Time-dependent State Research Articles

Deep Reinforcement Learning-Assisted Teaching Strategy for Industrial Robot Manipulator

This paper introduces an innovative algorithm aimed at enhancing robot learning using dynamic trajectory modeling and time-dependent state analysis. By integrating reinforcement learning (RL) and trajectory planning, the proposed approach enhances the robot’s adaptability in diverse environments and tasks. The framework begins with a comprehensive analysis of the robot’s operational space, focusing on Cartesian coordinates and configuration systems. By modeling trajectories and states within these systems, the robot achieves sequential tracking of arbitrary states, facilitating efficient task execution in various scenarios. Experimental results demonstrate the algorithm’s efficacy in manipulation tasks and path planning in dynamic environments. By integrating dynamic trajectory modeling and time-dependent state analysis, the robot’s adaptability and performance improve significantly, enabling precise task execution in complex environments. This research contributes to advancing robot learning methodologies, particularly in human–robot interaction scenarios, promising applications in manufacturing, healthcare, and logistics.

Dynamics of a small quantum system open to a bath with thermostat.

We investigate dynamics of a small quantum system open to a bath with thermostat. We introduce another bath, called a superbath, weakly coupled with the bath to provide it with a thermostat, which has either the Lindblad or Redfield type. We treat the interaction between the system and bath via a rigorous perturbation theory. Due to the thermostat, the bath behaves dissipative and stochastic, for which the usual Born-Markov assumption is not needed. We consider a specific example of a harmonic oscillator system of interest and a photonic bath in a large container, and a superbath of the Caldeira-Legget oscillators distributed on the inner surface of the container. After taking the trace over the superbath states, we use the P representation for the total harmonic system of the system and bath. We derive the reduced time-evolution equationfor the system by explicitly finding the correlation between the system and bath beyond the product state that was not obtainable in the previous theory for the system and bath isolated from environment, and marginalizing bath degrees of freedom. Remarkably, the associated dynamic equationfor the system density matrix is of the same form as the Redfield master equationwith different coefficients depending on thermostat used. We find the steady state does not depend on the thermostat but the time-dependent state does, which agrees with common expectation. We expect to apply our theory to general systems. Unlike the usual quantum master equations, our reduced dynamics allows investigation for time-dependent protocols, and nonequilibrium quantum stochastic dynamics will be investigated in the future.

Nonreciprocal nonlinear responses in moving charge density waves

The incommensurate charge density wave states (CDWs) can exhibit steady motion in the flow limit after depinning, behaving as a nonequilibrium system with time-dependent states. Since the moving CDW, like an electric current, breaks both time-reversal and inversion symmetries, one may speculate the emergence of nonreciprocal nonlinear responses from such motion. However, the moving CDW order parameter is intrinsically time-dependent in the lab frame, and it is known to be challenging to evaluate the responses of such a time-varying system. In this work, following the principle of Galilean relativity, we resolve this time-dependent hard problem in the lab frame by mapping the system to the comoving frame with static CDW states through the Galilean transformation. We explicitly show that the nonreciprocal nonlinear responses would be generated by the movement of CDW states through violating Galilean relativity.

Dynamics of Active Defects on the Anisotropic Surface of an Ellipsoidal Droplet

We investigate the steady state of an ellipsoidal active nematic shell using experiments and numerical simulations. We create the shells by coating microsized ellipsoidal droplets with a protein-based active cytoskeletal gel, thus obtaining ellipsoidal core-shell structures. This system provides the appropriate conditions of confinement and geometry to investigate the impact of nonuniform curvature on an orderly active nematic fluid that features the minimum number of defects required by topology. We identify new time-dependent states where topological defects periodically oscillate between translational and rotational regimes, resulting in the spontaneous emergence of chirality. Our simulations of active nematohydrodynamics demonstrate that, beyond topology and activity, the dynamics of the active material are profoundly influenced by the local curvature and viscous anisotropy of the underlying droplet, as well as by external hydrodynamic forces stemming from the self-sustained rotational motion of defects. These results illustrate how the incorporation of curvature gradients into active nematic shells orchestrates remarkable spatiotemporal patterns, offering new insights into biological processes and providing compelling prospects for designing bioinspired micromachines. Published by the American Physical Society 2024

Spectral phase pulse shaping reduces ground state depletion in high-order harmonic generation

High-order harmonic generation (HHG) has become an indispensable process for generating attosecond pulse trains and single attosecond pulses used in the observation of nuclear and electronic motion. As such, improved control of the HHG process is desirable, and one such possibility for this control is through the use of structured laser pulses. We present numerical results from solving the one-dimensional time-dependent Schrödinger equation for HHG from hydrogen using Airy and Gaussian pulses that differ only in their spectral phase. Airy pulses have identical power spectra to Gaussian pulses, but different spectral phases and temporal envelopes. We show that the use of Airy pulses results in less ground state depletion compared to the Gaussian pulse, while maintaining harmonic yield and cutoff. Our results demonstrate that Airy pulses with higher intensity can produce similar HHG spectra to lower intensity Gaussian pulses without depleting the ground state. The different temporal envelopes of the Gaussian and Airy pulses lead to changes in the dynamics of the HHG process, altering the time-dependence of the ground state population and the emission times of the high harmonics.Graphical abstractHigh-order harmonic generation (HHG) using an Airy pulse with a third order spectral phase results in less ground state depletion, but similar harmonic yield, compared to a Gaussian pulse. Top – schematic depiction of the 3-step HHG process for different intensity pulses. Bottom left – time-dependent ground state populations for Gaussian pulses showing that a more intense pulse causes more ground state depletion. Bottom middle – final ground state populations for Airy and Gaussian pulses as a function of intensity showing that Airy pulses result in less ground state depletion for a given intensity. Bottom right – HHG spectra for a more intense Airy pulse and a less intense Gaussian pulse exhibit similar shapes, magnitudes, and plateau cutoff values

A formulation of quantum fluid mechanics and trajectories

A formalism of classical mechanics is given for time-dependent many-body states of quantum mechanics, describing both fluid flow and point mass trajectories. The familiar equations of energy, motion, and those of Lagrangian mechanics are obtained. An energy and continuity equation is demonstrated to be equivalent to the real and imaginary parts of the time dependent Schrödinger equation, respectively, where the Schrödinger equation is in density matrix form. For certain stationary states, using Lagrangian mechanics and a Hamiltonian function for quantum mechanics, equations for point-mass trajectories are obtained. For 1-body states and fluid flows, the energy equation and equations of motion are the Bernoulli and Euler equations of fluid mechanics, respectively. Generalizations of the energy and Euler equations are derived to obtain equations that are in the same form as they are in classical mechanics. The fluid flow type is compressible, inviscid, irrotational, with the nonclassical element of local variable mass. Over all space mass is conserved. The variable mass is a necessary condition for the fluid flow to agree with the zero orbital angular momentum for s states of hydrogen. Cross flows are examined, where velocity directions are changed without changing the kinetic energy. For one-electron atoms, the velocity modification gives closed orbits for trajectories, and mass conservation, vortexes, and density stratification for fluid flows. For many body states, under certain conditions, and by hypotheses, Euler equations of orbital-flows are obtained. One-body Schrödinger equations that are a generalization of the Hartree–Fock equations are also obtained. These equations contain a quantum Coulomb’s law, involving the 2-body pair function of reduced density matrix theory that replace the charge densities.

Study on the suspending mechanism of gangue particle in coal-based solid waste slurry

In China's coal mine backfill mining projects, certain mines demonstrate an extensive filling distance that exceeds 3000 m. However, there are few researches concerning the theoretical underpinnings for slurry long-distance pipeline transportation. Gangue particles suspending in filling slurry is the prerequisite for successful long-distance pipeline transportation. This paper conducts theoretical researches on the heightened sensitivity issue of particle settling within coal-based solid waste filling slurry (CSWFS) for long-distance pipeline transportation, which can easily lead to unstable slurry concentration then pipe blockage or bursting accidents. The mechanical model for particle settling and critical non-settling particle diameter for long-distance pipeline transportation are developed based on the "solid-liquid two-phase carrier suspension fluid", and reveal the intrinsical mechanism of particle settling within CSWFS for long-distance pipeline transportation. Through the calculation of the mechanical model for critical non-settling particle diameter and particle settling, coupled with the particle diameter screening experiment, the value of critical non-settling particle diameter is determined to be 0.0067 m, and the density of solid-liquid two-phase carrier suspension fluid is 1712.37 kg/m3. The CSWFS is classified as a semi-stable slurry, lacking time-dependent suspending state required for long-distance pipeline transportation, which could lead to pipe blockage accidents. Further research into effective methods is urgently required to ensure adequate safety and adaptability for long-distance pipeline transportation of CSWFS.

Time-Dependent Extension of Grimme's Continuous Chirality Measure for Electronic Chirality Flips in Femto- and Attosecond Time Domains.

Grimme's Continuous Chirality Measure ( ) was developed for comparisons of the chirality of the electronic wave functions of molecules, typically in their ground states. For example, , and for alanine, hydrogen-peroxide, and for achiral molecules, respectively. Well-designed laser pulses can excite achiral molecules from the electronic ground state to time-dependent chiral superposition states, with chirality flips in the femto- or even attosecond (fs or as) time domains. Here we provide a time-dependent extension of Grimme's for trailing the electronic chirality flips. As examples, we consider two laser driven electronic wavefunctions which represent flips between opposite electronic enantiomers of oriented NaK within and . The corresponding vary respectively from or from to , and back.

Quantization of resistivity as consequence of symmetry invariance

The Schrödinger equation for a spinless electron under the influence of a constant electromagnetic field is analyzed based on the conserved operators of the system when the magnetic field is described by Landau’s gauge. For this specific situation, the Lorentz force can be recovered if two conserved generalized momentum operators are considered: one along the x-axis and the second along the y-axis. From the general solution obtained, a time-dependent ground state is constructed characterized by quantized resistivity proportional to integer multiples of von Klitzing’s constant when an invariance condition under a unitary transform is satisfied.

Finite-Time Dynamics of an Entanglement Engine: Current, Fluctuations and Kinetic Uncertainty Relations.

Entanglement engines are autonomous quantum thermal machines designed to generate entanglement from the presence of a particle current flowing through the device. In this work, we investigate the functioning of a two-qubit entanglement engine beyond the steady-state regime. Within a master equation approach, we derive the time-dependent state, the particle current, as well as the associated current correlation functions. Our findings establish a direct connection between coherence and internal current, elucidating the existence of a critical current that serves as an indicator for entanglement in the steady state. We then apply our results to investigate kinetic uncertainty relations (KURs) at finite times. We demonstrate that there is more than one possible definition for KURs at finite times. Although the two definitions agree in the steady-state regime, they lead to different parameter ranges for violating KUR at finite times.

Matrix product study of spin fractionalization in the one-dimensional Kondo insulator

The Kondo lattice is one of the classic examples of strongly correlated electronic systems. We conduct a controlled study of the Kondo lattice in one dimension, highlighting the role of excitations created by the composite fermion operator. Using time-dependent matrix product state methods, we compute various correlation functions and contrast them with both large-N mean-field theory and the strong-coupling expansion. We show that the composite fermion operator creates long-lived, charge-e and spin-1/2 excitations, which cover the low-lying single-particle excitation spectrum of the system. Furthermore, spin excitations can be thought to be composed of such fractionalized quasiparticles with a residual interaction which tend to disappear at weak Kondo coupling. Published by the American Physical Society 2024

Visible and Red Light-Triggered Anticancer Profile of a Ferrocene-Re(I)-Tricarbonyl Conjugate: Experimental and Theoretical Studies.

We have red-shifted the light absorbance property of a Re(I)-tricarbonyl complex via distant conjugation of a ferrocene moiety and developed a novel complex ReFctp, [Re(Fctp)(CO)3Cl], where Fctp = 4'-ferrocenyl-2,2':6',2″-terpyridine. ReFctp showed green to red light absorption ability and blue emission, indicating its potential for photodynamic therapy (PDT) application. The conjugation of ferrocene introduced ferrocene-based transitions, which lie at a higher wavelength within the PDT therapeutic window. The time-dependent density functional theory and excited state calculations revealed an efficient intersystem crossing for ReFctp, which is helpful for PDT. ReFctp elicited both PDT type I and type II pathways for reactive oxygen species (ROS) generation and facilitated NADH (1,4-dihydro-nicotinamide adenine dinucleotide) oxidation upon exposure to visible light. Importantly, ReFctp showed effective penetration through the layers of clinically relevant 3D multicellular tumor spheroids and localized primarily in mitochondria (Pearson's correlation coefficient, PCC = 0.65) of A549 cancer cells. ReFctp produced more than 20 times higher phototoxicity (IC50 ∼1.5 μM) by inducing ROS generation and altering mitochondrial membrane potential in A549 cancer cells than the nonferrocene analogue Retp, [Re(CO)3(tp)Cl], where tp = 2,2':6',2″-terpyridine. ReFctp induced apoptotic mode of cell death with a notable photocytotoxicity index (PI, PI = IC50dark/IC50light) and selectivity index (SI, SI = normal cell's IC50dark/cancer cell's IC50light) in the range of 25-33.

Controlling chaos using edge computing hardware

Machine learning provides a data-driven approach for creating a digital twin of a system – a digital model used to predict the system behavior. Having an accurate digital twin can drive many applications, such as controlling autonomous systems. Often, the size, weight, and power consumption of the digital twin or related controller must be minimized, ideally realized on embedded computing hardware that can operate without a cloud-computing connection. Here, we show that a nonlinear controller based on next-generation reservoir computing can tackle a difficult control problem: controlling a chaotic system to an arbitrary time-dependent state. The model is accurate, yet it is small enough to be evaluated on a field-programmable gate array typically found in embedded devices. Furthermore, the model only requires 25.0 ±7.0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\pm 7.0$$\\end{document} nJ per evaluation, well below other algorithms, even without systematic power optimization. Our work represents the first step in deploying efficient machine learning algorithms to the computing “edge.”

Energy landscape analysis and time-series clustering analysis of patient state multistability related to rheumatoid arthritis drug treatment: The KURAMA cohort study.

Rheumatoid arthritis causes joint inflammation due to immune abnormalities, resulting in joint pain and swelling. In recent years, there have been considerable advancements in the treatment of this disease. However, only approximately 60% of patients achieve remission. Patients with multifactorial diseases shift between states from day to day. Patients may remain in a good or poor state with few or no transitions, or they may switch between states frequently. The visualization of time-dependent state transitions, based on the evaluation axis of stable/unstable states, may provide useful information for achieving rheumatoid arthritis treatment goals. Energy landscape analysis can be used to quantitatively determine the stability/instability of each state in terms of energy. Time-series clustering is another method used to classify transitions into different groups to identify potential patterns within a time-series dataset. The objective of this study was to utilize energy landscape analysis and time-series clustering to evaluate multidimensional time-series data in terms of multistability. We profiled each patient's state transitions during treatment using energy landscape analysis and time-series clustering. Energy landscape analysis divided state transitions into two patterns: "good stability leading to remission" and "poor stability leading to treatment dead-end." The number of patients whose disease status improved increased markedly until approximately 6 months after treatment initiation and then plateaued after 1 year. Time-series clustering grouped patients into three clusters: "toward good stability," "toward poor stability," and "unstable." Patients in the "unstable" cluster are considered to have clinical courses that are difficult to predict; therefore, these patients should be treated with more care. Early disease detection and treatment initiation are important. The evaluation of state multistability enables us to understand a patient's current state in the context of overall state transitions related to rheumatoid arthritis drug treatment and to predict future state transitions.

Nuclear Quantum Effects on Nonadiabatic Dynamics of a Green Fluorescent Protein Chromophore Analogue: Ring-Polymer Surface-Hopping Simulation.

Herein, we have used the "on-the-fly" ring-polymer surface-hopping simulation method with the centroid approximation (RPSH-CA), in combination with the multireference OM2/MRCI electronic structure calculations to study the photoinduced dynamics of a green fluorescent protein (GFP) chromophore analogue in the gas phase, i.e., o-HBI, at 50, 100, and 300 K with 1, 5, 10, and 15 beads (3600 1 ps trajectories). The electronic structure calculations identified five new minimum-energy conical intersection (MECI) structures, which, together with the previous one, play crucial roles in the excited-state decay dynamics of o-HBI. It is also found that the excited-state intramolecular proton transfer (ESIPT) occurs in an ultrafast manner and is completed within 20 fs in all the simulation conditions because there is no barrier associated with this ESIPT process in the S1 state. However, the other excited-state dynamical results are strongly related to the number of beads. At 50 and 100 K, the nuclear quantum effects (NQEs) are very important; therefore, the excited-state dynamical results change significantly with the bead number. For example, the S1 decay time deduced from time-dependent state populations becomes longer as the bead number increases. Nevertheless, an essentially convergent trend is observed when the bead number is close to 10. In contrast, at 300 K, the NQEs become weaker and the above dynamical results converge very quickly even with 1 bead. Most importantly, the NQEs seriously affect the excited-state decay mechanism of o-HBI. At 50 and 100 K, most trajectories decay to the S0 state via perpendicular keto MECIs, whereas, at 300 K, only twisted keto MECIs are responsible for the excited-state decay. The present work not only comprehensively explores the temperature-dependent photoinduced dynamics of o-HBI, but also demonstrates the importance and necessity of NQEs in nonadiabatic dynamics simulations, especially at relatively low temperatures.

Role of interactions in nonequilibrium transformations.

For arbitrary nonequilibrium transformations in complex systems, we show that the distance between the current state and a target state can be decomposed into two terms: one corresponding to an independent estimate of the distance, and another corresponding to interactions, quantified using the relative mutual information between the variables. This decomposition is a special case of a more general decomposition involving successive orders of correlation or interactions among the degrees of freedom of the system. To illustrate its practical significance, we study the thermal relaxation of two interacting, optically trapped colloidal particles, where increasing pairwise interaction strength is shown to prolong the longevity of the time-dependent nonequilibrium state. Additionally, we study a system with both pairwise and triplet interactions, where our approach identifies their distinct contributions to the transformation. In more general setups where it is possible to control the strength of different orders of interactions, our findings provide a way to disentangle their effects and identify interactions that facilitate the transformation.

Controlling the charge-transfer dynamics of two-level systems around avoided crossings.

Two-level quantum systems are fundamental physical models that continue to attract growing interest due to their crucial role as a building block of quantum technologies. The exact analytical solution of the dynamics of these systems is central to control theory and its applications, such as that to quantum computing. In this study, we reconsider the two-state charge transfer problem by extending and using a methodology developed to study (pseudo)spin systems in quantum electrodynamics contexts. This approach allows us to build a time evolution operator for the charge transfer system and to show new opportunities for the coherent control of the system dynamics, with a particular emphasis on the critical dynamic region around the transition state coordinate, where the avoided crossing of the energy levels occurs. We identify and propose possible experimental implementations of a class of rotations of the charge donor (or acceptor) that endow the electronic coupling matrix element with a time-dependent phase that can be employed to realize controllable coherent dynamics of the system across the avoided level crossing. The analogy of these rotations to reference frame rotations in generalized semiclassical Rabi models is discussed. We also show that the physical rotations in the charge-transfer systems can be performed so as to implement quantum gates relevant to quantum computing. From an exquisitely physical-mathematical viewpoint, our approach brings to light situations in which the time-dependent state of the system can be obtained without resorting to the special functions appearing in the Landau-Zener approach.

Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions

A family of exactly solvable quantum square wells with discrete coordinates and with certain non-stationary Hermiticity-violating Robin boundary conditions is proposed and studied. Manifest non-Hermiticity of the model in conventional Hilbert space Hfriendly is required to coexist with the unitarity of system in another, ad hoc Hilbert space Hphysical . Thus, quantum mechanics in its non-Hermitian interaction picture (NIP) representation is to be used. We must construct the time-dependent states (say, ψ(t)) as well as the time-dependent observables (say, Λ(t)). Their evolution in time is generated by the operators denoted, here, by the respective symbols G(t) (a Schrödinger-equation generator) and Σ(t) (a Heisenberg-equation generator, a.k.a. quantum Coriolis force). The unitarity of evolution in Hphysical is then guaranteed by the reality of spectrum of the energy observable alias Hamiltonian H(t) = G(t) + Σ(t). The applicability of these ideas is illustrated via an N by N matrix model. At N = 2, closed formulae are presented not only for the measurable instantaneous energy spectrum but also for all of the eligible time-dependent physical inner-product metrics Θ(N=2)(t), for the related Dyson maps Ω(N=2)(t), for the Coriolis force Σ(N=2)(t) as well as, in the very ultimate step of the construction, for the truly nontrivial Schrödinger-equation generator G (N=2)(t).

Fixed-flux Rayleigh–Bénard convection in doubly periodic domains: generation of large-scale shear

This work studies two-dimensional fixed-flux Rayleigh–Bénard convection with periodic boundary conditions in both horizontal and vertical directions and analyses its dynamics using numerical continuation, secondary instability analysis and direct numerical simulation. The fixed-flux constraint leads to time-independent elevator modes with a well-defined amplitude. Secondary instability of these modes leads to tilted elevator modes accompanied by horizontal shear flow. For $Pr=1$ , where $Pr$ is the Prandtl number, a subsequent subcritical Hopf bifurcation leads to hysteresis behaviour between this state and a time-dependent direction-reversing state, followed by a global bifurcation leading to modulated travelling waves without flow reversal. Single-mode equations reproduce this moderate Rayleigh number behaviour well. At high Rayleigh numbers, chaotic behaviour dominated by modulated travelling waves appears. These transitions are characteristic of high wavenumber elevator modes since the vertical wavenumber of the secondary instability is linearly proportional to the horizontal wavenumber of the elevator mode. At a low $Pr$ , relaxation oscillations between the conduction state and the elevator mode appear, followed by quasi-periodic and chaotic behaviour as the Rayleigh number increases. In the high $Pr$ regime, the large-scale shear weakens, and the flow shows bursting behaviour that can lead to significantly increased heat transport or even intermittent stable stratification.

From the DeGroot Model to the DeGroot-Non-Consensus Model: The Jump States and the Frozen Fragment States

Non-consensus phenomena are widely observed in human society, but more attention is paid to consensus phenomena. One famous consensus model is the DeGroot model, and there are a series of outstanding works derived from it. By introducing the cognition bias, resulting in over-confidence and under-confidence in the DeGroot model, we propose a non-consensus model, namely the DeGroot-Non-Consensus model. It bridges consensus phenomena and non-consensus phenomena. While different in meaning, the new opinion model can reproduce the DeGroot model’s behaviors and supply a series of interesting non-consensus states. We find frozen fragment states for the over-confident population and time-dependent states for strong interaction strength. In frozen fragment states, the population is polarized into opinion clusters formed by extremists. In time-dependent states, agents jump between two opinions that only differ in the sign, which provides a possible explanation for the swing in opinions in elections and the fluctuations in open questions in the absence of external information. All of these states are summarized in the phase diagrams of the self-confidence and the interaction strength plane. Moreover, the transition scenarios along different parameter paths are studied. Meanwhile, the influence of the nodes’ degree is illustrated in the phase diagrams and the relationship is given. The finite size effect is found in the not quite over-confident population. An interesting phenomenon for small population sizes is that neutral populations with large opinion variance are robust to the fluctuations induced by a finite population size.