Dry Ten Martini Problem in the non-critical case
We solve the Dry Ten Martini Problem in the non-critical case, i.e., all possible spectral gaps are open for almost Mathieu operators with $λ\ne \pm 1$.
math-ph↗
arXiv subjects
Qi Zhou
Publications and source records attributed to Qi Zhou.
On an impulsive faecal-oral model in a periodically evolving environment
To understand how impulsive intervention and regional evolution jointly influence the spread of faecal-oral diseases, this paper develops an impulsive faecal-oral model in a periodically evolving environment. The well-posedness of the model is first checked. Then, the existence of the principal eigenvalue dependent on impulse intensity and evolving rate is proved based on Krein-Rutman theorem. With the help of this value, the threshold dynamical behaviours of the model are explored. More importantly, this paper also derives the monotonicity of the principal eigenvalue with respect to initial region and impulse intensity and estimates the principal eigenvalue in some special cases. Finally, numerical simulations are used to verify the correctness of the theoretical results and to explore the impact of regional evolution rate on the spread of the diseases. Our research shows that large impulsive intensity $1-g'(0)$ and small evolving rate $ρ(t)$ play a positive role in the prevention and control of the diseases.
math.AP↗
Universal relations for dilute systems with two-body decays in reduced dimensions
Physical systems in reduced dimensions exhibit intriguing properties. For instance, the dependences of two-body and many-body physics on scattering lengths are distinct from their counterparts in three dimensions. Whereas many studies of ultracold atoms and molecules in reduced dimensions have been focusing on closed systems, two-body losses may occur in such systems. Here, we show that the two-body inelastic loss rate in reduced dimensions can be expressed in universal relations that are governed by contacts. These universal relations correlate the two-body decay rate with other physical observables at arbitrary temperatures and interaction strengths. Our results will provide experimentalists with a new protocol to study inelastic scatterings in both few- and many-body systems in reduced dimensions.
cond-mat.quant-gas↗
Elucidating Structure Formation in Highly Oriented Triple Cation Perovskite Films
Metal halide perovskites are an emerging class of crystalline semiconductors of great interest for application in optoelectronics. Their properties are dictated not only by their composition, but also by their crystalline structure and microstructure. While significant efforts were dedicated to the development of strategies for microstructural control, significantly less is known about the processes that govern the formation of their crystalline structure in thin films, in particular in the context of crystalline orientation. In this work, we investigate the formation of highly oriented triple cation perovskite films fabricated by utilizing a range of alcohols as an antisolvent. Examining the film formation by in-situ grazing-incidence wide-angle X-ray scattering reveals the presence of a short-lived highly oriented crystalline intermediate, which we identify as FAI-PbI2-xDMSO. The intermediate phase templates the crystallisation of the perovskite layer, resulting in highly oriented perovskite layers. The formation of this DMSO containing intermediate is triggered by the selective removal of DMF when alcohols are used as an antisolvent, consequently leading to differing degrees of orientation depending on the antisolvent properties. Finally, we demonstrate that photovoltaic devices fabricated from the highly oriented films, are superior to those with a random polycrystalline structure in terms of both performance and stability.
physics.app-ph↗
Synthetic tensor gauge fields
Synthetic gauge fields have provided physicists with a unique tool to explore a wide range of fundamentally important phenomena. However, most experiments have been focusing on synthetic vector gauge fields. The very rich physics brought by coupling tensor gauge fields to fracton phase of matter remain unexplored in laboratories. Here, we propose schemes to realize synthetic tensor gauge fields that address dipoles instead of single-particles. A lattice tilted by a strong linear potential and a weak quadratic potential yields a rank-2 electric field for a lineon formed by a particle-hole pair. Such a rank-2 electric field leads to a new type of Bloch oscillations, which modulate the quadrupole moment and preserve the dipole moment of the system. In higher dimensions, the interplay between interactions and vector gauge potentials imprints a phase to the ring-exchange interaction and thus generates synthetic tensor gauge fields for planons. Such tensor gauge fields make it possible to realize a dipolar Harper-Hofstadter model in laboratories. The resultant dipolar Chern insulators feature chiral edge currents of dipoles in the absence of net charge currents.
cond-mat.quant-gas↗
Dynamic Gaussian Graph Operator: Learning parametric partial differential equations in arbitrary discrete mechanics problems
Deep learning methods have access to be employed for solving physical systems governed by parametric partial differential equations (PDEs) due to massive scientific data. It has been refined to operator learning that focuses on learning non-linear mapping between infinite-dimensional function spaces, offering interface from observations to solutions. However, state-of-the-art neural operators are limited to constant and uniform discretization, thereby leading to deficiency in generalization on arbitrary discretization schemes for computational domain. In this work, we propose a novel operator learning algorithm, referred to as Dynamic Gaussian Graph Operator (DGGO) that expands neural operators to learning parametric PDEs in arbitrary discrete mechanics problems. The Dynamic Gaussian Graph (DGG) kernel learns to map the observation vectors defined in general Euclidean space to metric vectors defined in high-dimensional uniform metric space. The DGG integral kernel is parameterized by Gaussian kernel weighted Riemann sum approximating and using dynamic message passing graph to depict the interrelation within the integral term. Fourier Neural Operator is selected to localize the metric vectors on spatial and frequency domains. Metric vectors are regarded as located on latent uniform domain, wherein spatial and spectral transformation offer highly regular constraints on solution space. The efficiency and robustness of DGGO are validated by applying it to solve numerical arbitrary discrete mechanics problems in comparison with mainstream neural operators. Ablation experiments are implemented to demonstrate the effectiveness of spatial transformation in the DGG kernel. The proposed method is utilized to forecast stress field of hyper-elastic material with geometrically variable void as engineering application.
cs.LG↗
MPIPN: A Multi Physics-Informed PointNet for solving parametric acoustic-structure systems
Machine learning is employed for solving physical systems governed by general nonlinear partial differential equations (PDEs). However, complex multi-physics systems such as acoustic-structure coupling are often described by a series of PDEs that incorporate variable physical quantities, which are referred to as parametric systems. There are lack of strategies for solving parametric systems governed by PDEs that involve explicit and implicit quantities. In this paper, a deep learning-based Multi Physics-Informed PointNet (MPIPN) is proposed for solving parametric acoustic-structure systems. First, the MPIPN induces an enhanced point-cloud architecture that encompasses explicit physical quantities and geometric features of computational domains. Then, the MPIPN extracts local and global features of the reconstructed point-cloud as parts of solving criteria of parametric systems, respectively. Besides, implicit physical quantities are embedded by encoding techniques as another part of solving criteria. Finally, all solving criteria that characterize parametric systems are amalgamated to form distinctive sequences as the input of the MPIPN, whose outputs are solutions of systems. The proposed framework is trained by adaptive physics-informed loss functions for corresponding computational domains. The framework is generalized to deal with new parametric conditions of systems. The effectiveness of the MPIPN is validated by applying it to solve steady parametric acoustic-structure coupling systems governed by the Helmholtz equations. An ablation experiment has been implemented to demonstrate the efficacy of physics-informed impact with a minority of supervised data. The proposed method yields reasonable precision across all computational domains under constant parametric conditions and changeable combinations of parametric conditions for acoustic-structure systems.
cs.LG↗
FoolSDEdit: Deceptively Steering Your Edits Towards Targeted Attribute-aware Distribution
Guided image synthesis methods, like SDEdit based on the diffusion model, excel at creating realistic images from user inputs such as stroke paintings. However, existing efforts mainly focus on image quality, often overlooking a key point: the diffusion model represents a data distribution, not individual images. This introduces a low but critical chance of generating images that contradict user intentions, raising ethical concerns. For example, a user inputting a stroke painting with female characteristics might, with some probability, get male faces from SDEdit. To expose this potential vulnerability, we aim to build an adversarial attack forcing SDEdit to generate a specific data distribution aligned with a specified attribute (e.g., female), without changing the input's attribute characteristics. We propose the Targeted Attribute Generative Attack (TAGA), using an attribute-aware objective function and optimizing the adversarial noise added to the input stroke painting. Empirical studies reveal that traditional adversarial noise struggles with TAGA, while natural perturbations like exposure and motion blur easily alter generated images' attributes. To execute effective attacks, we introduce FoolSDEdit: We design a joint adversarial exposure and blur attack, adding exposure and motion blur to the stroke painting and optimizing them together. We optimize the execution strategy of various perturbations, framing it as a network architecture search problem. We create the SuperPert, a graph representing diverse execution strategies for different perturbations. After training, we obtain the optimized execution strategy for effective TAGA against SDEdit. Comprehensive experiments on two datasets show our method compelling SDEdit to generate a targeted attribute-aware data distribution, significantly outperforming baselines.
cs.CV↗
Almost reducibility and oscillatory growth of Sobolev norms
For 1D quantum harmonic oscillator perturbed by a time quasi-periodic quadratic form of $(x,-{\rm i}\partial_x)$, we show its almost reducibility. The growth of Sobolev norms of solution is described based on the scheme of almost reducibility. In particular, an $o(t^s)-$upper bound is shown for the $\CH^s-$norm if the equation is non-reducible. Moreover, by Anosov-Katok construction, we also show the optimality of this upper bound, i.e., the existence of quasi-periodic quadratic perturbation for which the growth of ${\mathcal H}^s-$norm of the solution is $o(t^s)$ as $t\to\infty$ but arbitrarily ``close" to $t^s$ in an oscillatory way.
math.AP↗
Accurately recover global quasiperiodic systems by finite points
Quasiperiodic systems, related to irrational numbers, are space-filling structures without decay nor translation invariance. How to accurately recover these systems, especially for non-smooth cases, presents a big challenge in numerical computation. In this paper, we propose a new algorithm, finite points recovery (FPR) method, which is available for both smooth and non-smooth cases, to address this challenge. The FPR method first establishes a homomorphism between the lower-dimensional definition domain of the quasiperiodic function and the higher-dimensional torus, then recovers the global quasiperiodic system by employing interpolation technique with finite points in the definition domain without dimensional lifting. Furthermore, we develop accurate and efficient strategies of selecting finite points according to the arithmetic properties of irrational numbers. The corresponding mathematical theory, convergence analysis, and computational complexity analysis on choosing finite points are presented. Numerical experiments demonstrate the effectiveness and superiority of FPR approach in recovering both smooth quasiperiodic functions and piecewise constant Fibonacci quasicrystals. While existing spectral methods encounter difficulties in accurately recovering non-smooth quasiperiodic functions.
math.NA↗
Harnessing Transparent Learning Analytics for Individualized Support through Auto-detection of Engagement in Face-to-Face Collaborative Learning
Using learning analytics to investigate and support collaborative learning has been explored for many years. Recently, automated approaches with various artificial intelligence approaches have provided promising results for modelling and predicting student engagement and performance in collaborative learning tasks. However, due to the lack of transparency and interpretability caused by the use of "black box" approaches in learning analytics design and implementation, guidance for teaching and learning practice may become a challenge. On the one hand, the black box created by machine learning algorithms and models prevents users from obtaining educationally meaningful learning and teaching suggestions. On the other hand, focusing on group and cohort level analysis only can make it difficult to provide specific support for individual students working in collaborative groups. This paper proposes a transparent approach to automatically detect student's individual engagement in the process of collaboration. The results show that the proposed approach can reflect student's individual engagement and can be used as an indicator to distinguish students with different collaborative learning challenges (cognitive, behavioural and emotional) and learning outcomes. The potential of the proposed collaboration analytics approach for scaffolding collaborative learning practice in face-to-face contexts is discussed and future research suggestions are provided.
cs.CY↗
Regulating Intermediate 3D Features for Vision-Centric Autonomous Driving
Multi-camera perception tasks have gained significant attention in the field of autonomous driving. However, existing frameworks based on Lift-Splat-Shoot (LSS) in the multi-camera setting cannot produce suitable dense 3D features due to the projection nature and uncontrollable densification process. To resolve this problem, we propose to regulate intermediate dense 3D features with the help of volume rendering. Specifically, we employ volume rendering to process the dense 3D features to obtain corresponding 2D features (e.g., depth maps, semantic maps), which are supervised by associated labels in the training. This manner regulates the generation of dense 3D features on the feature level, providing appropriate dense and unified features for multiple perception tasks. Therefore, our approach is termed Vampire, stands for "Volume rendering As Multi-camera Perception Intermediate feature REgulator". Experimental results on the Occ3D and nuScenes datasets demonstrate that Vampire facilitates fine-grained and appropriate extraction of dense 3D features, and is competitive with existing SOTA methods across diverse downstream perception tasks like 3D occupancy prediction, LiDAR segmentation and 3D objection detection, while utilizing moderate GPU resources. We provide a video demonstration in the supplementary materials and Codes are available at github.com/cskkxjk/Vampire.
cs.CV↗
Dynamical classification of analytic one-frequency quasi-periodic $\mathrm{SO}(3,\mathbb{R})$-cocycles
We establish a close connection between acceleration and dynamical degree for one-frequency quasi-periodic compact cocycles, by showing that two vectors derived separately from each coincide. Based on this, we provide a dynamical classification of one-frequency quasi-periodic $\mathrm{SO}(3,\mathbb{R})$-cocycles.
math.DS↗
Spectrum of Hatano-Nelson model with strictly ergodic potentials
We provide a precise formula for the spectrum of the Hatano-Nelson model with strictly ergodic potentials in terms of its Lyapunov exponent. As applications, one clearly observes the real-complex spectrum transition. Moreover, if the Lyapunov exponent is continuous, the spectrum of the Hatano-Nelson model in $\ell^{2}(\mathbb{Z})$ can be approximated by the spectrum of its finite-interval truncation with periodic boundary conditions. Both of these results are strikingly different from the Hatano-Nelson model with random potentials \cite{Dav01A, Dav01, Dav02}.
math.SP↗
Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics
We show that quantum dynamics of any systems with $SU(1,1)$ symmetry give rise to emergent Anti-de Sitter spacetimes in 2+1 dimensions (AdS$_{2+1}$). Using the continuous circuit depth, a quantum evolution is mapped to a trajectory in AdS$_{2+1}$. Whereas the time measured in laboratories becomes either the proper time or the proper distance, quench dynamics follow geodesics of AdS$_{2+1}$. Such a geometric approach provides a unified interpretation of a wide range of prototypical phenomena that appear disconnected. For instance, the light cone of AdS$_{2+1}$ underlies expansions of unitary fermions released from harmonic traps, the onsite of parametric amplifications, and the exceptional points that represent the $PT$ symmetry breaking in non-Hermitian systems. Our work provides a transparent means to optimize quantum controls by exploiting shortest paths in the emergent spacetimes. It also allows experimentalists to engineer emergent spacetimes and induce tunnelings between different AdS$_{2+1}$.
cond-mat.quant-gas↗
Well-posedness of the discrete nonlinear Schrödinger equations and the Klein-Gordon equations
The primary objective of this paper is to investigate the well-posedness theories associated with the discrete nonlinear Schrödinger equation and Klein-Gordon equation. These theories encompass both local and global well-posedness, as well as the existence of blowing-up solutions for large and irregular initial data. The main results of this paper presented in this paper can be summarized as follows: 1. Discrete Nonlinear Schrödinger Equation: We establish global well-posedness in $l^p_h$ spaces for all $1\leq p\leq \infty$, regardless of whether it is in the defocusing or focusing cases. 2. Discrete Klein-Gordon Equation (including Wave Equation): We demonstrate local well-posedness in $l^p_h$ spaces for all $1\leq p\leq \infty$. Furthermore, in the defocusing case, we establish global well-posedness in $l^p_h$ spaces for any $2\leq p\leq 2σ+2$. In contrast, in the focusing case, we show that solutions with negative energy blow up within a finite time.
math.DS↗
The first Szegő limit theorem on multi-dimensional torus
In this paper, we consider the first Szegő limit theorems on $d$-torus $\mathbb{T}^d$ for $1\leq d\leq +\infty$. It is shown that for any Følner sequence $\{σ_N\}$ of $\mathbb{Z}^d$ and $φ\in L^1_+(\mathbb{T}^d)$, it holds that $$ \lim_{N\rightarrow \infty}\left(\det T_{σ_N}φ\right)^{\frac{1}{|σ_N|}}=\exp\left(\int_{\mathbb{T}^d} \logφ~dm_{d}\right). $$ In the case $d=+\infty$, we are associated with multiplicative Toeplitz matrix $T φ=\{\widehatφ(j/i)\}_{i,j\in\mathbb{N}}$ and the most concerned non-Følner truncation, that is, $T_N φ=\{\widehatφ(j/i)\}_{1\leq i,j\leq N}$, where $σ_N=\{1,\dots,N\}$. It is shown that for each $φ\in L^\infty_{\mathbb{R}}(\mathbb{T^{\infty}})$ and $f\in C[\text{ess-inf} ~φ,~\text{ess-sup}~φ]$, the limit $\lim_{N\rightarrow \infty} \frac{1}{N}\mathrm{Tr} f \big(T_N φ\big)$ exsits. Moreover, it is proven that the limit $\lim_{N\rightarrow \infty}\left(\det T_N φ\right)^{\frac{1}{N}}$ exists for any $φ\in L^1_+(\mathbb{T}^\infty)$ with strictly positive essential infimum. These results are directly related to two problems posed by Nikolski and Pushnitski.
math.FA↗
Multipolar condensates and multipolar Josephson effects
When single-particle dynamics are suppressed in certain strongly correlated systems, dipoles arise as elementary carriers of quantum kinetics. These dipoles can further condense, providing physicists with a rich realm to study fracton phases of matter. Whereas recent theoretical discoveries have shown that an unconventional lattice model may host a dipole condensate as the ground state, fundamental questions arise as to whether dipole condensation is a generic phenomenon rather than a specific one unique to a particular model and what new quantum macroscopic phenomena a dipole condensate may bring us with. Here, we show that dipole condensates prevail in bosonic systems. Because of a self-proximity effect, where single-particle kinetics inevitably induces a finite order parameter of dipoles, dipole condensation readily occurs in conventional normal phases of bosons. Our findings allow experimentalists to manipulate the phase of a dipole condensate and deliver dipolar Josephson effects, where supercurrents of dipoles arise in the absence of particle flows. The self-proximity effects can also be utilized to produce a generic multipolar condensate. The kinetics of the $n$-th order multipoles unavoidably creates a condensate of the $(n+1)$-th order multipoles, forming a hierarchy of multipolar condensates that will offer physicists a whole new class of macroscopic quantum phenomena.
cond-mat.quant-gas↗