Second-order Process Research Articles

Unveiling Weyl-related optical responses in semiconducting tellurium by mid-infrared circular photogalvanic effect

Elemental tellurium, conventionally recognized as a narrow bandgap semiconductor, has recently aroused research interests for exploiting Weyl physics. Chirality is a unique feature of Weyl cones and can support helicity-dependent photocurrent generation, known as circular photogalvanic effect. Here, we report circular photogalvanic effect with opposite signs at two different mid-infrared wavelengths which provides evidence of Weyl-related optical responses. These two different wavelengths correspond to two critical transitions relating to the bands of different Weyl cones and the sign of circular photogalvanic effect is determined by the chirality selection rules within certain Weyl cone and between two different Weyl cones. Further experimental evidences confirm the observed response is an intrinsic second-order process. With flexibly tunable bandgap and Fermi level, tellurium is established as an ideal semiconducting material to manipulate and explore chirality-related Weyl physics in both conduction and valence bands. These results are also directly applicable to helicity-sensitive optoelectronics devices.

A Modified Method of Successive Approximations for Stochastic Recursive Optimal Control Problems

Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal control problems. The second-order adjoint processes are introduced in the augmented Hamiltonian minimization step since the control domain is not necessarily convex. Thanks to the theory of bounded mean oscillation martingales (BMO martingales for short), we give a delicate proof of the error estimate and then prove the convergence of the modified MSA algorithm. In a special case, we obtain a logarithmic convergence rate. When the control domain is convex and compact, a sufficient condition which makes the control returned from the MSA algorithm be a near-optimal control is given for a class of linear FBSCSs.

Tutorial on the instrumentation of sum frequency generation vibrational spectroscopy: Using a Ti:sapphire based system as an example

Sum frequency generation vibrational spectroscopy (SFG-VS) is an intrinsically surface-selective vibrational spectroscopic technique based on the second-order nonlinear optical process. Since its birth in the 1980s, SFG-VS has been used to solve interfacial structure and dynamics in a variety of research fields including chemistry, physics, materials sciences, biological sciences, environmental sciences, etc. Better understanding of SFG-VS instrumentation is no doubt an essential step to master this sophisticated technique. To address this need, here we will present a Tutorial with respect to the classification, setup layout, construction, operation, and data processing about SFG-VS. We will focus on the steady state Ti:sapphire based broad bandwidth SFG-VS system and use it as an example. We hope this Tutorial is beneficial for newcomers to the SFG-VS field and for people who are interested in using SFG-VS technique in their research.

Examining AGN UV/Optical Variability beyond the Simple Damped Random Walk

We present damped harmonic oscillator (DHO) light-curve modeling for a sample of 12,714 spectroscopically confirmed quasars in the Sloan Digital Sky Survey Stripe 82 region. DHO is a second-order continuous-time autoregressive moving-average process, which can be fully described using four independent parameters: a natural oscillation frequency (ω 0), a damping ratio (ξ), a characteristic perturbation timescale (τ perturb), and an amplitude for the perturbing white noise (σ ϵ ). The asymptotic variability amplitude of a DHO process is quantified by σ DHO—a function of ω 0, ξ, τ perturb, and σ ϵ . We find that both τ perturb and σ ϵ follow different dependencies with rest-frame wavelength (λ RF) on either side of 2500 Å, whereas σ DHO follows a single power-law relation with λ RF. After correcting for wavelength dependence, σ DHO exhibits anticorrelations with both the Eddington ratio and the black hole mass, while τ perturb—with a typical value of days in the rest frame—shows an anticorrelation with the bolometric luminosity. Modeling active galactic nuclei (AGN) variability as a DHO offers more insight into the workings of accretion disks close to the supermassive black holes at the center of AGN. The newly discovered short-term variability (characterized by τ perturb and σ ϵ ) and its correlation with bolometric luminosity pave the way for new algorithms that will derive fundamental properties (e.g., Eddington ratio) of AGN using photometric data alone.

Design and implementation of high-order PID for second-order processes with time delay

In this study, a state-space pole placement approach is first proposed to design high-order PID controllers for high-order processes. The method makes use of a single parameter to determine the locations of closed-loop poles; thus, a high-order PID controller can be tuned with this parameter. To implement the high-order PID controller in practice, an observer-based PID structure is proposed. The structure utilizes a model-free observer to estimate the plant output and its derivatives, thus retaining the high-order PID structure but can filter the measurement noise and make the high-order derivatives of the plant output available for control. The proposed method is applied to design high-order PID controllers for second-order processes with time delay. Simulation results show that high-order PID can indeed improve the performance of conventional PID controllers for second-order processes with time delay in disturbance rejection and robustness.

Fractional resonances and prethermal states in Floquet systems

In periodically driven quantum systems, resonances can induce exotic nonequilibrium behavior and new phases of matter without static analog. We report on the emergence of fractional and integer resonances in a broad class of many-body Hamiltonians with a modulated hopping with a frequency that is either a fraction or an integer of the on-site interaction. We contend that there is a fundamental difference between these resonances when interactions bring the system to a Floquet prethermal state. Second-order processes dominate the dynamics in the fractional resonance case, leading to less entanglement and more localized quantum states than in the integer resonance case dominated by first-order processes. We demonstrate the dominating emergence of fractional resonances using the Magnus expansion of the effective Hamiltonian and quantify their effects on the many-body dynamics via quantum states' von Neumann entropy and Loschmidt echo. Our findings reveal novel features of the nonequilibrium quantum many-body system, such as the coexistence of Floquet prethermalization and localization, that may allow to development of quantum memories for quantum technologies and quantum information processing.

Activation and adsorption mechanisms of methylene blue removal by porous biochar adsorbent derived from eggshell membrane

The technology of producing porous biochar adsorbent using eggshell membranes is presented. The adsorption of methylene blue on biochar (CESM-KH) was carried out in a batch process to study the effects of solution pH, adsorbent dosage, temperature, and adsorption time. The porous biochar had a good affinity with methylene blue, and the adsorption capacity reached 110.38 mg·g−1 at pH = 9. The adsorption isotherm model is consistent with the Langmuir adsorption model, and its dynamic behavior follows the second-order kinetic process. Furthermore, there are physical and chemical adsorptions such as hydrogen bonding, electrostatic attraction, and ligand exchange during the adsorption process on porous biochar. Therefore, ESM can be used as a biomass carbon material to remove organic dyes from wastewater.

Towards compact phase-matched and waveguided nonlinear optics in atomically layered semiconductors

Nonlinear frequency conversion provides essential tools for light generation, photon entanglement, and manipulation. Transition metal dichalcogenides (TMDs) possess huge nonlinear susceptibilities and 3R-stacked TMD crystals further combine broken inversion symmetry and aligned layering, representing ideal candidates to boost the nonlinear optical gain with minimal footprint. Here, we report on the efficient frequency conversion of 3R-MoS2, revealing the evolution of its exceptional second-order nonlinear processes along the ordinary (in-plane) and extraordinary (out-of-plane) directions. By measuring second harmonic generation (SHG) of 3R-MoS2 with various thickness - from monolayer (~0.65 nm) to bulk (~1 {\mu}m) - we present the first measurement of the in-plane SHG coherence length (~530 nm) at 1520 nm and achieve record nonlinear optical enhancement from a van der Waals material, >10^4 stronger than a monolayer. It is found that 3R-MoS2 slabs exhibit similar conversion efficiencies of lithium niobate, but within propagation lengths >100-fold shorter at telecom wavelengths. Furthermore, along the extraordinary axis, we achieve broadly tunable SHG from 3R-MoS2 in a waveguide geometry, revealing the coherence length in such structure for the first time. We characterize the full refractive index spectrum and quantify both birefringence components in anisotropic 3R-MoS2 crystals with near-field nano-imaging. Empowered with these data we assess the intrinsic limits of the conversion efficiency and nonlinear optical processes in 3R-MoS2 attainable in waveguide geometries. Our analysis highlights the potential of 3R-stacked TMDs for integrated photonics, providing critical parameters for designing highly efficient on-chip nonlinear optical devices including periodically poled structures, resonators, compact optical parametric oscillators and amplifiers, and optical quantum circuits.

Ultra-low-power second-order nonlinear optics on a chip

Second-order nonlinear optical processes convert light from one wavelength to another and generate quantum entanglement. Creating chip-scale devices to efficiently control these interactions greatly increases the reach of photonics. Existing silicon-based photonic circuits utilize the third-order optical nonlinearity, but an analogous integrated platform for second-order nonlinear optics remains an outstanding challenge. Here we demonstrate efficient frequency doubling and parametric oscillation with a threshold of tens of micro-watts in an integrated thin-film lithium niobate photonic circuit. We achieve degenerate and non-degenerate operation of the parametric oscillator at room temperature and tune its emission over one terahertz by varying the pump frequency by hundreds of megahertz. Finally, we observe cascaded second-order processes that result in parametric oscillation. These resonant second-order nonlinear circuits will form a crucial part of the emerging nonlinear and quantum photonics platforms.

Detecting frequency modulation in stochastic time-series data.

We propose a statistical test to identify nonstationary frequency-modulated stochastic processes from time-series data. Our method uses the instantaneous phase as a discriminatory statistics with reliable critical values derived from surrogate data. We simulated an oscillatory second-order autoregressive process to evaluate the size and power of the test. We found that the test we propose is able to correctly identify more than 99% of nonstationary data when the frequency of the simulated data is doubled after the first half of the time series. Our method is easily interpretable, computationally cheap, and does not require choosing hyperparameters that are dependent on the data.

Output Tracking Control of Random Nonlinear Time-Varying Systems

This paper is concerned with the output tracking control problem for random nonlinear systems with time-varying powers. A distinct feature of this paper is that we consider time-varying powers and the second-order moment process simultaneously, which is more practical in real applications than the existing results where only one factor is considered. We propose a new design scheme, which ensures that the fourth moment of the tracking error can be adjusted to be arbitrarily small and all the states of the closed-loop system are bounded in probability. Finally, a numerical simulation is given to demonstrate the feasibility of the control idea.

Reward prediction errors, not sensory prediction errors, play a major role in model selection in human reinforcement learning

Model-based reinforcement learning enables an agent to learn in variable environments and tasks by optimizing its actions based on the predicted states and outcomes. This mechanism has also been considered in the brain. However, exactly how the brain selects an appropriate model for confronting environments has remained unclear. Here, we investigated the model selection algorithm in the human brain during a reinforcement learning task. One primary theory of model selection in the brain is based on sensory prediction errors. Here, we compared this theory with an alternative possibility of internal model selection with reward prediction errors. To compare these two theories, we devised a switching experiment from a first-order Markov decision process to a second-order Markov decision process that provides either reward- or sensory prediction error regarding environmental change. We tested two representative computational models driven by different prediction errors. One is the sensory prediction-error-driven Bayesian algorithm, which has been discussed as a representative internal model selection algorithm in the animal reinforcement learning task. The other is the reward-prediction-error-driven policy gradient algorithm. We compared the simulation results of these two computational models with human reinforcement learning behaviors. The model fitting result supports that the policy gradient algorithm is preferable to the Bayesian algorithm. This suggests that the human brain employs the reward prediction error to select an appropriate internal model in the reinforcement learning task.

Stability analysis and stabilization of linear symmetric matrix-valued continuous, discrete, and impulsive dynamical systems — A unified approach for the stability analysis and the stabilization of linear systems

Matrix-valued dynamical systems are an important class of systems that can describe important processes such as covariance/second-order moment processes, or processes on manifolds and Lie Groups. We address here the case of processes that leave the cone of positive semidefinite matrices invariant, thereby including covariance and second-order moment processes. Both the continuous-time and the discrete-time cases are first considered. In the LTV case, the obtained stability and stabilization conditions are expressed as differential and difference Lyapunov conditions which are equivalent, in the LTI case, to some spectral conditions for the generators of the processes. Convex stabilization conditions are also obtained in both the continuous-time and the discrete-time setting. It is proven that systems with constant delays are stable provided that the systems with zero-delays are stable—which mirrors existing results for linear positive systems. The results are then extended and unified into an impulsive formulation for which similar results are obtained. The proposed framework is very general and can recover and/or extend many of the existing results in the literature on linear systems related to (mean-square) exponential (uniform) stability. Several examples are discussed to illustrate this claim by deriving stability conditions for stochastic systems driven by Brownian motion and Poissonian jumps, Markov jump systems, (stochastic) switched systems, (stochastic) impulsive systems, (stochastic) sampled-data systems, and all their possible combinations.

Graphene as a source of entangled plasmons

We analyze nonlinear optics schemes for generating pairs of quantum entangled plasmons in the terahertz-infrared range in graphene. We predict that high plasmonic field concentration and strong optical nonlinearity of monolayer graphene enables pair-generation rates much higher than those of conventional photonic sources. The first scheme we study is spontaneous parametric down conversion in a graphene nanoribbon. In this second-order nonlinear process a plasmon excited by an external pump splits into a pair of plasmons, of half the original frequency each, emitted in opposite directions. The conversion is activated by applying a dc electric field that induces a density gradient or a current across the ribbon. Another scheme is degenerate four-wave mixing where the counter-propagating plasmons are emitted at the pump frequency. This third-order nonlinear process does not require a symmetry-breaking dc field. We suggest nano-optical experiments for measuring position-momentum entanglement of the emitted plasmon pairs. We estimate the critical pump fields at which the plasmon generation rates exceed their dissipation, leading to parametric instabilities.

Hybrid dual-loop control method for dead-time second-order unstable inverse response plants with a case study on CSTR

Abstract Unstable processes are hard to stabilize as they contain one or more positive poles which result in unbounded dynamic behavior. The occurrence of the delay and positive zeros often creates more difficulty in controlling such unstable plants. Most control strategies meant for first-order unstable processes fail to stabilize and control the higher-order unstable processes. Hence, a new dual-loop hybrid control structure is suggested for dead-time unbounded second-order processes with positive/negative zeros. Inner-loop has a stabilizing PID controller. The PID controller parameters are derived by comparing the numerator and characteristic polynomial coefficients in the transfer function for internal-loop servo action. A fractional-order internal model controller (FOIMC) is used in the external-loop. Methods for the selection of outer-loop tuning parameter and fractional-order are also discussed. By comparing the simulation results with a contemporary single-loop scheme, the usefulness of the suggested scheme is proved. The suggested scheme is capable of minimizing the overshoot and improving the overall dynamic performance. Finally, the usefulness of the suggested scheme is also demonstrated by a case study on temperature control of a continuous stirred tank reactor (CSTR) during a first-order irrevocable exothermic reaction.

Landau-Zener transition between two levels coupled to continuum

For a Landau-Zener transition in a two-level system, the probability for a particle, initially in the first level, i, to survive the transition and to remain in the first level, depends exponentially on the square of the tunnel matrix element between the two levels. This result remains valid when the second level, f, is broadened due to e.g. coupling to continuum (Akulin and Schleich (1992) [26]). If the level, i, is also coupled to continuum, albeit much weaker than the level f, a particle, upon surviving the transition, will eventually escape. However, for shorter times, the probability to find the particle in the level i after crossing f is enhanced due to the coupling to continuum. This, as shown in the present paper, is the result of a second-order process, which is an additional coupling between the levels. The underlying mechanism of this additional coupling is virtual tunneling from i into continuum followed by tunneling back into f.

Spinless fermions in a Z2 gauge theory on a triangular ladder

A study of spinless matter fermions coupled to a constrained ${\mathbb{Z}}_{2}$ lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared with a previous analysis on the square lattice. In the static case, the even and odd gauge theories for the empty and filled ladder are identical. The gauge field dynamics due to the electric coupling is drastically influenced by the absence of periodic boundary conditions, rendering the deconfinement-confinement process a crossover in general and a quantum phase transition (QPT) only for decorated couplings. At finite doping and in the static case, a staggered flux insulator at half-filling and vanishing magnetic energy competes with a uniform flux metal at elevated magnetic energy. As for the square lattice, a single QPT into a confined fermionic dimer gas is found vs electric coupling. Dimer resonances in the confined phase are, however, a second-order process only, likely reducing the tendency to phase separate for large magnetic energy. The results obtained employ a mapping to a pure spin model of ${\mathbb{Z}}_{2}$ gauge-invariant moments, adapted from the square lattice, and density matrix renormalization group calculations thereof for numerical purposes. Global scans of the quantum phases in the intermediate coupling regime are provided.

Deterministic approximation for the nucleation-growth type model of nanoparticle formation: A validation against stochastic simulations

A deterministic approximation method is introduced here for a complicated kinetic model that describes nanoparticle formation with nucleation and growth steps. The model starts from monomer units, some of which combine in a nucleation reaction, and the number of monomer units (n) in a kinetically effective nucleus is an unbounded integer parameter in the model. The growth steps are second-order processes between a particle and a monomer unit, the rate constant of which depends on the size of the growing nanoparticle in a way that is given in a kernel function. Four different kernels are considered: diffusion kernel (size independence), Brownian kernel (direct proportionality to the linear size), surface kernel (direct proportionality to the surface), mass kernel (direct proportionality to the volume or mass). Aggregation or coagulation are not part of the model. The approximation method works well for all four kernels and all integer values of n, and yields analytical formulas for the average and the most important moments (zeroth, first, and the one that is relevant for the kernel function) of the nanoparticle size distribution at every stage of the process. The approximation is validated against stochastic simulations using the Gillespie algorithm within the framework of the continuous time discrete state approach to stochastic kinetics. The comparison shows that the obtained analytical formulas are applicable for all practically important cases of the model and provide a way to interpret the dependence of average nanoparticle size on the ratio of the rate constants of nucleation and particle growth.

Experimenting with fog: Environmental infrastructures, infrastructuring environments, and the infrastructure of infrastructure

In coastal Peru, conservationists and scientists attend to fog as something that may be captured and transformed into water. This article draws on ethnographic fieldwork among Limeñan conservationists who tapped into this atmospheric phenomenon as an alternative water source for use in fog oasis ecosystem reforestation. As I demonstrate, experimental engagements with fog had reconfigured conservationists’ and other experimenters’ understanding about the connections between the atmosphere, vegetation, and the underground, thereby bringing into view a hitherto imperceptible environmental infrastructure of groundwater production. The infrastructural potentials of the landscape were in turn foregrounded by the conservationists through comparisons with other geographies well-known for their capacity to produce water. Against this backdrop, the article argues for renewed attention to the infrastructural as a comparative effect resulting from simultaneous fore/backgrounding. Rather than mere grounds for second-order processes, infrastructural relations can be understood as situated between foreground and background. As environmental calamities complicate the infrastructure–environment nexus, it is no longer clear what infrastructures consist of, nor what they are capable of doing. In this context, an understanding of infrastructures as comparative effects is useful for describing and speculatively amplifying potentially more sustainable infrastructural alternatives.

Comparing Results from Unobserved Components Model and Hodrick-Prescott Filter of Output-Gap in Barbados

An important macro-economic issue of developed and developing countries is how best to decompose an economic time series into permanent (trend) and transitory (cycle) components. The issue is vital in empirical macroeconomics since, among other things, it relates to how one can estimate the output gap-the deviation of an economy's output from its potential or trend output. This paper considers how well the unobserved components model and the Hodrick Prescott (HP) filter decomposes real gross domestic product (GDP) in a small island developing state, the state of Barbados. The correlated unobserved components model for Barbados studied in the Agbeyegbe (2020) is modified to allow a second-order Markov trend. The effect of this modification is to make it possible to recover the HP trend as a particular case. The paper then compares several methods useful for trend decomposition of real GDP in Barbados. The competing methods are variants of two widely used trend-cycle decompositions of GDP that give markedly different estimates. Namely, methods based on the unobserved components model (UC) and the HP filter. The correlated unobserved components model produces smaller output gaps in amplitude, whereas the HP filter generates significant and persistent cycles. More specifically, the methods are: (i) the HP filter; (ii) an augmented HP filter (HP-AR), that allows for cyclical components to be serially correlated, introduced by Grant and Chan (2017b); (iii) the correlated unobserved components model (UCUR), without a break; (iv) the correlated unobserved components model (UCUR-t), with a break at time t; and (v) a correlated unobserved components model that allows for a second-order Markov trend process UCUR-2M. The result shows that for Barbados, with data covering the period 1967-2017, the correlated unobserved components model that allows for a break in trend fits the data better than the HP specification. These results are significant from a policy perspective. Knowing the correct duration of the business cycle is essential to providing appropriate recommendations; the result argues against the use of HP-filter in analyzing Barbados' business cycle. The result also finds that for Barbados, it is empirically important to correlate permanent and transitory shocks. By ignoring this correlation, researchers risk providing a misleading analysis of how the Barbadian economy works.