-density Green's function acquires four branch points, eventually increasing the range of applicability. We discuss the fate of long time tails as well as implications for the quark gluon plasma.

Linear instability and weakly nonlinear effects in eastward dipoles

The linear instability and weakly nonlinear dynamics of eastward-propagating, steady-state Larichev–Reznik vortex dipoles are explored in terms of two-dimensional normal-mode analysis. To extract the fastest growing normal modes, we apply both breeding methodology based on solving the initial-value problem, as well as a direct-solution approach through the full-spectrum eigenproblem involving large matrices. We find that the amplification rate of dipole instability decreases with respect to increase in dipole intensity. In our study, both approaches yield consistent results and are systematically compared to provide guidance for further studies of vortex structures.We consider nonlinear self-interaction of the fastest growing mode, along with the induced eddy fluxes, their divergence and mechanical energy balance. Through this analysis, we find that the unstable mode leads to weakening of the dipole by extracting its energy and exchanging potential vorticity content in the down-gradient sense, thus, providing a nonlinear physical mechanism for the dipole destruction. In particular, we highlight the fundamental importance of the west-east asymmetry of the normal mode for destruction to be realized. In summary, we consider this work to be a foundational demonstration of useful methodology for future studies of dynamics and stability of isolated vortices without simplifying spatial symmetries, such as ubiquitous vortices in geophysical fluids.

Data-driven scale identification in oscillatory dynamos

ABSTRACT Parker’s mean-field model includes two processes generating large-scale oscillatory dynamo waves: stretching of magnetic field lines by small-scale helical flows and by differential rotation. In this work, we investigate the capacity of data-driven modal analysis, dynamic mode decomposition (DMD), to identify coherent magnetic field structures of this model. In its canonical form, the only existing field scale corresponds to the dynamo instability. To take into account multiscale nature of the dynamo, the model was augmented with coherent in time flow field, forcing small-scale magnetic field with a faster temporal evolution. Two clusters of DMD modes were obtained: the ‘slow’ cluster, located near the dynamo wave frequency and associated with its non-linear self-interaction, and the ‘fast’ cluster, centred around the forcing frequency and resulting from the interaction between the wave and the flow. Compared to other widely used methods of data analysis, such as Fourier transform, DMD provides a natural spatiotemporal basis for the dynamo, related to its non-linear dynamics. We assess how the parameters of the DMD model, rank, and delay, influence its accuracy, and finally discuss the limitations of this approach when applied to randomly forced, more complex dynamo flows.

Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction

Low Reynolds number turbulence in wall-bounded shear flows en route to laminar flow takes the form of spatially intermittent turbulent structures. In plane shear flows, these appear as a regular pattern of alternating turbulent and quasi-laminar flow. Both the physical and the spectral energy balance of a turbulent–laminar pattern in plane Couette flow are computed and compared to those of uniform turbulence. In the patterned state, the mean flow is strongly modulated and is fuelled by two mechanisms: primarily, the nonlinear self-interaction of the mean flow (via mean advection), and secondly, the extraction of energy from turbulent fluctuations (via negative spectral production, associated with an energy transfer from small to large scales). Negative production at large scales is also found in the uniformly turbulent state. Important features of the energy budgets are surveyed as a function of$Re$through the transition between uniform turbulence and turbulent–laminar patterns.

Adiabaticity in nonreciprocal Landau-Zener tunneling

We investigate the Landau-Zener tunneling (LZT) of a self-interacting two-level system in which the coupling between the levels is nonreciprocal. In such a non-Hermitian system, when the energy bias between two levels is adjusted very slowly, i.e., in the adiabatic limit, we find that a quantum state can still closely follow the eigenstate solution until it encounters the exceptional points (EPs) at which two eigenvalues and their corresponding eigenvectors coalesce. In the absence of the nonlinear self-interaction, we can obtain explicit expressions for the eigenvectors and eigenvalues and analytically derive the adiabatic LZT probability from invariants at EPs. In the presence of the nonlinear interaction, the dynamics of the adiabatic evolutions are explicitly demonstrated with the help of classical trajectories in the plane of the two canonical variables of the corresponding classical Josephson Hamiltonian. We show that the adiabatic tunneling probabilities can be precisely predicted by the classical action at EPs in the weak nonreciprocal regime. In a certain region of strong nonreciprocity, we find that interestingly, the nonlinear interaction effects can be completely suppressed so that the adiabatic tunneling probabilities are identical to their linear counterparts. We also obtain a phase diagram for large ranges of nonreciprocity and nonlinear interaction parameters to explicitly demonstrate where the adiabaticity can break down, i.e., the emergence of the nonzero tunneling probabilities even in adiabatic limit.

Nonlinear excitation of zonal flows by turbulent energy flux.

The nonlinear excitation of zonal flows (ZFs) generated by the ion-temperature-gradient turbulence in a tokamak plasma is investigated by using the global gyrokinetic code nlt. It is found that ZFs are initially driven by the nonlinear self-interaction of the eigenmode. In the nonlinear saturation, the modulational instability becomes important, and its contribution to ZFs can finally be comparable to that of the self-interaction mechanism. More importantly, both types of nonlinear wave-wave interactions can be well described by the turbulent energy flux model.

Kaon–baryon coupling schemes and kaon condensation in hyperon-mixed matter

Abstract The possible coexistence of kaon condensation and hyperons in highly dense matter [the (Y + K) phase] is investigated on the basis of the relativistic mean-field theory combined with the effective chiral Lagrangian. Two coupling schemes for the s-wave kaon–baryon interaction are compared regarding the onset density of kaon condensation in hyperon-mixed matter and the equation of state for the developed (Y + K) phase. One is the contact interaction scheme related to the nonlinear effective chiral Lagrangian. The other is the meson exchange scheme, where the interaction vertices between the kaon field and baryons are described by an exchange of mesons (σ, σ* mesons for scalar coupling, and ω, ρ, ϕ mesons for vector coupling). It is shown that in the meson exchange scheme, the contribution from the nonlinear scalar self-interaction gives rise to a repulsive effect for the kaon effective energy, pushing up the onset density of kaon condensation as compared with the contact interaction scheme. In general, the difference in kaon–baryon dynamics between the contact interaction scheme and the meson exchange scheme relies on the specific forms of the nonlinear self-interacting meson terms. They generate many-baryon forces through the equations of motion for the meson mean fields. However, they should have a definite effect on the ground state properties of nuclear matter only around the saturation density. It is shown that the nonlinear self-interacting term is not relevant to repulsive energy leading to stiffening of the equation of state at high densities, and that it cannot be compensated with a large attractive energy due to the appearance of the (Y + K) phase in the case of the contact interaction scheme. We also discuss what effects are necessary in the contact interaction scheme to make the equation of state with (Y + K) phase stiff enough to be consistent with recent observations of massive neutron stars.

Unifying the Sørensen-Mølmer gate and the Milburn gate with an optomechanical example

The S\o{}rensen-M\o{}lmer gate and Milburn gate are two geometric phase gates, generating nonlinear self-interaction of a target mode via its interaction with an auxiliary mechanical mode, in the continuous- and pulsed-interaction regimes, respectively. In this paper we aim at unifying the two gates by demonstrating that the S\o{}rensen-M\o{}lmer gate is the continuous limit of the Milburn gate, emphasizing the geometrical interpretation in the mechanical phase space. We explicitly consider imperfect gate parameters, focusing on relative errors in time for the S\o{}rensen-M\o{}lmer gate and in phase angle increment for the Milburn gate. We find that, although the purities of the final states increase for the two gates upon reducing the interaction strength together with traversing the mechanical phase space multiple times, the fidelities behave differently. We point out that the difference exists because the interaction strength depends on the relative error when taking the continuous limit from the pulsed regime, thereby unifying the mathematical framework of the two gates. We demonstrate this unification in the example of an optomechanical system, where mechanical dissipation is also considered. We highlight that the unified framework facilitates our method of deriving the dynamics of the continuous-interaction regime without solving differential equations.

Resonant Interactions and Chaotic Excitation in Nonlinear Surface Waves in Dense Plasma

By employing a quantum hydrodynamic (QHD) model with appropriate boundary conditions, the nonlinear self-interaction of an electrostatic surface wave on otherwise homogeneous semibounded plasma with degeneracy effects is investigated. It has been found that a part of the second harmonic generated through self-interaction does not have a true surface wave feature but propagates obliquely away from the plasma–vacuum interface into the bulk of the plasma. Such a situation is obtained in laser–plasma interaction during surface etching, plasma processing, and so on. In this article, we study the harmonics generation mechanism, associated Lagrangian chaos, and harmonic conversation rate when an intense laser is incident on an unmagnetized plasma. The dense plasma displays quantum diffraction effects and other quantum statistical effects. We made use of perturbative analysis for the field quantities. The findings will help workers dealing with laser–plasma interaction so as to enhance the tendency of harmonic generation and energy localization.

Thermal perturbations from cosmological constant relaxation

We probe the cosmological consequences of a recently proposed class of solutions to the cosmological constant problem. In these models, the universe undergoes a long period of inflation followed by a contraction and a bounce that sets the stage for the hot big bang era. A requirement of any successful early universe model is that it must reproduce the observed scale-invariant density perturbations at CMB scales. While these class of models involve a long period of inflation, the inflationary Hubble scale during their observationally relevant stages is at or below the current Hubble scale, rendering the de Sitter fluctuations too weak to seed the CMB anisotropies. We show that sufficiently strong perturbations can still be sourced thermally if the relaxion field serving as the inflaton interacts with a thermal bath, which can be generated and maintained by the same interaction. We present a simple model where the relaxion field is derivatively (i.e. technically naturally) coupled to a non-abelian gauge sector, which gets excited tachyonically and subsequently thermalizes due to its nonlinear self-interactions. This model explains both the smallness of the cosmological constant and the amplitude of CMB anisotropies.

Chiral quark-meson coupling models for finite nuclei and their (e,e′p) reactions

The chiral quark-meson coupling (CQMC) models are applied to revisiting static properties of spherical nuclei in comparison with the results from the conventional quantum hadrodynamics (QHD)-like models as well as the available experimental data. They are also used to describe the nuclei off which the electrons scatter to understand their dynamic properties. After calibrating the model parameters at equilibrium nuclear matter density, binding energies, charge radii, single-particle spectra, and density distributions of the nuclei are analyzed and compared. The nonlinear scalar self-interaction in each model is also discussed in consideration of the reproduction of nuclear saturation properties.

Rotating boson stars using finite differences and global Newton methods

We study rotating boson star data for numerical relativity using a 3 + 1 decomposition adapted to a curvilinear axisymmetric spacetime with regularization at the rotation axis. The Einstein–Klein–Gordon equations result in a system of six coupled, elliptic, nonlinear equations with an added unknown for the scalar field’s frequency ω. Utilizing a Cartesian two-dimensional grid, fourth-order finite differences, and global Newton methods, we generated seven data sets characterized by a rotation azimuthal integer l ∈ [0, 6]. Our numerical implementation is shown to correctly converge both with respect to the resolution size and boundary extension. Thus, global parameters such as the Komar masses and angular momenta can be precisely calculated to characterize these spacetimes. Furthermore, analyzing each family at fixed rotation integer l produces maximum masses and minimum rotation frequencies. Our results coincide with previous results in literature for l ∈ [0, 2] [as in references (Yoshida and Eriguchi 1997 Phys. Rev. D 56 6370; Lai 2004 PhD Thesis; Grandclément, et al 2014 Phys. Rev. D 90 024068; Liebling and Palenzuela 2017 Living Rev. Relativ. 20)], and are new for l > 2. In particular, the study of high-amplitude and localized scalar fields in axial symmetry is revealed to be only possible by adding the sixth regularization variable, thus reaffirming previous work on the importance of regularization in curvilinear-based numerical relativity. These results also provide the groundwork for extending this research to other self-gravitating systems, such as rotating boson stars with nonlinear self-interactions, or the case of massive vector fields.

Experimental generation of axisymmetric internal wave super-harmonics

In this paper, we present an experimental study of weakly non-linear interaction of axisymmetric internal gravity waves in a resonant cavity, supported by theoretical considerations. Contrary to plane waves in Cartesian coordinates, for which self-interacting terms are null in a linear stratifiation, the non-linear self-interaction of an internal wave mode in axisymmetric geometry is found to be efficient at producing super-harmonics, i.e. waves whose frequencies are integer multiples of the excitation frequency. Due to the range of frequencies tested in our experiments, the first harmonic frequency is below the cut-off imposed by the stratification so the lowest harmonic created can always propagate. The study shows that the super-harmonic wave field is a sum of standing waves satisfying both the dispersion relation for internal waves and the boundary conditions imposed by the cavity walls, while conserving the axisymmetry.

Intermittency of three-dimensional perturbations in a point-vortex model.

Three-dimensional (3D) instabilities on a (potentially turbulent) two-dimensional (2D) flow are still incompletely understood, despite recent progress. Here, based on known physical properties of such 3D instabilities, we propose a simple, energy-conserving model describing this situation. It consists of a regularized 2D point-vortex flow coupled to localized 3D perturbations ("ergophages"), such that ergophages can gain energy by altering vortex-vortex distances through an induced divergent velocity field, thus decreasing point-vortex energy. We investigate the model in three distinct stages of evolution: (i) The linear regime, where the amplitude of the ergophages grows or decays exponentially on average, with an instantaneous growth rate that fluctuates randomly in time. The instantaneous growth rate has a small auto-correlation time, and a probability distribution featuring a power-law tail with exponent between -2 and -5/3 (up to a cutoff) depending on the point-vortex base flow. Consequently, the logarithm of the ergophage amplitude performs a Lévy flight. (ii) The passive-nonlinear regime of the model, where the 2D flow evolves independently of the ergophage amplitudes, which saturate by non-linear self-interactions without affecting the 2D flow. In this regime the system exhibits a new type of on-off intermittency that we name Lévy on-off intermittency, which we define and study in a companion paper [van Kan et al., Phys. Rev. E 103, 052115 (2021)1063-651X10.1103/PhysRevE.103.052115]. We compute the bifurcation diagram for the mean and variance of the perturbation amplitude, as well as the probability density of the perturbation amplitude. (iii) Finally, we characterize the fully nonlinear regime, where ergophages feed back on the 2D flow, and study how the vortex temperature is altered by the interaction with ergophages. It is shown that when the amplitude of the ergophages is sufficiently large, the condensate is disrupted and the 2D flow saturates to a zero-temperature state. Given the limitations of existing theories, our model provides a new perspective on 3D instabilities growing on 2D flows, which will be useful in analyzing and understanding the much more complex results of DNS and potentially guide further theoretical developments.

φenics: Vainshtein screening with the finite element method

Within the landscape of modified theories of gravity, progress in understanding the behaviour of, and developing tests for, screening mechanisms has been hindered by the complexity of the field equations involved, which are nonlinear in nature and characterised by a large hierarchy of scales. This is especially true of Vainshtein screening, where the fifth force is suppressed by high-order derivative terms which dominate within a radius much larger than the size of the source, known as the Vainshtein radius.=-1In this work, we present the numerical code φenics, building on the FEniCS library, to solve the full equations of motion from two theories of interest for screening: a model containing high-order derivative operators in the equation of motion and one characterised by nonlinear self-interactions in two coupled scalar fields. We also include functionalities that allow the computation of higher-order operators of the scalar fields in post-processing, enabling us to check that the profiles we find are consistent solutions within the effective field theory. These two examples illustrate the different challenges experienced when trying to simulate such theories numerically, and we show how these are addressed within this code. The examples in this paper assume spherical symmetry, but the techniques may be straightforwardly generalised to asymmetric configurations. This article therefore also provides a worked example of how the finite element method can be employed to solve the screened equations of motion. φenics is publicly available and can be adapted to solve other theories of screening.

Stability of rotating scalar boson stars with nonlinear interactions

We study the stability of rotating scalar boson stars, comparing those made from a simple massive complex scalar (referred to as mini boson stars), to those with several different types of nonlinear interactions. To that end, we numerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D, beginning with stationary boson star solutions. We show that the linear, non-axisymmetric instability found in mini boson stars with azimuthal number $m=1$ persists across the entire parameter space for these stars, though the timescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$ that is sufficiently far into the non-relativistic regime, where the leading order mass term dominates, will be unstable, independent of the nonlinear scalar self-interactions. However, we do find regions of $m=1$ boson star parameter space where adding nonlinear interactions to the scalar potential quenches the non-axisymmetric instability, both on the non-relativistic, and the relativistic branches of solutions. We also consider select boson stars with $m=2$, finding instability in all cases. For the cases exhibiting instability, we follow the nonlinear development, finding a range of dynamics including fragmentation into multiple unbound non-rotating stars, and formation of binary black holes. Finally, we comment on the relationship between stability and criteria based on the rotating boson star's frequency in relation to that of a spherical boson star or the existence of a co-rotation point. The boson stars that we find not to exhibit instability when evolved for many dynamical times include rapidly rotating cases where the compactness is comparable to that of a black hole or neutron star.

Interaction of waves in one-dimensional dusty gas flow

Abstract The present study uses the theory of weakly nonlinear geometrical acoustics to derive the high-frequency small amplitude asymptotic solution of the one-dimensional quasilinear hyperbolic system of partial differential equations characterizing compressible, unsteady flow with generalized geometry in ideal gas flow with dust particles. The method of multiple time scales is applied to derive the transport equations for the amplitude of resonantly interacting high-frequency waves in a dusty gas. These transport equations are used for the qualitative analysis of nonlinear wave interaction process and self-interaction of nonlinear waves which exist in the system under study. Further, the evolutionary behavior of weak shock waves propagating in ideal gas flow with dust particles is examined here. The progressive wave nature of nonresonant waves terminating into the shock wave and its location is also studied. Further, we analyze the effect of the small solid particles on the propagation of shock wave.