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Wen Huang

Wen Huang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.DScond-mat.supr-conArtificial Intelligencecond-mat.mtrl-scicond-mat.str-elmath.CAmath.NTmath.PRcond-mat.mes-hallcond-mat.quant-gasMachine Learningmath.APmath.COquant-phComputationComputer VisionDistributed, Parallel, and Cluster Computingmath.FAmath.GNmath.GRmath.MGmath.OAmath.OCphysics.opticsRobotics

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Published work

53 published item(s)

preprint2026arXiv

AdaptiveLoad: Towards Efficient Video Diffusion Transformer Training

In video generation models, particularly world models, training large-scale video diffusion Transformers (such as DiT and MMDiT) poses significant computational challenges due to the extreme variance in sequence lengths within mixed-mode datasets. Existing bucket-based data loading strategies typically rely on "equal token length" constraints. This approach fails to account for the quadratic complexity of self-attention mechanisms, leading to severe load imbalance and underutilization of GPU resources. This paper proposes \textit{AdaptiveLoad}, an integrated optimization framework consisting of two core components: (1) A dual-constraint adaptive load balancing system, which eliminates long-sequence bottlenecks by simultaneously limiting memory consumption and computational load ($B \times S^p \le M_{\text{comp}}$); (2) A fused LayerNorm-Modulate CUDA kernel, which utilizes a D-tile coalesced reduction strategy to increase throughput and alleviate memory pressure. Experimental results on the Wan 2.1 world model demonstrate that our method reduces the computational imbalance rate from 39\% to 18.9\%, improves peak VRAM utilization efficiency by 22.7\%, and achieves an overall training throughput increase of 27.2\%.

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preprint2026arXiv

D-VLA: A High-Concurrency Distributed Asynchronous Reinforcement Learning Framework for Vision-Language-Action Models

The rapid evolution of Embodied AI has enabled Vision-Language-Action (VLA) models to excel in multimodal perception and task execution. However, applying Reinforcement Learning (RL) to these massive models in large-scale distributed environments faces severe systemic bottlenecks, primarily due to the resource conflict between high-fidelity physical simulation and the intensive VRAM/bandwidth demands of deep learning. This conflict often leaves overall throughput constrained by execution-phase inefficiencies. To address these challenges, we propose D-VLA, a high-concurrency, low-latency distributed RL framework for large-scale embodied foundation models. D-VLA introduces "Plane Decoupling," physically isolating high-frequency training data from low-frequency weight control to eliminate interference between simulation and optimization. We further design a four-thread asynchronous "Swimlane" pipeline, enabling full parallel overlap of sampling, inference, gradient computation, and parameter distribution. Additionally, a dual-pool VRAM management model and topology-aware replication resolve memory fragmentation and optimize communication efficiency. Experiments on benchmarks like LIBERO show that D-VLA significantly outperforms mainstream RL frameworks in throughput and sampling efficiency for billion-parameter VLA models. In trillion-parameter scalability tests, our framework maintains exceptional stability and linear speedup, providing a robust system for high-performance general-purpose embodied agents.

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preprint2026arXiv

Missing Old Logits in Asynchronous Agentic RL: Semantic Mismatch and Repair Methods for Off-Policy Correction

Asynchronous reinforcement learning improves rollout throughput for large language model agents by decoupling sample generation from policy optimization, but it also introduces a critical failure mode for PPO-style off-policy correction. In heterogeneous training systems, the total importance ratio should ideally be decomposed into two semantically distinct factors: a \emph{training--inference discrepancy term} that aligns inference-side and training-side distributions at the same behavior-policy version, and a \emph{policy-staleness term} that constrains the update from the historical policy to the current policy. We show that practical asynchronous pipelines with delayed updates and partial rollouts often lose the required historical training-side logits, or old logits. This missing-old-logit problem entangles discrepancy repair with staleness correction, breaks the intended semantics of decoupled correction, and makes clipping and masking thresholds interact undesirably. To address this issue, we study both exact and approximate correction routes. We propose three exact old-logit acquisition strategies: snapshot-based version tracking, a dedicated old-logit model, and synchronization via partial rollout interruption, and compare their system trade-offs. From the perspective of approximate correction, we focus on preserving the benefits of decoupled correction through a more appropriate approximate policy when exact old logits cannot be recovered at low cost, without incurring extra system overhead. Following this analysis, we adopt a revised PPO-EWMA method, which achieves significant gains in both training speed and optimization performance.

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preprint2026arXiv

Multiple nodal superconducting phases and order-parameter evolution in pressurized UTe$_2$

Spin-triplet superconductivity (SC) offers a unique avenue for realizing non-Abelian Majorana zero modes and thus the fault-tolerant topological quantum computation, and has attracted a broad audience for both fundamental research and potential applications. The recently discovered heavy-fermion spin-triplet superconductor candidate UTe$_2$ has sparked great interest for its ultrahigh upper critical field and reentrant SC phases in the proximity to a field-polarized magnetic state. Despite extensive studies on the phase diagrams and competing orders induced by pressure and magnetic field, limited has been known about its SC order parameters and their evolution with these control parameters, largely due to the lack of appropriate symmetry-sensitive detections. Here, we report comprehensive point-contact spectroscopy measurements of pressurized UTe$_2$ on the (0~0~1) surface. The observation of Andreev bound state strongly suggests the presence of a $p_z$ component in the SC order parameters. Quantitative analysis based on an extended Blonder-Tinkham-Klapwijk model unveils $B_{2u}$ or $B_{3u}$ as the most likely representation for both ambient and pressurized UTe$_2$, and remarkably, the multiple SC phases can be distinguished by a single parameter $\langle Δ_{z}\rangle/\langleΔ_{x(y)}\rangle$, the relative weight between the $p_z$-wave and $p_{x(y)}$-wave pairings. These findings not only impose stringent constraints on the superconducting order parameter in UTe$_2$, but also provide key spectroscopic evidence for the existence of multiple SC phases tuned through pressure.

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preprint2026arXiv

Sword: Style-Robust World Models as Simulators via Dynamic Latent Bootstrapping for VLA Policy Post-Training

The integration of Vision-Language-Action (VLA) models with World Models has gained increasing attention. One representative approach treats learned World Models as generative simulators, enabling policy optimization entirely within "imagination." However, when deployed as simulators for specific environments such as the LIBERO benchmark, existing World Models often suffer from poor generalization and long-horizon error accumulation. During closed-loop rollouts, these models are highly sensitive to initial-state perturbations; minor changes in color, illumination, and other visual factors can trigger cascading hallucinations, leading to severe blurriness or overexposure. Moreover, long-horizon error accumulation further degrades the quality and fidelity of predicted future states. These issues limit the reliability of World Models as simulators. To mitigate these problems, we propose Sword, a robust World Model framework. Our method introduces Structure-Guided Style Augmentation to disentangle the visual textures of interactive environments from task-relevant dynamics, thereby improving generalization. We further propose Dynamic Latent Bootstrapping, which maintains consistency between training and inference while keeping memory consumption low. Extensive experiments on the LIBERO benchmark show that our method significantly outperforms the baseline WoVR in terms of generalization, generation quality, robustness, fidelity, and the success rate of reinforcement-learning post-training for VLA models.

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preprint2023arXiv

Polynomial Furstenberg joinings and its applications

In this paper, a polynomial version of Furstenberg joining is introduced and its structure is investigated. Particularly, it is shown that if all polynomials are non-linear, then almost every ergodic component of the joining is a direct product of an infinity-step pro-nilsystem and a Bernoulli system. As applications, some new convergence theorems are obtained. Particularly, it is proved that if $T$ and $S$ are ergodic measure preserving transformations on a probability space $(X,{\mathcal X},μ)$ and $T$ has zero entropy, then for all $c_i\in {\mathbb Z}\setminus \{0\}$, all integral polynomials $p_j$ with $°{p_j}\ge 2$, and for all $f_i, g_j\in L^\infty(X,μ)$, $1\le i\le m$ and $1\le j\le d$, $$\lim_{N\to\infty} \frac{1}{N}\sum_{n=0}^{N-1}f_1(T^{c_1n}x)\cdots f_m(T^{c_mn}x)\cdot g_1(S^{p_1(n)}x)\cdots g_d(S^{p_d(n)}x),$$ exists in $L^2(X,μ)$, which extends the recent result by Host and Frantzikinakis. Moreover, it is shown that for an ergodic measure-preserving system $(X,{\mathcal X},μ,T)$, a non-linear integral polynomial $p$ and $f\in L^\infty(X,μ)$, the Furstenberg systems of $\big(f(T^{p(n)})x\big)_{n\in {\mathbb Z}}$ are ergodic and isomorphic to direct products of infinite-step pro-nilsystems and Bernoulli systems for almost every $x\in X$, which answers a problem by Frantzikinakis.

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preprint2023arXiv

Topological dynamical systems induced by polynomials and combinatorial consequences

Let $d\in {\mathbb N}$ and $p_i$ be an integral polynomial with $p_i(0)=0$, $1\le i\le d$. It is shown that if $S$ is piecewise syndetic in $\mathbb Z$, then $$\{(m,n)\in{\mathbb Z}^2: m+p_1(n),\ldots,m+p_d(n)\in S\}$$ is piecewise syndetic in ${\mathbb Z}^2$, which extends the result by Glasner and Furstenberg for linear polynomials. Our result is obtained by showing the density of minimal points of a dynamical system of ${\mathbb Z}^2$ action associated with the piecewise syndetic set $S$ and the polynomials $\{p_1,\ldots,p_d\}$. Moreover, it is proved that if $(X,T)$ is minimal, then for each non-empty open subset $U$ of $X$, there is $x\in U$ with $\{n\in {\mathbb Z}: T^{p_1(n)}x\in U, \ldots, T^{p_d(n)}x\in U\}$ piecewise syndetic.

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preprint2022arXiv

Solving Stackelberg Prediction Game with Least Squares Loss via Spherically Constrained Least Squares Reformulation

The Stackelberg prediction game (SPG) is popular in characterizing strategic interactions between a learner and an attacker. As an important special case, the SPG with least squares loss (SPG-LS) has recently received much research attention. Although initially formulated as a difficult bi-level optimization problem, SPG-LS admits tractable reformulations which can be polynomially globally solved by semidefinite programming or second order cone programming. However, all the available approaches are not well-suited for handling large-scale datasets, especially those with huge numbers of features. In this paper, we explore an alternative reformulation of the SPG-LS. By a novel nonlinear change of variables, we rewrite the SPG-LS as a spherically constrained least squares (SCLS) problem. Theoretically, we show that an $ε$ optimal solution to the SCLS (and the SPG-LS) can be achieved in $\tilde{O}(N/\sqrtε)$ floating-point operations, where $N$ is the number of nonzero entries in the data matrix. Practically, we apply two well-known methods for solving this new reformulation, i.e., the Krylov subspace method and the Riemannian trust region method. Both algorithms are factorization free so that they are suitable for solving large scale problems. Numerical results on both synthetic and real-world datasets indicate that the SPG-LS, equipped with the SCLS reformulation, can be solved orders of magnitude faster than the state of the art.

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preprint2020arXiv

Edge current and orbital angular momentum of chiral superfluids revisited

Cooper pairs in chiral superfluids carry quantized units of relative orbital angular momentum (OAM). Various predictions of the intrinsic OAM density or the macroscopic OAM of a two-dimensional chiral superfluid differ by several orders of magnitude, which constitute the so-called Angular Momentum Paradox. Following several previous studies, we substantiate the semiclassical Bogoliubov-de Gennes theory of the single-particle edge current and OAM in two-dimensional chiral superfluids in the BCS limit. The analysis provides a simple intuitive understanding for the vanishing of OAM for a non-p-wave chiral superfluid (such as $d+id$) confined in a rigid potential. When generalized to anisotropic chiral superconductors and three-dimensional chiral superfluids, the theory similarly returns an accurate description. We also present a detailed numerical study of the chiral phases in the BEC limit. Our study suggests that, in both BCS and BEC phases the relative OAM of the individual Cooper pairs contribute to the total OAM additively, and that in both phases the corresponding macroscopic OAM density distribution is localized at the boundary.

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preprint2020arXiv

Half-Magnetic Topological Insulator

Topological magnets are a new family of quantum materials providing great potential to realize emergent phenomena, such as quantum anomalous Hall effect and axion-insulator state. Here we present our discovery that stoichiometric ferromagnet MnBi8Te13 with natural heterostructure MnBi2Te4-(Bi2Te3)3 is an unprecedented half-magnetic topological insulator, with the magnetization existing at the MnBi2Te4 surface but not at the opposite surface terminated by triple Bi2Te3 layers. Our angle-resolved photoemission spectroscopy measurements unveil a massive Dirac gap at the MnBi2Te4 surface, and gapless Dirac cone on the other side. Remarkably, the Dirac gap (~28 meV) at MnBi2Te4 surface decreases monotonically with increasing temperature and closes right at the Curie temperature, thereby representing the first smoking-gun spectroscopic evidence of magnetization-induced topological surface gap among all known magnetic topological materials. We further demonstrate theoretically that the half-magnetic topological insulator is desirable to realize the half-quantized surface anomalous Hall effect, which serves as a direct proof of the general concept of axion electrodynamics in condensed matter systems.

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preprint2020arXiv

Half-quantum vortices on c-axis domain walls in chiral p-wave superconductors

Chiral superconductors are two-fold degenerate and domains of opposite chirality can form, separated by domain walls. There are indications of such domain formation in the quasi two-dimensional putative chiral $p$-wave superconductor Sr$_2$RuO$_4$, yet no experiment has explicitly resolved individual domains in this material. In this work, $c$-axis domain walls lying parallel to the layers in chiral $p$-wave superconductors are explored from a theoretical point of view. First, using both a phenomenological Ginzburg-Landau and a quasiclassical Bogoliubov-deGennes approach, a consistent qualitative description of the domain wall structure is obtained. While these domains are decoupled in the isotropic limit, there is a finite coupling in anisotropic systems and the domain wall can be treated as an effective Josephson junction. In the second part, the formation and structure of half-quantum vortices (HQV) on such $c$-axis domain walls are discussed.

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preprint2020arXiv

Minimal systems with finitely many ergodic measures

In this paper it is proved that if a minimal system has the property that its sequence entropy is uniformly bounded for all sequences, then it has only finitely many ergodic measures and is an almost finite to one extension of its maximal equicontinuous factor. This result is obtained as an application of a general criteria which states that if a minimal system is an almost finite to one extension of its maximal equicontinuous factor and has no infinite independent sets of length $k$ for some $k\ge 2$, then it has only finitely many ergodic measures.

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preprint2020arXiv

Polynomial mean complexity and Logarithmic Sarnak conjecture

In this paper, we reduce the logarithmic Sarnak conjecture to the $\{0,1\}$-symbolic systems with polynomial mean complexity. By showing that the logarithmic Sarnak conjecture holds for any topologically dynamical system with sublinear complexity, we provide a variant of the $1$-Fourier uniformity conjecture, where the frequencies are restricted to any subset of $[0,1]$ with packing dimension less than one.

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preprint2020arXiv

Positive entropy implies chaos along any infinite sequence

Let $G$ be an infinite countable discrete amenable group. For any $G$-action on a compact metric space $(X,ρ)$, it turns out that if the action has positive topological entropy, then for any sequence $\{s_i\}_{i=1}^{+\infty}$ with pairwise distinct elements in $G$ there exists a Cantor subset $K$ of $X$ which is Li-Yorke chaotic along this sequence, that is, for any two distinct points $x,y\in K$, one has \[\limsup_{i\to+\infty}ρ(s_i x,s_iy)>0,\ \text{and}\ \liminf_{i\to+\infty}ρ(s_ix,s_iy)=0.\]

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preprint2020arXiv

Topological characteristic factors and nilsystems

We prove that the maximal infinite step pro-nilfactor $X_\infty$ of a minimal dynamical system $(X,T)$ is the topological characteristic factor in a certain sense. Namely, we show that by an almost one to one modification of $π:X \rightarrow X_\infty$, the induced open extension $π^*:X^* \rightarrow X^*_\infty$ has the following property: for $x$ in a dense $G_δ$ set of $X^*$, the orbit closure $L_x=\overline{\mathcal{O}}((x,x,\ldots,x), T\times T^2\times \ldots \times T^d)$ is $(π^*)^{(d)}$-saturated, i.e. $L_x=((π^*)^{(d)})^{-1}(π^*)^{(d)}(L_x)$. Using results derived from the above fact, we are able to answer several open questions: (1) if $(X,T^k)$ is minimal for some $k\ge 2$, then for any $d\in {\mathbb N}$ and any $0\le j<k$ there is a sequence $\{n_i\}$ of $\mathbb Z$ with $n_i\equiv j\ (\text{mod}\ k)$ such that $T^{n_i}x\rightarrow x, T^{2n_i}x\rightarrow x, \ldots, T^{dn_i}x\rightarrow x$ for $x$ in a dense $G_δ$ subset of $X$; (2) if $(X,T)$ is totally minimal, then $\{T^{n^2}x:n\in {\mathbb Z}\}$ is dense in $X$ for $x$ in a dense $G_δ$ subset of $X$; (3) for any $d\in\mathbb N$ and any minimal system, which is an open extension of its maximal distal factor, ${\bf RP}^{[d]}={\bf AP}^{[d]}$, where the latter is the regionally proximal relation of order $d$ along arithmetic progressions.

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preprint2020arXiv

Vortex end Majorana zero modes in superconducting Dirac and Weyl semimetals

Time-reversal invariant (TRI) Dirac and Weyl semimetals in three dimensions (3D) can host open Fermi arcs and spin-momentum locking Fermi loops on the surfaces. We find that when they become superconducting with $s$-wave pairing and the doping is lower than a critical level, straight $π$-flux vortex lines terminating at surfaces with Fermi arcs or spin-momentum locking Fermi loops can realize 1D topological superconductivity and harbor Majorana zero modes at their ends. Remarkably, we find that the vortex-generation-associated Zeeman field can open (when the surfaces have only Fermi arcs) or enhance the topological gap protecting Majorana zero modes, which is contrary to the situation in superconducting topological insulators. By studying the tilting effect of bulk Dirac and Weyl cones, we further find that type-I Dirac and Weyl semimetals in general have a much broader topological regime than type-II ones. Our findings build up a connection between TRI Dirac and Weyl semimetals and Majorana zero modes in vortices.

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preprint2019arXiv

Synchronization in discrete-time, discrete-state Random Dynamical Systems

We characterize synchronization phenomenon in discrete-time, discrete-state random dynamical systems, with random and probabilistic Boolean networks as particular examples. In terms of multiplicative ergodic properties of the induced linear cocycle, we show such a random dynamical system with finite state synchronizes if and only if the Lyapunov exponent $0$ has simple multiplicity. For the case of countable state space, characterization of synchronization is provided in terms of the spectral subspace corresponding to the Lyapunov exponent $-\infty$. In addition, for both cases of finite and countable state spaces, the mechanism of partial synchronization is described by partitioning the state set into synchronized subsets. Applications to biological networks are also discussed.

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preprint2016arXiv

Analogues of Auslander-Yorke theorems for multi-sensitivity

In this paper we study multi-sensitivity and thick sensitivity for continuous surjective selfmaps on compact metric spaces. We show that multi-sensitivity implies thick sensitivity, and the converse holds true for transitive systems. Our main result is an analog of the Auslander-Yorke dichotomy theorem: a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor. Furthermore, we refine it by introducing the concept of syndetically equicontinuous points: a transitive system is either thickly sensitive or contains syndetically equicontinuous points.

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preprint2016arXiv

Auslander-Yorke dichotomy theorem, multi-sensitivity and Lyapunov numbers

In this paper we study several stronger forms of sensitivity for continuous surjective selfmaps on compact metric spaces and relations between them. The main result of the paper states that a minimal system is either multi-sensitive or an almost one-to-one extension of its maximal equicontinuous factor, which is an analog of the Auslander-Yorke dichotomy theorem. For minimal dynamical systems, we also show that all notions of thick sensitivity, multi-sensitivity and thickly syndetical sensitivity are equivalent, and all of them are much stronger than sensitivity.

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preprint2016arXiv

Concentration and limit behaviors of stationary measures

In this paper, we study limit behaviors of stationary measures of the Fokker-Planck equations associated with a system of ordinary differential equations perturbed by a class of multiplicative including additive white noises. As the noises are vanishing, various results on the invariance and concentration of the limit measures are obtained. In particular, we show that if the noise perturbed systems admit a uniform Lyapunov function, then the stationary measures form a relatively sequentially compact set whose weak$^*$-limits are invariant measures of the unperturbed system concentrated on its global attractor. In the case that the global attractor contains a strong local attractor, we further show that there exists a family of admissible multiplicative noises with respect to which all limit measures are actually concentrated on the local attractor; and on the contrary, in the presence of a strong local repeller in the global attractor, there exists a family of admissible multiplicative noises with respect to which no limit measure can be concentrated on the local repeller. Moreover, we show that if there is a strongly repelling equilibrium in the global attractor, then limit measures with respect to typical families of multiplicative noises are always concentrated away from the equilibrium. As applications of these results, an example of stochastic Hopf bifurcation is provided. Our study is closely related to the problem of noise stability of compact invariant sets and invariant measures of the unperturbed system.

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preprint2016arXiv

Dynamical compactness and sensitivity

To link the Auslander point dynamics property with topological transitivity, in this paper we introduce dynamically compact systems as a new concept of a chaotic dynamical system $(X,T)$ given by a compact metric space $X$ and a continuous surjective self-map $T:X \to X$. Observe that each weakly mixing system is transitive compact, and we show that any transitive compact M-system is weakly mixing. Then we discuss the relationships among it and other several stronger forms of sensitivity. We prove that any transitive compact system is Li-Yorke sensitive and furthermore multi-sensitive if it is not proximal, and that any multi-sensitive system has positive topological sequence entropy. Moreover, we show that multi-sensitivity is equivalent to both thick sensitivity and thickly syndetic sensitivity for M-systems. We also give a quantitative analysis for multi-sensitivity of a dynamical system.

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preprint2016arXiv

Leggett modes and multi-band superconductivity in Sr2RuO4

Sr$_2$RuO$_4$ is a prototypical multi-band superconductor with three bands crossing the Fermi level. These bands exhibit distinct dimensional characteristics, with one quasi-2D $γ$-band and two quasi-1D $α$- and $β$-bands. This leads to the expectation that the superconductivity on the $γ$-band may be only weakly Josephson-coupled to that on the other two bands. Based on an explicit microscopic weak coupling calculation appropriate for Sr$_2$RuO$_4$, we study the collective Leggett modes associated with the relative phase oscillations between the bands and show that a relatively soft Leggett mode exists due to the comparatively weaker inter-band Josephson coupling. These calculations also provide insight into why the superconducting gap magnitudes may be comparable on all three bands, despite the noticeable differences between the $γ$ and $α, β$ bands. The analyses can be readily applied to other multi-band superconductors.

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preprint2016arXiv

ManifoldOptim: An R Interface to the ROPTLIB Library for Riemannian Manifold Optimization

Manifold optimization appears in a wide variety of computational problems in the applied sciences. In recent statistical methodologies such as sufficient dimension reduction and regression envelopes, estimation relies on the optimization of likelihood functions over spaces of matrices such as the Stiefel or Grassmann manifolds. Recently, Huang, Absil, Gallivan, and Hand (2016) have introduced the library ROPTLIB, which provides a framework and state of the art algorithms to optimize real-valued objective functions over commonly used matrix-valued Riemannian manifolds. This article presents ManifoldOptim, an R package that wraps the C++ library ROPTLIB. ManifoldOptim enables users to access functionality in ROPTLIB through R so that optimization problems can easily be constructed, solved, and integrated into larger R codes. Computationally intensive problems can be programmed with Rcpp and RcppArmadillo, and otherwise accessed through R. We illustrate the practical use of ManifoldOptim through several motivating examples involving dimension reduction and envelope methods in regression.

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preprint2016arXiv

Topological correspondence of multiple ergodic averages of nilpotent group actions

Let $(X,Γ)$ be a topological system, where $Γ$ is a nilpotent group generated by $T_1,\ldots, T_d$ such that for each $T\in Γ$, $T\neq e_Γ$, $(X,T)$ is weakly mixing and minimal. For $d,k\in \mathbb{N}$, let $p_{i,j}(n), 1\le i\le k, 1\le j\le d$ be polynomials with rational coefficients taking integer values on the integers and $p_{i,j}(0)=0$. We show that if the expressions $g_i(n)=T_1^{p_{i,1}(n)}\cdots T_d^{p_{i,d}(n)}$ depends nontrivially on $n$ for $i=1,2,\cdots,k$, and for all $i\neq j\in \{1,2,\ldots,k\}$ the expressions $g_i(n)g_j(n)^{-1}$ depend nontrivially on $n$, then there is a residual set $X_0$ of $X$ such that for all $x\in X_0$ \begin{equation*} \{(g_1(n)x, g_2(n)x,\ldots, g_k(n)x)\in X^k:n\in \mathbb{Z}\} \end{equation*} is dense in $X^k$.

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preprint2015arXiv

Entropy, chaos and weak horseshoe for infinite dimensional random dynamical systems

In this paper, we study the complicated dynamics of infinite dimensional random dynamical systems which include deterministic dynamical systems as their special cases in a Polish space. Without assuming any hyperbolicity, we proved if a continuous random map has a positive topological entropy, then it contains a topological horseshoe. We also show that the positive topological entropy implies the chaos in the sense of Li-Yorke. The complicated behavior exhibiting here is induced by the positive entropy but not the randomness of the system.

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preprint2015arXiv

Integral identity and measure estimates for stationary Fokker-Planck equations

We consider a Fokker-Planck equation in a general domain in ${\mathbb{R}}^n$ with $L^p_{\mathrm{loc}}$ drift term and $W^{1,p}_{\mathrm{loc}}$ diffusion term for any $p>n$. By deriving an integral identity, we give several measure estimates of regular stationary measures in an exterior domain with respect to diffusion and Lyapunov-like or anti-Lyapunov-like functions. These estimates will be useful to problems such as the existence and nonexistence of stationary measures in a general domain as well as the concentration and limit behaviors of stationary measures as diffusion vanishes.

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preprint2015arXiv

Positive topological entropy and $Δ$-weakly mixing sets

The notion of $Δ$-weakly mixing set is introduced, which shares similar properties of weakly mixing sets. It is shown that if a dynamical system has positive topological entropy, then the collection of $Δ$-weakly mixing sets is residual in the closure of the collection of entropy sets in the hyperspace. The existence of $Δ$-weakly mixing sets in a topological dynamical system admitting an ergodic invariant measure which is not measurable distal is obtained. Moreover, Our results generalize several well known results and also answer several open questions.

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preprint2015arXiv

Sequences from zero entropy noncommutative toral automorphisms and Sarnak Conjecture

In this paper we study $C^*$-algebra version of Sarnak Conjecture for noncommutative toral automorphisms. Let $A_Θ$ be a noncommutative torus and $α_Θ$ be the noncommutative toral automorphism arising from a matrix $S\in GL(d,\mathbb{Z})$. We show that if the Voiculescu-Brown entropy of $α_Θ$ is zero, then the sequence $\{ρ(α_Θ^nu)\}_{n\in \mathbb{Z}}$ is a sum of a nilsequence and a zero-density-sequence, where $u\in A_Θ$ and $ρ$ is any state on $A_Θ$. Then by a result of Green and Tao, this sequence is linearly disjoint from the Möbius function.

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preprint2014arXiv

Affine embeddings and intersections of Cantor sets

Let $E, F\subset \R^d$ be two self-similar sets. Under mild conditions, we show that $F$ can be $C^1$-embedded into $E$ if and only if it can be affinely embedded into $E$; furthermore if $F$ can not be affinely embedded into $E$, then the Hausdorff dimension of the intersection $E\cap f(F)$ is strictly less than that of $F$ for any $C^1$-diffeomorphism $f$ on $\R^d$. Under certain circumstances, we prove the logarithmic commensurability between the contraction ratios of $E$ and $F$ if $F$ can be affinely embedded into $E$. As an application, we show that $\dim_HE\cap f(F)<\min\{\dim_HE, \dim_HF\}$ when $E$ is any Cantor-$p$ set and $F$ any Cantor-$q$ set, where $p,q\geq 2$ are two integers with $\log p/\log q\not \in \Q$. This is related to a conjecture of Furtenberg about the intersections of Cantor sets.

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preprint2014arXiv

Asymptotic pairs, stable sets and chaos in positive entropy systems

We consider positive entropy $G$-systems for certain countable, discrete, infinite left-orderable amenable groups $G$. By undertaking local analysis, the existence of asymptotic pairs and chaotic sets will be studied in connecting with the stable sets. Examples are given for the case of integer lattice groups, the Heisenberg group, and the groups of integral unipotent upper triangular matrices.

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preprint2014arXiv

Convergence to global equilibrium for Fokker-Planck equations on a graph and Talagrand-type inequalities

In recent work, Chow, Huang, Li and Zhou introduced the study of Fokker-Planck equations for a free energy function defined on a finite graph. When $N\ge 2$ is the number of vertices of the graph, they show that the corresponding Fokker-Planck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. The different choices for inner products on the space of probability distributions result in different Fokker-Planck equations for the same process. Each of these Fokker-Planck equations has a unique global equilibrium, which is a Gibbs distribution. In this paper we study the {\em speed of convergence} towards global equilibrium for the solution of these Fokker-Planck equations on a graph, and prove that the convergence is indeed exponential. The rate as measured by the decay of the $L_2$ norm can be bound in terms of the spectral gap of the Laplacian of the graph, and as measured by the decay of (relative) entropy be bound using the modified logarithmic Sobolev constant of the graph. With the convergence result, we also prove two Talagrand-type inequalities relating relative entropy and Wasserstein metric, based on two different metrics introduced in [CHLZ] The first one is a local inequality, while the second is a global inequality with respect to the "lower bound metric" from [CHLZ].

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preprint2014arXiv

Invariant scrambled sets, uniform rigidity and weak mixing

We show that for a non-trivial transitive dynamical system, it has a dense Mycielski invariant strongly scrambled set if and only if it has a fixed point, and it has a dense Mycielski invariant $δ$-scrambled set for some $δ>0$ if and only if it has a fixed point and not uniformly rigid. We also provide two methods for the construction of completely scrambled systems which are weakly mixing, proximal and uniformly rigid.

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preprint2014arXiv

Nil Bohr-sets and almost automorphy of higher order

Two closely related topics: higher order Bohr sets and higher order almost automorphy are investigated in this paper. Both of them are related to nilsystems. In the first part, the problem which can be viewed as the higher order version of an old question concerning Bohr sets is studied: for any $d\in {\mathbb N}$ does the collection of $\{n\in {\mathbb Z}: S\cap (S-n)\cap\ldots\cap (S-dn)\neq \emptyset\}$ with $S$ syndetic coincide with that of Nil$_d$ Bohr$_0$-sets? It is proved that Nil$_d$ Bohr$_0$-sets could be characterized via generalized polynomials, and applying this result one side of the problem is answered affirmatively: for any Nil$_d$ Bohr$_0$-set $A$, there exists a syndetic set $S$ such that $A\supset \{n\in {\mathbb Z}: S\cap (S-n)\cap\ldots\cap (S-dn)\neq \emptyset\}.$ Moreover, it is shown that the answer of the other side of the problem can be deduced from some result by Bergelson-Host-Kra if modulo a set with zero density. In the second part, the notion of $d$-step almost automorphic systems with $d\in{\mathbb N}\cup\{\infty\}$ is introduced and investigated, which is the generalization of the classical almost automorphic ones. It is worth to mention that some results concerning higher order Bohr sets will be applied to the investigation. For a minimal topological dynamical system $(X,T)$ it is shown that the condition $x\in X$ is $d$-step almost automorphic can be characterized via various subsets of ${\mathbb Z}$ including the dual sets of $d$-step Poincaré and Birkhoff recurrence sets, and Nil$_d$ Bohr$_0$-sets. Moreover, it turns out that the condition $(x,y)\in X\times X$ is regionally proximal of order $d$ can also be characterized via various subsets of ${\mathbb Z}$.

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preprint2014arXiv

Non-topological nature of the edge current in a chiral p-wave superconductor

The edges of time reversal symmetry breaking topological superconductors support chiral Majorana bound states as well as spontaneous charge currents. The Majorana modes are a robust, topological property, but the charge currents are non-topological--and therefore sensitive to microscopic details--even if we neglect Meissner screening. We give insight into the non-topological nature of edge currents in chiral p-wave superconductors using a variety of theoretical techniques, including lattice Bogoliubov-de Gennes equations, the quasiclassical approximation, and the gradient expansion, and describe those special cases where edge currents do have a topological character. While edge currents are not quantized, they are generically large, but can be substantially reduced for a sufficiently anisotropic gap function, a scenario of possible relevance for the putative chiral p-wave superconductor Sr$_2$RuO$_4$.

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preprint2014arXiv

Stable sets and mean Li-Yorke chaos in positive entropy systems

It is shown that in a topological dynamical system with positive entropy, there is a measure-theoretically "rather big" set such that a multivariant version of mean Li-Yorke chaos happens on the closure of the stable or unstable set of any point from the set. It is also proved that the intersections of the sets of asymptotic tuples and mean Li-Yorke tuples with the set of topological entropy tuples are dense in the set of topological entropy tuples respectively.

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preprint2014arXiv

Suppression of spontaneous currents in Sr$_2$RuO$_4$ by surface disorder

A major challenge to the chiral $p$-wave hypothesis for the pairing symmetry of the unconventional superconductor Sr$_2$RuO$_4$ is the null result of sensitive scanning magnetometry experiments designed to detect the expected spontaneous charge currents. Motivated by junction tunneling conductance measurements which indicate the quenching of superconductivity at the surfaces of even high-purity samples, we examine the spontaneous currents in a chiral $p$-wave superconductor near a normal metal / superconductor interface using the lattice Bogoliubov-de Gennes equations and Ginzburg-Landau theory, and find that the edge current is suppressed by more than an order of magnitude compared to previous estimates. These calculations demonstrate that interface details can have a quantitatively meaningful effect on the expectations for magnetometry experiments.

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preprint2014arXiv

Two-axis spin squeezing of two-component BEC via a continuous driving

In two-component BEC, the one-axis twisting Hamiltonian leads to spin squeezing with the limitation that scales with the number of atoms as $N^{-\frac{2}{3}}$. We propose a scheme to transform the one-axis twisting Hamiltonian into a two-axis twisting Hamiltonian, resulting in enhanced spin squeezing $\propto N^{-1}$ approaching the Heisenberg limit. Instead of pulse sequences, only one continuous driving field is required to realizing such transforming, thus the scheme is promising for experiment realizations, to an one-axis twisting Hamiltonian. Quantum information processing and quantum metrology may benefit from this method in the future.

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preprint2014arXiv

Vanishing edge currents in non-$p$-wave topological chiral superconductors

The edge currents of two dimensional topological chiral superconductors with nonzero Cooper pair angular momentum---e.g., chiral $p$-, $d$-, and $f$-wave superconductivity---are studied. Bogoliubov-de Gennes and Ginzburg--Landau calculations are used to show that in the continuum limit, \emph{only} chiral $p$-wave states have a nonzero edge current. Outside this limit, when lattice effects become important, edge currents in non-$p$-wave superconductors are comparatively smaller, but can be nonzero. Using Ginzburg--Landau theory, a simple criterion is derived for when edge currents vanish for non-$p$-wave chiral superconductivity on a lattice. The implications of our results for putative chiral superconductors such as Sr2RuO4 and UPt3 are discussed.

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preprint2014arXiv

Variational principle for weighted topological pressure

Let $π:X\to Y$ be a factor map, where $(X,T)$ and $(Y,S)$ are topological dynamical systems. Let ${\bf a}=(a_1,a_2)\in {\Bbb R}^2$ with $a_1>0$ and $a_2\geq 0$, and $f\in C(X)$. The ${\bf a}$-weighted topological pressure of $f$, denoted by $P^{\bf a}(X, f)$, is defined by resembling the Hausdorff dimension of subsets of self-affine carpets. We prove the following variational principle: $$ P^{\bf a}(X, f)=\sup\left\{a_1h_μ(T)+a_2h_{μ\circπ^{-1}}(S)+\int f \;dμ\right\}, $$ where the supremum is taken over the $T$-invariant measures on $X$. It not only generalizes the variational principle of classical topological pressure, but also provides a topological extension of dimension theory of invariant sets and measures on the torus under affine diagonal endomorphisms. A higher dimensional version of the result is also established.

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preprint2013arXiv

Lowering topological entropy over subsets revisited

Let $(X, T)$ be a topological dynamical system. Denote by $h (T, K)$ and $h^B (T, K)$ the covering entropy and dimensional entropy of $K\subseteq X$, respectively. $(X, T)$ is called D-{\it lowerable} (resp. {\it lowerable}) if for each $0\le h\le h (T, X)$ there is a subset (resp. closed subset) $K_h$ with $h^B (T, K_h)= h$ (resp. $h (T, K_h)= h$); is called D-{\it hereditarily lowerable} (resp. {\it hereditarily lowerable}) if each Souslin subset (resp. closed subset) is D-lowerable (resp. lowerable). In this paper it is proved that each topological dynamical system is not only lowerable but also D-lowerable, and each asymptotically $h$-expansive system is D-hereditarily lowerable. A minimal system which is lowerable and not hereditarily lowerable is demonstrated.

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preprint2013arXiv

Strictly ergodic models and the convergence of non-conventional pointwise ergodic averages

The well-known Jewett-Krieger's Theorem states that each ergodic system has a strictly ergodic model. Strengthening the model by requiring that it is strictly ergodic under some group actions, and building the connection of the new model with the convergence of pointwise non-conventional ergodic averages we prove that for an ergodic system $(X,\X,μ, T)$, $d\in\N$, $f_1, \ldots, f_d \in L^{\infty}(μ)$, %and any tempered F{\rm $ø$}lner sequence $F_n$ of $\Z^2$, the averages \begin{equation*} \frac{1}{N^2} \sum_{(n,m)\in F_N} f_1(T^nx)f_2(T^{n+m}x)\ldots f_d(T^{n+(d-1)m}x) \end{equation*} converge $μ$ a.e. We remark that the same method can be used to show the pointwise convergence of ergodic averages along cubes which was firstly proved by Assani and then extended to a general case by Chu and Franzikinakis.

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preprint2012arXiv

Experimental Upconversion of Images

We experimentally demonstrate the up-conversion of light carrying an image from the infrared spectrum to the visible spectrum using four-wave mixing via a ladder-type configuration in an atomic vapor. The results we obtained show the high correlation between the input image and the up-converted image. We also discuss the possible influences of experimental parameters on the resolution. Our work might be useful for research in astrophysics, night-vision technology, and chemical sensing.

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preprint2011arXiv

Circuit Modeling of Tunneling Real-Space Transfer Transistors: Toward Terahertz Frequency Operation

High frequency operation of tunneling real-space transfer transistor (TRSTT) in the negative differential resistance (NDR) regime is assessed by calculating the device common source unity current gain frequency (fT) range with a small signal equivalent circuit model including tunneling. Our circuit model is based on an In0.2Ga0.8As and delta-doped GaAs dual channel structure with various gate lengths. The calculated TRSTT fT agrees very well with experimental data, limiting factor being the resistance of the delta-doped GaAs layer. By optimizing the gate dimensions and channel materials, we find fT in the NDR region approaches terahertz range, which anticipates potential use of TRSTT as terahertz sources.

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preprint2011arXiv

Higher order almost automorphy, recurrence sets and the regionally proximal relation

In this paper, $d$-step almost automorphic systems are studied for $d\in\N$, which are the generalization of the classical almost automorphic ones. For a minimal topological dynamical system $(X,T)$ it is shown that the condition $x\in X$ is $d$-step almost automorphic can be characterized via various subsets of $\Z$ including the dual sets of $d$-step Poincaré and Birkhoff recurrence sets, and Nil$_d$ Bohr$_0$-sets by considering $N(x,V)=\{n\in\Z: T^nx\in V\}$, where $V$ is an arbitrary neighborhood of $x$. Moreover, it turns out that the condition $(x,y)\in X\times X$ is regionally proximal of order $d$ can also be characterized via various subsets of $\Z$ including $d$-step Poincaré and Birkhoff recurrence sets, $SG_d$ sets, the dual sets of Nil$_d$ Bohr$_0$-sets, and others by considering $N(x,U)=\{n\in\Z: T^nx\in U\}$, where $U$ is an arbitrary neighborhood of $y$.

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preprint2011arXiv

Local entropy theory for a countable discrete amenable group action

In the paper we throw the first light on studying systematically the local entropy theory for a countable discrete amenable group action. For such an action, we introduce entropy tuples in both topological and measure-theoretic settings and build the variational relation between these two kinds of entropy tuples by establishing a local variational principle for a given finite open cover. Moreover, based the idea of topological entropy pairs, we introduce and study two special classes of such an action: uniformly positive entropy and completely positive entropy. Note that in the building of the local variational principle, following Romagnoli's ideas two kinds of measure-theoretic entropy are introduced for finite Borel covers. These two kinds of entropy turn out to be the same, where Danilenko's orbital approach becomes an inevitable tool.

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preprint2011arXiv

Lowering topological entropy over subsets

Let $(X, T)$ be a topological dynamical system (TDS), and $h (T, K)$ the topological entropy of a subset $K$ of $X$. $(X, T)$ is {\it lowerable} if for each $0\le h\le h (T, X)$ there is a non-empty compact subset with entropy $h$; is {\it hereditarily lowerable} if each non-empty compact subset is lowerable; is {\it hereditarily uniformly lowerable} if for each non-empty compact subset $K$ and each $0\le h\le h (T, K)$ there is a non-empty compact subset $K_h\subseteq K$ with $h (T, K_h)= h$ and $K_h$ has at most one limit point. It is shown that each TDS with finite entropy is lowerable, and that a TDS $(X, T)$ is hereditarily uniformly lowerable if and only if it is asymptotically $h$-expansive.

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preprint2011arXiv

Nil Bohr$_0$-sets, Poincaré recurrence and generalized polynomials

The problem which can be viewed as the higher order version of an old question concerning Bohr sets is investigated: for any $d\in \N$ does the collection of $\{n\in \Z: S\cap (S-n)\cap...\cap (S-dn)\neq \emptyset\}$ with $S$ syndetic coincide with that of Nil$_d$ Bohr$_0$-sets? In this paper it is proved that Nil$_d$ Bohr$_0$-sets could be characterized via generalized polynomials, and applying this result one side of the problem could be answered affirmatively: for any Nil$_d$ Bohr$_0$-set $A$, there exists a syndetic set $S$ such that $A\supset \{n\in \Z: S\cap (S-n)\cap...\cap (S-dn)\neq \emptyset\}.$ Note that other side of the problem can be deduced from some result by Bergelson-Host-Kra if modulo a set with zero density. As applications it is shown that the two collections coincide dynamically, i.e. both of them can be used to characterize higher order almost automorphic points.

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preprint2010arXiv

Family-independence for topological and measurable dynamics

For a family F (a collection of subsets of Z_+), the notion of F-independence is defined both for topological dynamics (t.d.s.) and measurable dynamics (m.d.s.). It is shown that there is no non-trivial {syndetic}-independent m.d.s.; a m.d.s. is {positive-density}-independent if and only if it has completely positive entropy; and a m.d.s. is weakly mixing if and only if it is {IP}-independent. For a t.d.s. it is proved that there is no non-trivial minimal {syndetic}-independent system; a t.d.s. is weakly mixing if and only if it is {IP}-independent. Moreover, a non-trivial proximal topological K system is constructed, and a topological proof of the fact that minimal topological K implies strong mixing is presented.

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preprint2010arXiv

Variational principles for topological entropies of subsets

Let $(X,T)$ be a topological dynamical system. We define the measure-theoretical lower and upper entropies $\underline{h}_μ(T)$, $\bar{h}_μ(T)$ for any $μ\in M(X)$, where $M(X)$ denotes the collection of all Borel probability measures on $X$. For any non-empty compact subset $K$ of $X$, we show that $$\htop^B(T, K)= \sup \{\underline{h}_μ(T): μ\in M(X),\; μ(K)=1\}, $$ $$\htop^P(T, K)= \sup \{\bar{h}_μ(T): μ\in M(X),\; μ(K)=1\}. $$ where $\htop^B(T, K)$ denotes Bowen's topological entropy of $K$, and $\htop^P(T, K)$ the packing topological entropy of $K$. Furthermore, when $\htop(T)<\infty$, the first equality remains valid when $K$ is replaced by an arbitrarily analytic subset of $X$. The second equality always extends to any analytic subset of $X$.

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