Nonlinear Response Theory Research Articles

Random matrix approach to time-dependent forcing in many-body quantum systems

Changing some of its parameters over time is a paradigmatic way of driving an otherwise isolated many-body quantum system out of equilibrium, and a vital ingredient for building quantum computers and simulators. Here, we further develop a recently proposed nonlinear response theory which is based on typicality and random-matrix methods, and which is applicable to a wide variety of such parametrically perturbed systems in and out of equilibrium: We derive analytical approximations of the characteristic response function for the two limiting cases of fast driving and of strong and short-ranged-in-energy driving. Furthermore, we work out implications and predictions for common applications, including finite-time quenches and time-dependent forcing that breaks conservation laws of the underlying undriven system. Finally, we verify all predictions by numerical examples and discuss the theory's scope and limitations. Published by the American Physical Society 2024

Closure to the PRISM equation derived from nonlinear response theory.

Nonlinear response theory is employed to derive a closure to the polymer reference interaction site model equation. The closure applies to a liquid of neutral polymers at melt densities. It can be considered a molecular generalization of the mean spherical approximation (MSA) closure of Lebowitz and Percus to the atomic Ornstein-Zernike (OZ) equation and is similar in some aspects to the reference "molecular" MSA (R-MMSA) closure of Schweizer and Yethiraj to PRISM. For a model binary blend of freely-jointed chains, the new closure predicts an unmixing critical temperature, Tc, via the susceptibility route that scales linearly with molecular weight, N, in agreement with Flory theory. Predictions for Tc of the new closure differ greatest from those of the R-MMSA at intermediate N, the latter being about 40% higher than the former there, but at large N, both theories give about the same values. For an isotopic blend of polyethylene, the new and R-MMSA closures predict a Tc about 25% higher than the experimental value, which is only moderately less accurate than the prediction of atomic OZ-MSA theory for Tc of methane. In this way, the derivation and its consequences help to identify the ingredients in a theory needed to properly model the equilibrium properties of a polymeric liquid at both short and long lengthscales.

Nonlinear Langevin functionals for a driven probe.

When a probe particle immersed in a fluid with nonlinear interactions is subject to strong driving, the cumulants of the stochastic force acting on the probe are nonlinear functionals of the driving protocol. We present a Volterra series for these nonlinear functionals by applying nonlinear response theory in a path integral formalism, where the emerging kernels are shown to be expressed in terms of connected equilibrium correlation functions. The first cumulant is the mean force, the second cumulant characterizes the non-equilibrium force fluctuations (noise), and higher order cumulants quantify non-Gaussian fluctuations. We discuss the interpretation of this formalism in relation to Langevin dynamics. We highlight two example scenarios of this formalism. (i) For a particle driven with the prescribed trajectory, the formalism yields the non-equilibrium statistics of the interaction force with the fluid. (ii) For a particle confined in a moving trapping potential, the formalism yields the non-equilibrium statistics of the trapping force. In simulations of a model of nonlinearly interacting Brownian particles, we find that nonlinear phenomena, such as shear-thinning and oscillating noise covariance, appear in third- or second-order response, respectively.

Deformation theory and nonlinear dynamic behavior of PVC gel actuators

Polyvinyl chloride (PVC) gel generates complex nonlinear vibration behavior under an alternating current voltage excitation, which has potential application as a dynamic electromechanical actuator. However, there are few studies on the deformation theory of PVC gel actuators, especially the dynamic nonlinear response theory. In this paper, a complex dynamic model is established according to the electrodeformation mechanism of PVC film, and the nonlinear dynamic behavior of the actuator is numerically studied by a differential equation. The effects of applied voltage amplitude, voltage frequency, dibutyl adipate content, mechanical tension, and bias voltage on the dynamic properties of PVC film were analyzed under the condition of equal biaxial tension. The variation of amplitude and the generation and disappearance of the beat frequency during vibration are analyzed by using time-domain characteristics. The degree of PVC actuator nonlinearity as well as vibration stability and periodicity is also reflected based on the phase path and Poincare map. Finally, the law of influence of external condition parameters on the dynamic response of the PVC actuator is obtained.

Nonlinear response theory of molecular machines

Chemical affinities are responsible for driving active matter systems out of equilibrium. At the nano-scale, molecular machines interact with the surrounding environment and are subjected to external forces. The mechano-chemical coupling which arises naturally in these systems reveals a complex interplay between chemical and mechanical degrees of freedom with strong impact on their active mechanism. By considering various models far from equilibrium, we show that the tuning of applied forces gives rise to a nonlinear response that causes a non-monotonic behaviour in the machines’ activity. Our findings have implications in understanding, designing, and triggering such processes by controlled application of external fields, including the collective dynamics of larger non-equilibrium systems where the total dissipation and performance might be affected by internal and inter-particle interactions.

Light-induced nonlinear spin Hall current in single-layer WTe2

In this theoretical investigation, we analyze light-induced nonlinear spin Hall currents in a gated single-layer 1T ′ -WTe2, flowing transversely to the incident laser polarization direction. Our study encompasses the exploration of the second and third-order rectified spin Hall currents using an effective low-energy Hamiltonian and employing the Kubo’s formalism. We extend our analysis to a wide frequency range spanning both transparent and absorbing regimes, investigating the influence of light frequency below and above the optical band gap. Additionally, we investigate the influence of an out-of-plane gate potential on the system, disrupting inversion symmetry and effectively manipulating both the strength and sign of nonlinear spin Hall responses. We predict a pronounced third-order spin Hall current relative to its second-order counterpart. The predicted nonlinear spin currents show strong anisotropic dependence on the laser polarization angle. The outcomes of our study contribute to a generalized framework for nonlinear response theory within the spin channel will impact the development of emerging field of opto-spintronic.

A Quantum Algorithm from Response Theory: Digital Quantum Simulation of Two-Dimensional Electronic Spectroscopy.

Multidimensional optical spectroscopies are powerful techniques to investigate energy transfer pathways in natural and artificial systems. Because of the high information content of the spectra, numerical simulations of the optical response are of primary importance to assist the interpretation of spectral features. However, the increasing complexity of the investigated systems and their quantum dynamics call for the development of novel simulation strategies. In this work, we consider using digital quantum computers. By combining quantum dynamical simulation and nonlinear response theory, we present a quantum algorithm for computing the optical response of molecular systems. The quantum advantage stems from the efficient quantum simulation of the dynamics governed by the molecular Hamiltonian, and it is demonstrated by explicitly considering exciton-vibrational coupling. The protocol is tested on a near-term quantum device, providing the digital quantum simulation of the linear and nonlinear response of simple molecular models.

A semi-analytical sinusoidal shear deformation theory for nonlinear dynamic response and vibration of CNT–FGM doubly curved shallow shells

A semi-analytical sinusoidal shear deformation theory for nonlinear dynamic response and vibration of CNT–FGM doubly curved shallow shells

Homogeneous Dephasing in Photosynthetic Bacterial Reaction Centers: Time Correlation Function Approach.

A new tractable linear electronic transition dipole moment time correlation function (ETDMTCF) that accurately accounts for electronic dephasing, asymmetry, and width of 1-phonon profile, which the zero-phonon line (ZPL) contributes to it, in Rhodopseudomonas viridis bacterial reaction center is derived. This time correlation function proves to be superior to other frequency-domain expressions in case of strong electron-phonon coupling (which is often the case in bacterial RCs and pigment-protein complexes), many vibrational modes involved, and high temperature, whereby more vibronic and electronic (sequence) transitions would arise. The Fourier transform of this ETDMTCF leads to asymmetric multiphonon profiles composed of Lorentzian distribution and Gaussian distribution on the high- and low-energy sides, respectively, whereby the overtone widths fold themselves with that of the one-phonon profile. This ETDMTCF also features expedient computation in large systems using asymmetric phonon profiles to account correctly for dephasing and pigment-protein interaction (electron-phonon coupling). The derived ETDMTCF allows computing all nonlinear optical signals in both time and frequency domains, through the nonlinear dipole moment time correlation functions (as guided by nonlinear optical response theory) in line with the eight Liouville space pathways. The linear transition dipole moment time correlation function is of a central value as the nonlinear transition dipole moment time correlation function is expressed in terms of the linear transition dipole moment time correlation function, derived herein. One of the great advantages of presenting this ETDMTCF is its applicability to nonlinear transition dipole moment time correlation functions in line with the eight Liouville space pathways needed in computing nonlinear signals. As such, there is more to the utility and applicability of the presented ETDMTCF besides computational expediency and efficiency. Results show good agreement with the reported literature. The intimate connection between a one-phonon profile and the corresponding bath spectral density in photosynthetic complexes is discussed.

Nonlinear Optical Spectroscopy of Molecular Assemblies: What Is Gained and Lost in Action Detection?

This study elucidates the information content that is extracted from action-2D electronic spectroscopy (A-2DES) when the output intensity is not proportional to the number of excitations generated. Such a scenario can be realized in both fluorescence and photocurrent detection because of direct interaction like exciton-exciton annihilation or indirect effects in the signal generation or detection. By means of an intuitive probabilistic model supported by nonlinear response theory, the study concludes that in molecular assemblies the ground-state bleaching contribution can dominate the nonlinear signal and partially or completely hide the stimulated emission. In this case, the spectral effect resembles incoherent mixing, even in the absence of exciton-exciton annihilation, implying reduced information about the excited-state dynamics with an increasing number of chromophores. This finding has important implications for the selection of samples for A-2DES as well as for its interpretation.

Detecting a periodic signal by a population of spiking neurons in the weakly nonlinear response regime

Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic signal to be detected. Specifically, we study the response of a population of stochastic leaky integrate-and-fire (LIF) neurons to two periodic signals and focus in particular on the question, whether the presence of one of the stimuli can be detected from the population activity. As a detection criterion, we use a simple threshold-crossing of the population activity over a certain time window. We show by means of the receiver operating characteristics (ROC) that the detectability depends only weakly on the time window of observation but rather strongly on the stimulus amplitude. Counterintuitively, the detection of the weak periodic signal can be facilitated by the presence of a strong periodic input current depending on the frequencies of the two signals and on the dynamical regime in which the neurons operate. Beside numerical simulations of the model, we present an analytical approximation for the ROC curve that is based on the weakly nonlinear response theory for a stochastic LIF neuron.Graphic abstract

Unravelling the nonlinear ideal density response of many-body systems

Nonlinear density response theory is revisited focusing on the harmonically perturbed finite temperature uniform electron gas. Within the non-interacting limit, brute force quantum kinetic theory calculations for the quadratic, cubic, quartic and quintic responses reveal a deep connection with the linear response. Careful analysis of the static long wavelength limit led us to conjecture a canonical non-interacting form that expresses arbitrary order nonlinear responses as the weighted sum of the linear responses evaluated at all multiple harmonics. This harmonic expansion is successfully validated against ab initio path integral Monte Carlo simulations.

Материалы для сверхбыстрой терагерцовой фотоники

Designing of the ultrafast terahertz photonics devices requires materials with the biggest nonlinear refractive index coefficient n2 and the lowest settling time of the nonlinear response τ in the terahertz spectral range. In the present study, we show that the ratio n2/τ for media with the vibrational nonlinearity in the terahertz range is determined by the square of the medium thermal expansion coefficient and the fifth power of its dominative stretching vibrational mode frequency. These findings are based on the theory of the media vibrational nature nonlinear polarization response to incident THz radiation. We provide estimated values of the n2/τ ratio for a group of liquids and crystal materials. According to our evaluations, n2/τ value for alpha-pinene in the terahertz spectral range is about 10^6 cm^2/J and is almost the biggest one compared to materials with different nonlinearity types in various spectral ranges.

Nonlinear response theory for Markov processes. IV. The asymmetric double-well potential model revisited.

The dielectric response of noninteracting dipoles is discussed in the framework of the classical model of stochastic reorientations in an asymmetric double-well potential (ADWP). In the nonlinear regime, this model exhibits some pecularities in the static response. We find that the saturation behavior of the symmetric double-well potential model does not follow the Langevin function and only in the linear regime are the standard results recovered. If a finite asymmetry is assumed, then the nonlinear susceptibilities are found to change the sign at a number of characteristic temperatures that depend on the magnitude of the asymmetry, as has been observed earlier for the third-order and fifth-order responses. If the kinetics of the barrier crossing in the ADWP model is described as a two-state model, then we can give analytical expressions for the values of the characteristic temperatures. The results for the response obtained from a (numerical) solution of the Fokker-Planck equationfor the Brownian motion in a model ADWP behaves very similarly to the two-state model for high barriers. For small barriers no clear-cut timescale separation between the barrier crossing process and the intrawell relaxation exists and the model exhibits a number of timescales. In this case, the frequency-dependent linear susceptibility at low temperatures is dominated by the fast intrawell transitions and at higher temperatures by the barrier crossing kinetics. We find that for nonlinear susceptibilities the latter process appears to be more important and the intrawell transitions play only a role at the lowest temperatures.

Nonlinear Landauer formula: Nonlinear response theory of disordered and topological materials

The Landauer formula provides a general scattering formulation of electrical conduction. Despite its utility, it has been mainly applied to the linear-response regime, and a scattering theory of nonlinear response has yet to be fully developed. Here, we extend the Landauer formula to the nonlinear-response regime. We show that while the linear conductance is directly related to the transmission probability, the nonlinear conductance is given by its derivatives with respect to energy. This sensitivity to the energy derivatives is shown to produce unique nonlinear transport phenomena of mesoscopic systems including disordered and topological materials. By way of illustration, we investigate nonlinear conductance of disordered chains and identify their universal behavior according to symmetry. In particular, we find large singular nonlinear conductance for zero modes, including Majorana zero modes in topological superconductors. We also show the critical behavior of nonlinear response around the mobility edges due to the Anderson transitions. Moreover, we study nonlinear response of graphene as a prime example of topological materials featuring quantum anomaly. Furthermore, considering the geometry of electronic wave functions, we develop a scattering theory of the nonlinear Hall effect. We establish a new connection between the nonlinear Hall response and the nonequilibrium quantum fluctuations. We also discuss the influence of disorder and Anderson localization on the nonlinear Hall effect. Our work opens a new avenue in quantum physics beyond the linear-response regime.

Quantum theory of nonlinear thermal response

The Linear behavior of thermal transport has been widely explored, both theoretically and ex?perimentally. On the other hand, the nonlinear thermal response has not been fully discussed. In light of the thermal vector potential theory [Phys. Rev. Lett. 114, 196601 (2015)], we develop a general formulation to calculate the linear and nonlinear dynamic thermal responses. In the DC limit, we recover the well-known Mott relation and the Wiedemann-Franz (WF) law at the linear order response, which link the thermoelectric conductivity {\eta}, thermal conductivity \k{appa} and electric conductivity {\sigma} together. To be specific, the linear Mott relation describes the linear {\eta} is proportional to the first derivative of {\sigma} with respect to Fermi energy (for brevity we call the first derivative, the others are similar); and the linear WF law shows the linear \k{appa} is proportional to the zero derivative (i.e. the {\sigma} itself). We found there are higher-order Mott relation and WF law which follow an order-dependent relation. At the second order, the Mott relation indicates that the second order {\sigma} is proportional to the zero derivative of the second order {\eta}; but the second WF law shows that the second {\sigma} is proportional to the first derivative of \k{appa}. At the third order, the derivative order in?creases once. Although we only did explicit calculate up to the third order response, we can deduce that the n-th order electric conductivity is proportional to the n-2-th derivative of the n-th order thermoelectric conductivity for the nonlinear Mott relation; and the n-th order electric conductivity is proportional to the n-1-th derivative of the n-th order thermal conductivity for the nonlinear WF law.

Density Functional Theory Perspective on the Nonlinear Response of Correlated Electrons across Temperature Regimes.

We explore a new formalism to study the nonlinear electronic density response based on Kohn–Sham density functional theory (KS-DFT) at partially and strongly quantum degenerate regimes. It is demonstrated that the KS-DFT calculations are able to accurately reproduce the available path integral Monte Carlo simulation results at temperatures relevant for warm dense matter research. The existing analytical results for the quadratic and cubic response functions are rigorously tested. It is demonstrated that the analytical results for the quadratic response function closely agree with the KS-DFT data. Furthermore, the performed analysis reveals that currently available analytical formulas for the cubic response function are not able to describe simulation results, neither qualitatively nor quantitatively, at small wavenumbers q < 2qF, with qF being the Fermi wavenumber. The results show that KS-DFT can be used to describe warm dense matter that is strongly perturbed by an external field with remarkable accuracy. Furthermore, it is demonstrated that KS-DFT constitutes a valuable tool to guide the development of the nonlinear response theory of correlated quantum electrons from ambient to extreme conditions. This opens up new avenues to study nonlinear effects in a gamut of different contexts at conditions that cannot be accessed with previously used path integral Monte Carlo methods.

Series Expansion of the Excess Work Using Nonlinear Response Theory

The calculation of observable averages in non-equilibrium regimes is one of the most important problems in statistical physics. Using the Hamiltonian approach of nonlinear response theory, we obtain a series expansion of the average excess work and illustrate it with specific examples of thermally isolated systems. We report the emergence of non-vanishing contributions for large switching times when the system is subjected to strong driving. The problem is solved by using an adapted multiple-scale method to suppress these secular terms. Our paradigmatic examples show how the method is implemented generating a truncated series that obeys the Second Law of Thermodynamics.

Detection of Topological Spin Textures via Nonlinear Magnetic Responses.

Topologically nontrivial spin textures, such as skyrmions and dislocations, display emergent electrodynamics and can be moved by spin currents over macroscopic distances. These unique properties and their nanoscale size make them excellent candidates for the development of next-generation race-track memory and unconventional computing. A major challenge for these applications and the investigation of nanoscale magnetic structures in general is the realization of suitable detection schemes. We study magnetic disclinations, dislocations, and domain walls in FeGe and reveal pronounced responses that distinguish them from the helimagnetic background. A combination of magnetic force microscopy (MFM) and micromagnetic simulations links the response to the local magnetic susceptibility, that is, characteristic changes in the spin texture driven by the MFM tip. On the basis of the findings, which we explain using nonlinear response theory, we propose a read-out scheme using superconducting microcoils, presenting an innovative approach for detecting topological spin textures and domain walls in device-relevant geometries.

Theory of nonlinear response for charge and spin currents

The nonlinear Hall effect, which is the second-order harmonic charge Hall effect from the Berry curvature dipole in momentum space, has received much attention recently. As the responses to higher harmonics of the driving ac electric field are prominent and measurable, we develop a general nonlinear theory by taking the charge and spin currents as well as the longitudinal and transverse effects into account. We introduce the expansion order of the electric field and Berry curvature multipole moment, where the Berry curvature dipole is a particular one manifesting itself at the second harmonic order and the second expansion order of the electric field. There are four cases with conserving or breaking the time-reversal symmetry (TRS) and inversion symmetry (IS). We find a specific ``selection rule" that only longitudinal odd harmonic order charge currents exist for conserving both the TRS and IS, and with breaking both symmetries, all harmonic order charge and spin currents are nonzero. With conserving TRS and breaking IS, the charge Hall current exists at even harmonic order, and the longitudinal charge current occurs at odd harmonic order. Only the longitudinal spin current survives at even harmonic order. With breaking TRS and conserving IS, only odd harmonic order charge and spin currents can appear. Moreover, we observe that every harmonic order current contains a series of infinite-order expansion of the electric field. We further show that the Berry curvature dipole and quadrupole can be determined by measuring the second and fourth harmonic order currents in experiments. This may open a way to explore the higher responses of an ac driving system.