arXiv subjects

Kai Du

Publications and source records attributed to Kai Du.

At least 37 records · Page 2Linked to original sources

arXiv2025

Self-interacting approximation to McKean-Vlasov long-time limit: a Markov chain Monte Carlo method

For a certain class of McKean-Vlasov processes, we introduce proxy processes that substitute the mean-field interaction with self-interaction, employing a weighted occupation measure. Our study encompasses two key achievements. First, we demonstrate the ergodicity of the self-interacting dynamics, under broad conditions, by applying the reflection coupling method. Second, in scenarios where the drifts are negative intrinsic gradients of convex mean-field potential functionals, we use entropy and functional inequalities to demonstrate that the stationary measures of the self-interacting processes approximate the invariant measures of the corresponding McKean-Vlasov processes. As an application, we show how to learn the optimal weights of a two-layer neural network by training a single neuron.

math.PR↗

arXiv2025

Well-posedness of the obstacle problem for stochastic nonlinear diffusion equations: an entropy formulation

In this paper, we establish the existence, uniqueness and stability results for the obstacle problem associated with a degenerate nonlinear diffusion equation perturbed by conservative gradient noise. Our approach revolves round introducing a new entropy formulation for stochastic variational inequalities. As a consequence, we obtain a novel well-posedness result for the obstacle problem of deterministic porous medium equations with nonlinear reaction terms.

math.PR↗

arXiv2025

Universal Superconductivity in FeTe and All-Iron-Based Ferromagnetic Superconductor Heterostructures

Ferromagnetism (FM) and superconductivity (SC) are two of the most famous macroscopic quantum phenomena. However, nature normally does not allow SC and FM to coexist without significant degradation. Here, we introduce the first fully iron-based SC/FM heterostructures, composed of Fe(Te,Se) and Fe3GeTe2, and show that in this platform strong FM and high-temperature SC robustly coexist. We subsequently discover that chemical proximity effect from neighboring layers can universally drive the otherwise non-superconducting FeTe films into a SC state. This suggests that the ground state of FeTe is so close to the SC state that it could be driven in and out of the SC state with various other perturbations. Altogether, this shows that Fe-Te-based heterostructures provide a unique opportunity to manipulate magnetism, superconductivity and topological physics, paving the way toward new superconducting technologies.

cond-mat.supr-con↗

arXiv2024

A structure-preserving collisional particle method for the Landau kinetic equation

In this paper, we propose and implement a structure-preserving stochastic particle method for the Landau equation. The method is based on a particle system for the Landau equation, where pairwise grazing collisions are modeled as diffusion processes. By exploiting the unique structure of the particle system and a spherical Brownian motion sampling, the method avoids additional temporal discretization of the particle system, ensuring that the discrete-time particle distributions exactly match their continuous-time counterparts. The method achieves $O(N)$ complexity per time step and preserves fundamental physical properties, including the conservation of mass, momentum and energy, as well as entropy dissipation. It demonstrates strong long-time accuracy and stability in numerical experiments. Furthermore, we also apply the method to the spatially non-homogeneous equations through a case study of the Vlasov--Poisson--Landau equation.

math.NA↗

arXiv2024

Directionally asymmetric nonlinear optics in planar chiral MnTiO$_3$

Planar chiral structures possess a two dimensional handedness that is associated with broken mirror symmetry. Such motifs span vast length scales; examples include certain pinwheel molecules, nautilus shells, cyclone wind patterns and spiral galaxies. Although pervasive in nature, it has only recently been found that condensed matter systems can exhibit a form of planar chirality through toroidal arrangements of electric dipoles, known as ferro-rotational (FR) order. A key characteristic of such order is that enantiomorph conversion occurs when the solid is flipped by 180 degrees about an in-plane axis. Consequently, ferro-rotationally ordered materials may exhibit directionally asymmetric response functions, even while preserving inversion and time-reversal symmetry. Such an effect, however, has yet to be observed. Using second harmonic interferometry, we show here that when circularly polarized light is incident on MnTiO$_3$, the generated nonlinear signal exhibits directional asymmetry. Depending on whether the incident light is parallel or anti-parallel to the FR axis, we observe a different conversion efficiency of two right (left) circularly polarized photons into a frequency-doubled left (right) circularly polarized photon. Our work uncovers a fundamentally new optical effect in ordered solids and opens up the possibility for developing novel nonlinear and directionally asymmetric optical devices.

physics.optics↗

arXiv2024

A collision-oriented interacting particle system for Landau-type equations and the molecular chaos

We propose a collision-oriented particle system to approximate a class of Landau-type equations. This particle system is formally derived from a particle system with random collisions in the grazing regime, and happens to be a special random batch system with random interaction in the diffusion coefficient. The difference from usual random batch systems with random interaction in the drift is that the batch size has to be $p=2$. We then analyze the convergence rate of the proposed particle system to the Landau-type equations using the tool of relative entropy, assuming that the interaction kernels are regular enough. A key aspect of our approach is the gradient estimates of logarithmic densities, applied to both the Landau-type equations and the particle systems. Compared to existing particle systems for the approximation of Landau-type equations, our proposed system not only offers a more intrinsic reflection of the underlying physics but also reduces the computational cost to $O(N)$ per time step when implemented numerically.

math.PR↗

arXiv2024

Empirical approximation to invariant measures of mean-field Langevin dynamics

This paper is concerned with the approximation to invariant measures for Langevin dynamics of McKean--Vlasov type. Under dissipativity and Lipschitz conditions, we prove that the empirical measures of both the mean-field and self-interacting Langevin dynamics converge to the invariant measure in the Wasserstein distance. Numerical experiments are conducted to illustrate theoretical results.

math.PR↗

arXiv2024

Kibble-Zurek mechanism of Ising domains

The formation of topological defects after a symmetry-breaking phase transition is an overarching phenomenon that encodes rich information about the underlying dynamics. Kibble-Zurek mechanism (KZM), which describes these nonequilibrium dynamics, predicts defect densities of these second-order phase transitions driven by thermal fluctuations. It has been verified as a successful model in a wide variety of physical systems, finding applications from structure formation in the early universe to condensed matter systems. However, whether topologically-trivial Ising domains, one of the most common and fundamental types of domains in condensed matter systems, also obey the KZM has never been investigated in the laboratory. We examined two different kinds of three-dimensional (3D) structural Ising domains: clockwise (CW)/counter-clockwise (CCW) ferro-rotation domains in NiTiO3 and up/down polar domains in BiTeI. While the KZM slope of ferro-rotation domains in NiTiO3 agrees well with the prediction of the 3D Ising model, the KZM slope of polar domains in BiTeI surprisingly far exceeds the theoretical limit, setting an exotic example where possible weak long-range dipolar interactions play a critical role in steepening the KZM slope of non-topological quantities. Our results demonstrate the validity of KZM for Ising domains and reveal an enhancement of the power-law exponent and a possible reduction of the dynamic critical exponent z for transitions with long-range interactions.

cond-mat.stat-mech↗

arXiv2024

Particle approximation for a conditional McKean--Vlasov stochastic differential equation

In this paper, we construct a type of interacting particle systems to approximate a class of stochastic different equations whose coefficients depend on the conditional probability distributions of the processes given partial observations. After proving the well-posedness and regularity of the particle systems, we establish a quantitative convergence result for the empirical measures of the particle systems in the Wasserstein space, as the number of particles increases. Moreover, we discuss an Euler--Maruyama scheme of the particle system and validate its strong convergence. A numerical experiment is conducted to illustrate our results.

math.PR↗

arXiv2024

Integration of cognitive tasks into artificial general intelligence test for large models

During the evolution of large models, performance evaluation is necessarily performed to assess their capabilities and ensure safety before practical application. However, current model evaluations mainly rely on specific tasks and datasets, lacking a united framework for assessing the multidimensional intelligence of large models. In this perspective, we advocate for a comprehensive framework of cognitive science-inspired artificial general intelligence (AGI) tests, aimed at fulfilling the testing needs of large models with enhanced capabilities. The cognitive science-inspired AGI tests encompass the full spectrum of intelligence facets, including crystallized intelligence, fluid intelligence, social intelligence, and embodied intelligence. To assess the multidimensional intelligence of large models, the AGI tests consist of a battery of well-designed cognitive tests adopted from human intelligence tests, and then naturally encapsulates into an immersive virtual community. We propose increasing the complexity of AGI testing tasks commensurate with advancements in large models and emphasizing the necessity for the interpretation of test results to avoid false negatives and false positives. We believe that cognitive science-inspired AGI tests will effectively guide the targeted improvement of large models in specific dimensions of intelligence and accelerate the integration of large models into human society.

cs.AI↗

arXiv2024

Giant X-ray circular dichroism in a time-reversal invariant altermagnet

X-ray circular dichroism, arising from the contrast in X-ray absorption between opposite photon helicities, serves as a spectroscopic tool to measure the magnetization of ferromagnetic materials and identify the handedness of chiral crystals. Antiferromagnets with crystallographic chirality typically lack X-ray magnetic circular dichroism because of time-reversal symmetry, yet exhibit weak X-ray natural circular dichroism. Here, we report the observation of giant natural circular dichroism in the Ni $L_3$-edge X-ray absorption of Ni$_3$TeO$_6$, a polar and chiral antiferromagnet with effective time-reversal symmetry. To unravel this intriguing phenomenon, we propose a phenomenological model that classifies the movement of photons in a chiral crystal within the same symmetry class as that of a magnetic field. The coupling of X-ray polarization with the induced magnetization yields giant X-ray natural circular dichroism, revealing the altermagnetism of Ni$_3$TeO$_6$. Our findings provide evidence for the interplay between magnetism and crystal chirality in natural optical activity. Additionally, we establish the first example of a new class of magnetic materials exhibiting circular dichroism with time-reversal symmetry.

cond-mat.str-el↗

arXiv2024

Empirical approximation to invariant measures of non-degenerate McKean-Vlasov dynamics

This paper studies the approximation of invariant measures of McKean-Vlasov dynamics with non-degenerate additive noise. While prior findings necessitated a strong monotonicity condition on the McKean-Vlasov process, we expand these results to encompass dissipative and weak interaction scenarios. Utilizing a reflection coupling technique, we prove that the empirical measures of the McKean-Vlasov process and its path-dependent counterpart can converge to the invariant measure in the Wasserstein metric. The Curie-Weiss mean-field lattice model serves as a numerical example to illustrate empirical approximation.

math.PR↗

arXiv2024

Light-induced electronic polarization in antiferromagnetic Cr2O3

In a solid, the electronic subsystem can exhibit incipient order with lower point group symmetry than the crystal lattice. External fields that couple to electronic order parameters have rarely been investigated, however, despite their potential importance to inducing exotic effects. Here, we show that when inversion symmetry is broken by the antiferromagnetic (AFM) order in Cr2O3, transmitting a linearly polarized light pulse through the crystal gives rise to an in-plane rotational symmetry breaking (from C3 to C1) via optical rectification. Using interferometric time-resolved second harmonic generation, we show that the ultrafast timescale of the symmetry reduction is indicative of a purely electronic response; the underlying spin and crystal structures remain unaffected. The symmetry-broken state exhibits a dipole moment, and its polar axis can be controlled with the incident light. Our results establish a coherent nonlinear optical protocol by which to break electronic symmetries and produce unconventional electronic effects in solids.

cond-mat.str-el↗

arXiv2023

Hydrogen-induced tunable remanent polarization in a perovskite nickelate

Materials with field-tunable polarization are of broad interest to condensed matter sciences and solid-state device technologies. Here, using hydrogen (H) donor doping, we modify the room temperature metallic phase of a perovskite nickelate NdNiO3 into an insulating phase with both metastable dipolar polarization and space-charge polarization. We then demonstrate transient negative differential capacitance in thin film capacitors. The space-charge polarization caused by long-range movement and trapping of protons dominates when the electric field exceeds the threshold value. First-principles calculations suggest the polarization originates from the polar structure created by H doping. We find that polarization decays within ~1 second which is an interesting temporal regime for neuromorphic computing hardware design, and we implement the transient characteristics in a neural network to demonstrate unsupervised learning. These discoveries open new avenues for designing novel ferroelectric materials and electrets using light-ion doping.

cond-mat.str-el↗

arXiv2023

Entropy solutions to the Dirichlet problem for nonlinear diffusion equations with conservative noise

Motivated by porous medium equations with randomly perturbed velocity field, this paper considers a class of nonlinear degenerate diffusion equations with nonlinear conservative noise in bounded domains. The existence, uniqueness and $L_{1}$-stability of non-negative entropy solutions under the homogeneous Dirichlet boundary condition are proved. The approach combines Kruzhkov's doubling variables technique with a revised strong entropy condition that is automatically satisfied by the solutions of approximate equations.

math.PR↗

arXiv2023

Counterfactual Graph Transformer for Traffic Flow Prediction

Traffic flow prediction (TFP) is a fundamental problem of the Intelligent Transportation System (ITS), as it models the latent spatial-temporal dependency of traffic flow for potential congestion prediction. Recent graph-based models with multiple kinds of attention mechanisms have achieved promising performance. However, existing methods for traffic flow prediction tend to inherit the bias pattern from the dataset and lack interpretability. To this end, we propose a Counterfactual Graph Transformer (CGT) model with an instance-level explainer (e.g., finding the important subgraphs) specifically designed for TFP. We design a perturbation mask generator over input sensor features at the time dimension and the graph structure on the graph transformer module to obtain spatial and temporal counterfactual explanations. By searching the optimal perturbation masks on the input data feature and graph structures, we can obtain the concise and dominant data or graph edge links for the subsequent TFP task. After re-training the utilized graph transformer model after counterfactual perturbation, we can obtain improved and interpretable traffic flow prediction. Extensive results on three real-world public datasets show that CGT can produce reliable explanations and is promising for traffic flow prediction.

cs.LG↗

arXiv2023

A maximum principle for progressive optimal control of mean-filed forward-backward stochastic system involving random jumps and impulse controls

In this paper, we study an optimal control problem of a mean-field forward-backward stochastic system with random jumps in progressive structure, where both regular and singular controls are considered in our formula. In virtue of the variational technology, the related stochastic maximum principle (SMP) has been obtained, and it is essentially different from that in the classical predictable structure. Specifically, there are three parts in our SMP, i.e. continuous part, jump part and impulse part, and they are respectively used to characterize the characteristics of the optimal controls at continuous time, jump time and impulse time. This shows that the progressive structure can more accurately describe the characteristics of the optimal control at the jump time. We also give two linear-quadratic (LQ) examples to show the significance of our results.

math.OC↗

arXiv2023

UAV Obstacle Avoidance by Human-in-the-Loop Reinforcement in Arbitrary 3D Environment

This paper focuses on the continuous control of the unmanned aerial vehicle (UAV) based on a deep reinforcement learning method for a large-scale 3D complex environment. The purpose is to make the UAV reach any target point from a certain starting point, and the flying height and speed are variable during navigation. In this work, we propose a deep reinforcement learning (DRL)-based method combined with human-in-the-loop, which allows the UAV to avoid obstacles automatically during flying. We design multiple reward functions based on the relevant domain knowledge to guide UAV navigation. The role of human-in-the-loop is to dynamically change the reward function of the UAV in different situations to suit the obstacle avoidance of the UAV better. We verify the success rate and average step size on urban, rural, and forest scenarios, and the experimental results show that the proposed method can reduce the training convergence time and improve the efficiency and accuracy of navigation tasks. The code is available on the website https://github.com/Monnalo/UAV_navigation.

cs.RO↗