Nonlinear Response Coefficients Research Articles

Gravito-magnetic polarization of Schwarzschild black hole

We determine the gravito-magnetic Love numbers of non-rotating black holes in all spacetime dimensions through a novel and direct derivation. The Ishibashi-Kodama master field and its associated field equation are avoided. The matching to the EFT variables is simple. This method allows us to correct the values in the literature. Moreover, we highlight a parity-based selection rule for nonlinear terms that include both electric-type and magnetic-type gravitational field tensors, enabling us to conclude that many of the nonlinear response coefficients in the Schwarzschild black hole effective action vanish.

Anomalous thermal relaxation and pump-probe spectroscopy of two-dimensional topologically ordered systems

We study the behavior of linear and nonlinear spectroscopic quantities in two-dimensional topologically ordered systems, which host anyonic excitations exhibiting fractional statistics. We highlight the role that braiding phases between anyons have on the dynamics of such quasiparticles, which as we show dictates the behavior of both linear response coefficients at finite temperatures, as well as nonlinear pump-probe response coefficients. These quantities, which act as probes of temporal correlations in the system, are shown to obey distinctive universal forms at sufficiently long timescales. As well as providing an experimentally measurable fingerprint of anyonic statistics, the universal behavior that we find also demonstrates anomalously fast thermal relaxation: correlation functions decay as a “squished exponential” C(t)∼exp(−[t/τ]3/2) at long times. We attribute this unusual asymptotic form to the nonlocal nature of interactions between anyons, which allows relaxation to occur much faster than in systems with quasiparticles interacting via local, nonstatistical interactions. While our results apply to any Abelian or non-Abelian topological phase in two-dimensions, we discuss in particular the implications for candidate quantum spin liquid materials, wherein the relevant quantities can be measured using pre-existing time-resolved terahertz-domain spectroscopic techniques. Published by the American Physical Society 2024

Probing the nuclear deformation with three-particle asymmetric cumulant in RHIC isobar runs

4496Ru+4496Ru and 4096Zr+4096Zr collisions at sNN=200 GeV provide unique opportunities to study the geometry and fluctuations raised from the deformation of the colliding nuclei. Using iEBE-VISHNU hybrid model, we predict ac2{3} ratios between these two collision systems and demonstrate that the ratios of ac2{3}, as well as the ratios of the involving flow harmonics and event-plane correlations, are sensitive to quadrupole and octupole deformations, which could provide strong constrains on the shape differences between 96Ru and 96Zr. We also study the nonlinear response coefficients χ4,22, which show insensitivity to the deformation effect.

Theoretical investigation of tritium concentration quantification method for DT fuel system using β-ray induced X-rays

Tritium measurement is one of the most important issues in DT fuel system of a fusion reactor. Beta-ray Induced X-ray Spectrometry (BIXS) method is a promising way to obtain tritium concentration in-line, especially for fuel processing system. However, till now there is no theory to establish the quantification relationship between tritium concentration and gas information including gas composition and pressure. Theoretical relationship between tritium concentration and X-ray spectrum in BIXS measurement is derived, and a quantitative method was proposed to determine tritium concentration directly by using the counts of X-ray spectrum. Non-linear Response Coefficients (NRCs) are introduced in the method to indicate the response of X-ray detector at different gas pressures for different gas compositions. Effects of both gas compositions (hydrogen/deuterium/tritium) and gas pressure (over five orders of magnitude, 1 Pa to 100 kPa) have been investigated quantitatively by Monte-Carlo simulations to determine the key parameters in the proposed method. Results show that for gas composed of hydrogen, deuterium, and tritium, NRCs are independent of gas composition within gas pressure from 1 Pa to 100 kPa. And NRCs can be obtained from the counts calculated within any energy region of X-ray spectrum detected in BIXS measurements. With the calculated NRCs, the tritium concentration can be obtained using only one reference experiment performed at any gas pressure (1 Pa to 100 kPa) for gas composed of any hydrogen isotopes. For gas composition including hydrogen, deuterium and tritium with different concentration, the error of NRCs in the proposed method is estimated to be 1.4%.

Investigations of the linear and non-linear flow harmonics using the a multi-phase transport model

The multi-phase transport model (AMPT) is used to study the effects of the parton-scattering cross-sections (σ pp) and hadronic re-scattering on the linear contributions to the flow harmonic v 4, the non-linear response coefficients, and the correlations between different order flow symmetry planes in Au + Au collisions at 200 GeV. The model results, which agree with current experimental measurements, indicate that the higher-order flow harmonics are sensitive to the σ pp variations. However, the non-linear response coefficients and the correlations between different order flow symmetry planes are σ pp independent. These results suggest that further detailed experimental measurements which span a broad range of collision systems and beam energies could serve as an additional constraint for the theoretical models’ calculations.

High-order nonlinear response correction method for infrared radiation detector

The infrared detector can generate nonlinear response error when the Fourier transform infrared spectrometer is used for implementing the radiometric calibration or observing the high temperature targets. Based on the relationship between the incident radiation intensity and the electron concentration in the optical conduction band, the mechanism of the nonlinear response error caused by the high incident photon flow is analyzed. According to Planck radiation law and interference principle, the effect of nonlinear error on spectrum is studied by simulating blackbody radiation data with nonlinear error. It is found that the nonlinear response with a different order has a different influence region, and the higher-order nonlinear response has a wider influence range and generates a larger nonlinear response error. By the general nonlinear response correction method the nonlinear response coefficient is obtained through constructing the nonlinear response model of the interference data and then the spectral distortion produced by the detector is corrected. According to the convolution iteration method, the polar orbit meteorological satellite CrIS constructs the convolution equation to correct the second-order nonlinear response by taking the low-wave number band of 50－500 cm<sup>–1</sup> as the characteristic region. The European Meteorological Agency’s Airborne Infrared Interferometer Evaluation System (ARIES) selected two feature areas, 50－500 cm<sup>–1</sup> and 2000－2500 cm<sup>–1</sup>, and iteratively corrected the second-order and third-order nonlinear response. The gradient descent method is often used to solve the optimization problems of unconstrained multivariate functions. Based on the gradient descent algorithm, an iterative method suitable for correcting the high-order nonlinear response errors is proposed in this paper. In this method, the information about the iteration point is obtained by constructing the nonlinear response function of the high-order detector and setting the appropriate iteration initialization. According to the initial value of the iteration and the information about the known iteration point, the gradient of the iteration variable is calculated to determine the iteration value of the next unknown variable, thus quickly searching for the global minimum point and determining the nonlinear response coefficient. We use Fourier transform infrared spectrometer to carry out radiometric calibration experiment and compare the effects of three correction methods: convolution, cross iteration and gradient descent method. The results show that the three correction methods can effectively reduce the nonlinear error, and improve the fitting extent by 0.15%, 0.29% and 0.39% respectively. The spectral data corrected by gradient descent method are more accurate.

Hydrodynamization in systems with detailed transverse profiles

The observation of fluid-like behavior in nucleus-nucleus (AA), proton-nucleus (pA) and high-multiplicity proton-proton (pp) collisions motivates systematic studies of how different measurements approach their fluid-dynamic limit. We have developed numerical methods to solve the ultra-relativistic Boltzmann equation for systems of arbitrary size and transverse geometry. Here, we apply these techniques for the first time to the study of azimuthal flow coefficients vn including non-linear mode-mode coupling and to an initial condition with realistic event-by-event fluctuations. We show how both linear and non-linear response coefficients extracted from vn develop as a function of opacity from free streaming to perfect fluidity. We note in particular that away from the fluid-dynamic limit, the signal strength of linear and non-linear response coefficients does not reduce uniformly, but that their hierarchy and relative size shows characteristic differences.

On nonlinearity in hydrodynamic response to the initial geometry in relativistic heavy-ion collisions

In the context of event-by-event hydrodynamic description, we analyze the implications of two models characterized by distinct initial conditions. The initial energy density of the first model adopts a Gaussian-type distribution, while those of the second one are features by high energy peripheral tubes. We calibrate the initial conditions of both models so that their initial probability distribution of eccentricity are mostly identical. Subsequently, the resultant scaled probability distributions of collective flow and the correlations between flow harmonic and eccentricity coefficients are investigated. Besides, the calculations are carried out for particle correlations regarding the symmetric cumulant, mixed harmonics, and nonlinear response coefficients. Although the resultant two-particle correlations possess similar shapes, numerical calculations indicate a subtle difference between the two models. To be specific, the difference resides in more detailed observables such as the probability distributions of elliptic flow as well as Pearson correlation coefficient regarding higher-order harmonics. We discuss several essential aspects concerning the linearity and nonlinearity between initial eccentricities and final state anisotropies. Further implications are addressed.

Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in mathrm {PbPb} collisions at sqrt{smash [b]{s_{_{mathrm {NN}}}}} = 2.76 and 5.02,text {TeV}

Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in mathrm {PbPb} collisions at nucleon-nucleon center-of-mass energies sqrt{smash [b]{s_{_{mathrm {NN}}}}} = 2.76 and 5.02,text {TeV} with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

Nearly isentropic flow at sizeable η/s

Non-linearities in the harmonic spectra of hadron–nucleus and nucleus–nucleus collisions provide evidence for the dynamical response to azimuthal spatial eccentricities. Here, we demonstrate within the framework of transport theory that even the mildest interaction correction to a picture of free-streaming particle distributions, namely the inclusion of one perturbatively weak interaction (“one-hit dynamics”), will generically give rise to all observed linear and non-linear structures. We further argue that transport theory naturally accounts within the range of its validity for realistic signal sizes of the linear and non-linear response coefficients observed in azimuthal momentum anisotropies with a large mean free path of the order of the system size in peripheral (∼50% centrality) PbPb or central pPb collisions. As a non-vanishing mean free path is indicative of non-minimal dissipation, this challenges the perfect fluid paradigm of ultra-relativistic nucleus–nucleus and hadron–nucleus collisions.

Universal Majorana thermoelectric noise

Thermoelectric phenomena resulting from an interplay between particle flows induced by electric fields and temperature inhomogeneities are extremely insightful as a tool providing substantial knowledge about the microscopic structure of a given system. Tuning, e.g., parameters of a nanoscopic system coupled via tunneling mechanisms to two contacts one may achieve various situations where the electric current induced by an external bias voltage competes with the electric current excited by the temperature difference of the two contacts. Even more exciting physics emerges when the system's electronic degrees freedom split to form Majorana fermions which make the thermoelectric dynamics universal. Here we propose revealing this unique universal signatures of Majorana fermions in strongly nonequilibrium quantum dots via noise of the thermoelectric transport beyond linear response. It is demonstrated that whereas mean thermoelectric quantities are only universal at large bias voltages, the noise of the electric current excited by an external bias voltage and the temperature difference of the contacts is universal at any bias voltage. We provide truly universal, i.e. independent of the system's parameters, thermoelectric ratios between nonlinear response coefficients of the noise and mean current at large bias voltages where experiments may easily be performed to uniquely detect these truly universal Majorana thermoelectric signatures.

CMS results on collectivity in PbPb collisions at √sNN = 2.76 and 5.02 TeV

Nonlinear response coeffcients of higher-order vn anisotropy harmonics for charged particles, as a function of transverse momentum (pT) and collision centrality, are measured in PbPb collisions at √sNN = 2.76 and 5.02 TeV. The nonlinear response coefficients are obtained using vn harmonics measured with respect to their own plane and the mixed harmonics. Using a fine splitting between v2{4} and v2{6} cumulants, the centrality dependence of the elliptic flow skewness is measured at 5.02 TeV PbPb collisions. The CMS also measured the v2 and v3 anisotropy harmonics of charged particles and prompt D0 mesons at |y| ≤ 1 as a function of pT and centrality in PbPb data at √sNN = 5.02 TeV collected with the CMS detector. Prompt D0 mesons, formed from the c quarks produced via initial hard scatterings, are separated up to a high extent from nonprompt D0 mesons emerged from decays of b hadrons. The results indicate that the charm quarks interact strongly with the QGP medium. Comparisons between theoretical models and data provide new constraints on the initial-state conditions and the interaction between charm quarks and the QGP medium.

Stochastic thermodynamics of periodically driven systems: Fluctuation theorem for currents and unification of two classes.

Periodic driving is used to operate machines that go from standard macroscopic engines to small nonequilibrium microsized systems. Two classes of such systems are small heat engines driven by periodic temperature variations, and molecular pumps driven by external stimuli. Well-known results that are valid for nonequilibrium steady states of systems driven by fixed thermodynamic forces, instead of an external periodic driving, have been generalized to periodically driven heat engines only recently. These results include a general expression for entropy production in terms of currents and affinities, and symmetry relations for the Onsager coefficients from linear-response theory. For nonequilibrium steady states, the Onsager reciprocity relations can be obtained from the more general fluctuation theorem for the currents. We prove a fluctuation theorem for the currents for periodically driven systems. We show that this fluctuation theorem implies a fluctuation dissipation relation, symmetry relations for Onsager coefficients, and further relations for nonlinear response coefficients. The setup in this paper is more general than previous studies, i.e., our results are valid for both heat engines and molecular pumps. The external protocol is assumed to be stochastic in our framework, which leads to a particularly convenient way to treat periodically driven systems.

Mixed higher-order flow harmonics and nonlinear response coefficients in PbPb collisions at 2.76 and 5.02 TeV with CMS

The mixed higher-order flow harmonics and nonlinear response coefficients of charged particles are presented as a function of pT and centrality in PbPb collisions at sNN=2.76 TeV and 5.02 TeV with the CMS detector. The results are obtained using the scalar product method, and cover a pT range from 0.3 GeV/c to 8.0 GeV/c, pseudorapidity |η|<2.4, and a centrality range of 0-60%. The mixed harmonic results at 5.02 TeV are compared to the matching higher-order flow harmonics from two-particle correlations, which measure vn values with respect to the n-th order event plane. It is observed that the nonlinear response coefficients of the odd harmonics are larger than the even harmonics ones. The results are compared with hydrodynamic predictions using different shear viscosity to entropy density ratios and different initial conditions.

Probing non-linearity of higher order anisotropic flow in Pb–Pb collisions

The second and the third order anisotropic flow, V2 and V3, are determined by the corresponding initial spatial anisotropy coefficients, ε2 and ε3, in the initial density distribution. On the contrary, the higher order anisotropic flow Vn(n>3), in addition to their dependence on the same order initial anisotropy coefficient εn, have a significant contribution from lower order initial anisotropy coefficients, which leads to mode-coupling effects. In this contribution, we present the investigations on linear and non-linear modes in higher order anisotropic flow (V4, V5 and V6) in Pb–Pb collisions at sNN=2.76 TeV using the ALICE detector at the Large Hadron Collider (LHC). A significant contribution from a non-linear mode is observed. A new observable, the non-linear response coefficient, is measured as well. The comparison to theoretical calculations provides crucial information on dynamic of the created system especially at the freeze-out conditions, which are poorly known from previous flow measurements.

A Detailed Study and Synthesis of Flow Observables in the IP-Glasma+MUSIC+UrQMD Framework

In this work we use the IP-Glasma+MUSIC+UrQMD framework to systematically study a wide range of hadronic flow observables at 2.76 TeV. In addition to the single particle spectra and anisotropic flow coefficients vn previously studied in [S. McDonald, C. Shen, F. Fillion-Gourdeau, S. Jeon and C. Gale, arXiv:1609.02958 [hep-ph]], we consider event-plane correlations, non-linear response coefficients χnpq, and event shape engineering. Taken together, these observables provide a wealth of insight into the collective behavior of the QGP and initial state fluctuations. They shed light on flow fluctuations, flow at fixed system size but different initial geometries, as well as the non-linear hydrodynamic response to the initial state spatial eccentricities. By synthesizing this information we can gain further insight into the transport properties of the QGP as well as the fluctuation spectrum of the initial state.

Collective flow in 2.76 and 5.02 A TeV Pb\xa0+\xa0Pb collisions

In this paper, we study and predict flow observables in 2.76 and 5.02 A TeV Pb + Pb collisions, using the iEBE-VISHNU hybrid model with TRENTo and AMPT initial conditions and with different forms of the QGP transport coefficients. With properly chosen and tuned parameter sets, our model calculations can nicely describe various flow observables in 2.76 A TeV Pb + Pb collisions, as well as the measured flow harmonics of all charged hadrons in 5.02 A TeV Pb + Pb collisions. We also predict other flow observables, including v_n(p_T) of identified particles, event-by-event v_n distributions, event-plane correlations, (normalized) symmetric cumulants, non-linear response coefficients and p_T-dependent factorization ratios, in 5.02 A TeV Pb + Pb collisions. We find many of these observables to remain approximately the same values as the ones in 2.76 A TeV Pb + Pb collisions. Our theoretical studies and predictions could shed light to the experimental investigations in the near future.

Nonlinear hydrodynamic response confronts LHC data

Higher harmonics of anisotropic flow (vn with n≥4) in heavy-ion collisions can be measured either with respect to their own plane, or with respect to a plane constructed using lower-order harmonics. By assuming that higher flow harmonics are the superposition of medium nonlinear and linear responses to initial anisotropies, we propose a set of nonlinear response coefficients χn's, which are independent of initial state by construction. In experiments, χn's can be extracted as the ratio between higher order harmonic flow measured in the plane constructed by v2 and v3, and moments of lower order harmonic flow. Simulations with single-shot hydrodynamics and AMPT model lead to results of these nonlinear response coefficients in good agreement with the experimental data at the LHC energy. Predictions for v7 and v8 measured with respect to plane of lower order harmonics are given accordingly.

Mode-coupling effects in anisotropic flow in heavy-ion collisions

Higher-order anisotropic flows in heavy-ion collisions are affected by nonlinear mode coupling effects. It has been suggested that the associated nonlinear hydrodynamic response coefficients probe the transport properties and are largely insensitive to the spectrum of initial density fluctuations of the medium created in these collisions. To test this suggestion, we explore nonlinear mode coupling effects in event-by-event viscous fluid dynamics, using two different models for the fluctuating initial density profiles, and compare the nonlinear coupling coefficients between the initial eccentricity vectors before hydrodynamic expansion and the final flow vectors after the expansion. For several mode coupling coefficients we find significant sensitivity to the initial fluctuation spectrum. They all exhibit strong sensitivity to the specific shear viscosity at freeze-out, but only weak dependence on the shear viscosity during hydrodynamic evolution.

Numerical study of the optical nonlinearity of doped and gapped graphene: From weak to strong field excitation

Numerically solving the semiconductor Bloch equations within a phenomenological relaxation time approximation, we extract both the linear and nonlinear optical conductivities of doped graphene and gapped graphene under excitation by a laser pulse. We discuss in detail the dependence of second harmonic generation, third harmonic generation, and the Kerr effects on the doping level, the gap, and the electric field amplitude. The numerical results for weak electric fields agree with those calculated from available analytic perturbation formulas. For strong electric fields when saturation effects are important, all the effective third order nonlinear response coefficients show a strong field dependence.