Nonlinear Realization Research Articles

Gravity, dual gravity and A1+++

We construct the nonlinear realisation of the semidirect product of the very extended algebra [Formula: see text] and its vector representation. This theory has an infinite number of fields that depend on a space–time with an infinite number of coordinates. Discarding all except the lowest level field and coordinates the dynamics is just Einstein’s equation for the graviton field. We show that the gravity field is related to the dual graviton field by a duality relation and we also derive the equation of motion for the dual gravity field.

Experimental realization of arbitrary activation functions for optical neural networks.

We experimentally demonstrate an on-chip electro-optic circuit for realizing arbitrary nonlinear activation functions for optical neural networks (ONNs). The circuit operates by converting a small portion of the input optical signal into an electrical signal and modulating the intensity of the remaining optical signal. Electrical signal processing allows the activation function circuit to realize any optical-to-optical nonlinearity that does not require amplification. Such line shapes are not constrained to those of conventional optical nonlinearities. Through numerical simulations, we demonstrate that the activation function improves the performance of an ONN on the MNIST image classification task. Moreover, the activation circuit allows for the realization of nonlinearities with far lower optical signal attenuation, paving the way for much deeper ONNs.

Nonlinear Dynamics, Switching Kinetics and Physical Realization of the Family of Chua Corsage Memristors

This article reviews the nonlinear dynamical attributes, switching kinetics, bifurcation analysis, and physical realization of a family of generic memristors, namely, Chua corsage memristors (CCM). CCM family contains three 1-st order generic memristor dubbed as 2-lobe, 4-lobe, and 6-lobe Chua corsage memristors and can be distinguished in accordance with their asymptotic stable states. The 2-lobe CCM has two asymptotically stable equilibrium states and regarded as a binary memory device. In contrast, the versatile 4-lobe CCM and 6-lobe CCM are regarded as a multi-bit-per-cell memory device as they exhibit three and four asymptotic stable states, respectively, on their complex and diversified dynamic routes. Due to the diversified dynamic routes, the CC memristors exhibit a highly nonlinear DC V-I curve. Unlike most published highly-nonlinear DC V-I curves with several disconnected branches, the DC V-I curves of CCMs are contiguous along with a locally active negative slope region. Moreover, the DC V-I curves and parametric representations of the CCMs are explicitly analytical. Switching kinetics of the CCM family can be demonstrated with universal formulas of exponential state trajectories xn(t), time period tfn, and applied minimum pulse amplitude VA and width Δw. These formulas are regarded universal as they can be applied to any piecewise linear dynamic routes for any DC or pulse input and with any number of segments. When local activity, and bifurcation and chaos theorems are employed, CMMs exhibit unique stable limit cycles spawn from a supercritical Hopf bifurcation along with static attractors. In addition, the nonlinear circuit and system theoretic approach is applied to explain the asymptotic stability behavior of CCMs and to design real memristor emulators using off-the-shelf circuit components.

Complete theory of Maxwell and Proca fields

We present the most general ghost-free classical Lagrangian containing first-order derivatives and describing interacting real Abelian spin-one fields on Minkowski spacetime. We study both massive Proca and massless Maxwell fields and allow for a non-linear realization of mass, in the form of derivative self-interactions. Within this context, our construction notoriously extends the existing literature, which is limited to the case of a single Proca field and to multiple interacting Proca fields in the presence of a global rotational symmetry. In the limit of a single Proca field, we reproduce the known healthy interaction terms. We provide the necessary and sufficient conditions to ensure ghost-freedom in any multi-field setup. We observe that, in general, the said conditions are not satisfied by the rotationally symmetric multi-Proca interactions suggested so far, which implies that they propagate ghosts. Our theory admits a plethora of applications in a wide range of subjects. For illustrative purposes, we provide concrete proposals in holographic condensed matter and black hole physics.

Maxwell-Proca theory: Definition and construction

We present a systematic construction of the most general first order Lagrangian describing an arbitrary number of interacting Maxwell and Proca fields on Minkowski spacetime. To this aim, we first formalize the notion of a Proca field, in analogy to the well known Maxwell field. Our definition allows for a non-linear realization of the Proca mass, in the form of derivative self-interactions. Consequently, we consider so-called generalized Proca/vector Galileons. We explicitly demonstrate the ghost-freedom of this complete Maxwell-Proca theory by obtaining its constraint algebra. We find that, when multiple Proca fields are present, their interactions must fulfill non-trivial differential relations in order to ensure the propagation of the correct number of degrees of freedom. These relations had so far been overlooked, which means previous multi-Proca proposals generically contain ghosts. This is a companion paper to arXiv:1905.06968 [hep-th]. It puts on a solid footing the theory there introduced.

Extending Complex Conjugate Control to Nonlinear Wave Energy Converters

This paper extends the concept of Complex Conjugate Control (CCC) of linear wave energy converters (WECs) to nonlinear WECs by designing optimal limit cycles with Hamiltonian Surface Shaping and Power Flow Control (HSSPFC). It will be shown that CCC for a regular wave is equivalent to a power factor of one in electrical power networks, equivalent to mechanical resonance in a mass-spring-damper (MSD) system, and equivalent to a linear limit cycle constrained to a Hamiltonian surface defined in HSSPFC. Specifically, the optimal linear limit cycle is defined as a second-order center in the phase plane projection of the constant energy orbit across the Hamiltonian surface. This concept of CCC described by a linear limit cycle constrained to a Hamiltonian surface will be extended to nonlinear limit cycles constrained to a Hamiltonian surface for maximum energy harvesting by the nonlinear WEC. The case studies presented confirm increased energy harvesting which utilizes nonlinear geometry realization for reactive power generation.

Gravity and Nonlinear Symmetry Realization

Application of nonlinear symmetry realization technique to gravity is studied. We identify the simplest extensions of the Poincare group suitable for nonlinear realization at the level of physical fields. Two simple models are proposed. The first one introduces additional scalar degrees of freedom that may be suitable for driving inflation. The second one describes states with well-defined mass that lack a linear interaction with matter states. We argue that this phenomenon points out a necessity to draw a distinction between gravitational states with well-defined masses and states that participate in interaction with matter.

Construction principle of NES shock absorber and its application in frame structure

PurposeThe purpose of this paper is to describe the structure of nonlinear dampers and the dynamic equations, and nonlinear realization principles and optimize the parameters of nonlinear dampers. Using the finite element method to analyze the seismic performance of the frame structure with shock absorber.Design/methodology/approachThe nonlinear shock absorber was installed in a six-storey reinforced concrete frame structure to study its seismic performance. The main structure was designed according to the eight degree seismic fortification intensity, and the time history dynamic analysis was carried out by Abaqus finite element software. EL-Centro, Taft and Wenchuan seismic record were selected to analyze the seismic response of the structure under different magnitudes and different acceleration peaks.FindingsThrough the principle study and parameter analysis of the nonlinear shock absorber, combined with the finite element simulation results, the shock absorption performance and shock absorption effect of the nonlinear energy sink (NES) nonlinear shock absorber are given as follows: first, the damping of the NES shock absorber is satisfied, and the linear spring stiffness and nonlinear stiffness of the shock absorber are based on the relationship k1=kn×kl2, so that the spring design length is fixed, and the linear stiffness of the shock absorber can be obtained. The nonlinear shock absorber has the characteristics of high rigidity and frequency bandwidth, so that the frequency is infinitely close to the frequency of the main structure, and when the mass of the shock absorber satisfies between 0.056 and 1, a good shock absorption effect can be obtained, and the reinforced concrete with the shock absorber is obtained. The frame structure can effectively reduce the seismic response, increase the natural vibration period of the structure and reduce the damage loss of the structure. Second, the spacer and each additional shock absorber have a small difference in shock absorption effect. After the shock absorber parameters are accurately calculated, the number of installations does not affect the shock absorption effect of the structure. Therefore, the shock absorber is properly constructed and accurately calculated. Parameters can reduce costs.Originality/valueNew shock absorbers reduce earthquake-induced damage to buildings.

Is Higgsium a possibility in 2HDMs?

We investigate the possibility of a Higgs-Higgs bound state in the two Higgs doublet model. Specifically we look for the effect of dimension six operators, generated by new physics at a scale of a few TeV, on the self-couplings of the heavy CP even scalar field in the model. Following the pioneering work of Grinstein and Trott [1], we construct an effective field theory formalism to examine the physics of the Higgs sector. The magnitudes of the attractive and repulsive coupling strengths are compared to estimate the possibility of the formation of the H−H bound state. Another way to check if a bound state is formed or not is from the formation and decay times of the bound state. The possibilities in various types of two Higgs doublet models have been discussed elaborately in the paper. The bound state energy has been evaluated and the allowed parameter space has been studied in the linear and non-linear realizations.

Finite-dimensional pair coherent state engendered via the nonlinear Bose operator realization and its Wigner phase-space distributions

We theoretically analyze the photon number distribution, entanglement entropy, and Wigner phase-space distribution, considering the finite-dimensional pair coherent state (FDPCS) generated in the nonlinear Bose operator realization. Our results show that the photon number distribution is governed by the two-mode photon number sum q of the FDPCS, the entanglement of the FDPCS always increases quickly at first and then decreases slowly for any q, and the nonclassicality of the FDPCS for odd q is more stronger than that for even q.

An algebraic classification of exceptional EFTs. Part II. Supersymmetry

We present a novel approach to classify supersymmetric effective field theories (EFTs) whose scattering amplitudes exhibit enhanced soft limits. These enhancements arise due to non-linearly realised symmetries on the Goldstone modes of such EFTs and we classify the algebras that these symmetries can form. Our main focus is on so-called exceptional algebras which lead to field-dependent transformation rules and EFTs with the maximum possible soft enhancement at a given derivative power counting. We adapt existing techniques for Poincaré invariant theories to the supersymmetric case, and introduce superspace inverse Higgs constraints as a method of reducing the number of Goldstone modes while maintaining all symmetries. Restricting to the case of a single Goldstone supermultiplet in four dimensions, we classify the exceptional algebras and EFTs for a chiral, Maxwell or real linear supermultiplet. Moreover, we show how our algebraic approach allows one to read off the soft weights of the different component fields from superspace inverse Higgs trees, which are the algebraic cousin of the on-shell soft data one provides to soft bootstrap EFTs using on-shell recursion. Our Lie-superalgebraic approach extends the results of on-shell methods and provides a complementary perspective on non-linear realisations.

E theory in seven dimensions

We construct the nonlinear realisation of the semi-direct product of [Formula: see text] and its vector representation in its decomposition into the subalgebra [Formula: see text] to find a seven-dimensional theory. The resulting equations of motion essentially follow from the Dynkin diagram of [Formula: see text] and if one restricts them to contain only the usual fields of supergravity and the derivatives with respect to the usual coordinates of space–time then these are the equations of motion of seven-dimensional supergravity.

Affine-Goldstone/Quartet-Metric Gravity and Beyond

As a group-theoretic foundation of gravity, it is considered an affine-Goldstone nonlinear model based upon the nonlinear realization of the global affine symmetry spontaneously broken at the Planck scale to the Poincare symmetry. It is shown that below this scale the model justifies and elaborates an earlier introduced effective field theory of the quartet-metric gravity incorporating the gravitational dark substances emerging in addition to the tensor graviton. The prospects for subsequent going beyond the nonlinear model above the Planck scale are indicated.

A general model for taper coupling of multiple modes of whispering gallery resonators and application to analysis of coupling-induced Fano interference in a single cavity.

In this paper, we give a general model for analysis of multimode Whispering Gallery Mode (WGM) resonators coupled to multimode tapered fibers based on the coupled-mode theory. Such formulation takes into account the asymmetry of the taper-resonator coupling. Simulations for a microsphere show that the tapered fiber coupling mechanism induces cross-coupling between coherent orthonormal WGMs. We show that the degree of such cross-coupling depends basically on the fiber diameter, air-gap between the taper and resonator, intrinsic losses and eccentricity. The WGM cross-coupling affects the total transmission and spectral line-shape of the internal powers resulting in a controllable transformation of the line-shape to non-Lorentzian spectra. This analysis can be utilized to precisely determine the output and intra-cavity intensity of multimode microresonators, which is important in lasers, nonlinear optical signal generation and realization of optical delays.

Component d = 6 Born-Infeld theory with N = (2, 0) \u2192 N = (1, 0) supersymmetry breaking

The formalism of nonlinear realizations is used to construct a theory with 1/2 partial breaking of global supersymmetry with the N = (1, 0), d = 6 abelian vector multiplet as a Goldstone superfield. Much like the case of the N = 2, d = 4 Born-Infeld theory, proper irreducibility conditions of the multiplet are selected by the invariance with respect to the external automorphisms of the Poincaré superalgebra. They are found in the lowest nontrivial order in the auxiliary field. The fermionic contributions to the Bianchi identity are restored by assuming its covariance with respect to broken supersymmetry. The invariance of the action with respect to unbroken supersymmetry is checked in the lowest order in the fermionic fields. The supersymmetry preserving reduction of the d = 6 action to four dimensions is performed, resulting in the N = 4, d = 4 Born-Infeld theory. As expected, the reduced action enjoys U(1) self-duality.

Minimal positive continuous-time realizations of positive response maps

Positive nonlinear continuous-time local realizations of positive response maps are studied. The realizations are minimal if they are positively reachable and positively observable. Necessary and sufficient conditions for a response map to have a minimal positive local realization are provided. It is also shown that a minimal positive local realization has the minimal dimension among all positive local realizations of the given response map and that it is unique up to an isomorphism of systems.

Schwarzian mechanics via nonlinear realizations

The method of nonlinear realizations is used to clarify some conceptual and technical issues related to the Schwarzian mechanics. It is shown that the Schwarzian derivative arises naturally, if one applies the method to SL(2,R)×R group and decides to keep the number of the independent Goldstone fields to a minimum. The Schwarzian derivative is linked to the invariant Maurer–Cartan one–forms, which make its SL(2,R)–invariance manifest. A Lagrangian formulation for a variant of the Schwarzian mechanics studied recently in A. Galajinsky (2018) [5] is built and its geometric description in terms of 4d metric of the ultrahyperbolic signature is given.

Cosmic Microwave Background from Effective Field Theory

In this work, we study the key role of generic Effective Field Theory (EFT) framework to quantify the correlation functions in a quasi de Sitter background for an arbitrary initial choice of the quantum vacuum state. We perform the computation in unitary gauge, in which we apply the Stückelberg trick in lowest dimensional EFT operators which are broken under time diffeomorphism. In particular, using this non-linear realization of broken time diffeomorphism and truncating the action by considering the contribution from two derivative terms in the metric, we compute the two-point and three-point correlations from scalar perturbations and two-point correlation from tensor perturbations to quantify the quantum fluctuations observed in the Cosmic Microwave Background (CMB) map. We also use equilateral limit and squeezed limit configurations for the scalar three-point correlations in Fourier space. To give future predictions from EFT setup and to check the consistency of our derived results for correlations, we use the results obtained from all classes of the canonical single-field and general single-field P ( X , ϕ ) model. This analysis helps us to fix the coefficients of the relevant operators in EFT in terms of the slow-roll parameters and effective sound speed. Finally, using CMB observations from Planck we constrain all these coefficients of EFT operators for the single-field slow-roll inflationary paradigm.

Light-front bootstrap for Chern-Simons matter theories

We propose a new approach to solve conformal field theories and apply it to Chern-Simons Matter theories and three-dimensional bosonization duality. All three-point correlation functions of single-trace operators are obtained in the large-N as a simple application. The idea is to construct, as an effective weakly-coupled theory, a nonlinear realization of the conformal algebra in terms of physical, gauge-invariant, operators. The efficiency of the method is also in the use of an analog of the light-cone gauge and of the momentum-space on the CFT side. AdS/CFT is used as a convenient regulator and as a source of the canonical bracket. The uniqueness of the nonlinear realization manifests the three-dimensional bosonization duality at this order. We also find two more non-unitary solutions which should be analogous to the fishnet theories. The results can also be viewed as an explicit realization of the slightly-broken higher spin symmetry.As a by-product, the cubic action of the Higher Spin Gravity in AdS4 is constructed. While generic Higher Spin Gravities are obstructed at higher orders by nonlocality, we point out the existence of two especially simple and well-defined theories: chiral and anti-chiral whose three-point functions correspond to the two new solutions. These two theories are supposed to give a quantum complete and local example of gravitational bulk duals.

A Consistency Check for the Free Scalar Field Theory Realization of the Doubly Spacial Relativity**Supported by Research Institute for Astronomy and Astrophysics of Maragha (RIAAM) under Research Project No. 1/6025-73

We study a free scalar field theory in the framework of the Magueijo-Smolin model of the “Doubly Special Relativity” (DSR) which is a non-linear realization of the action of the Lorentz group on momentum space admitting an invariant energy cutoff. We show that unlike the standard quantum field theory, the Klein-Gordon equation obtained via Euler-Lagrange field equation and Heisenberg picture equation of motion of the field are not equivalent in this framework, at least up to the first order of the Planck length scale.