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In this work, we study the causality of near-wall inner and outer turbulent motions. Here we define the inner motions as the self-sustained near-wall cycle and the outer motions as those living in the logarithmic layer exhibiting a footprint on the near-wall region. We perform causal analysis using two different methods: one is the transfer entropy, based on the information theory, and the other one is the Liang--Kleeman information-flow theory. The causal-analysis methods are applied to several scenarios, including a linear and a non-linear problem, a low-dimensional model of the near-wall cycle of turbulence, as well as the interaction between inner and outer turbulent motions in a channel at a friction Reynolds number of $Re_{\tau}=1000$. We find that both methods can well predict the causal links in the linear problem, and the information flow can identify more of the nonlinear problem. Despite richer causalities revealed by the transfer entropy for turbulent-flow problems, both methods can successfully identify the streak-vortex regeneration mechanism that majorly sustains the near-wall turbulence. It is also indicated that both bottom-up and top-down influences of inner and outer motions may coexist in addition to the multiscale self-sustaining mechanism. Lastly, we mention that the computation of the information flow is much more efficient than the transfer entropy. The present study suggests that the information flow can have great potential in causal inference for turbulent-flow problems besides the transfer entropy., Comment: 13th International Symposium on Turbulence and Shear Flow Phenomena (TSFP13), Montreal, Canada, June 25--28, 2024

In this paper, we propose an adaptive panoramic video semantic transmission (APVST) framework enabled by rate splitting multiple access (RSMA). The APVST framework consists of a semantic transmitter and receiver, utilizing a deep joint source-channel coding structure to adaptively extract and encode semantic features from panoramic frames. To achieve higher spectral efficiency and conserve bandwidth, APVST employs an entropy model and a dimension-adaptive module to control the transmission rate. Additionally, we take weighted-to-spherically-uniform peak signal-to-noise ratio (WS-PSNR) and weighted-to-spherically-uniform structural similarity (WS-SSIM) as distortion evaluation metrics for panoramic videos and design a weighted self-attention module for APVST. This module integrates weights and feature maps to enhance the quality of the immersive experience. Considering the overlap in the field of view when users watch panoramic videos, we further utilize RSMA to split the required panoramic video semantic streams into common and private messages for transmission. We propose an RSMA-enabled semantic stream transmission scheme and formulate a joint problem of latency and immersive experience quality by optimizing the allocation ratios of power, common rate, and channel bandwidth, aiming to maximize the quality of service (QoS) scores for users. To address the above problem, we propose a deep reinforcement learning algorithm based on proximal policy optimization (PPO) with high efficiency to handle dynamically changing environments. Simulation results demonstrate that our proposed APVST framework saves up to 20% and 50% of channel bandwidth compared to other semantic and traditional video transmission schemes, respectively. Moreover, our study confirms the efficiency of RSMA in panoramic video transmission, achieving performance gains of 13% and 20% compared to NOMA and OFDMA.

We report on the development and performance evaluation of an ultra-stable clock laser for an $\rm ^{27}Al^+$ optical clock. The thermal noise limited ultra-stable laser is developed based on a 30 cm long ultra-stable cavity. Three independent evaluation methods, including the frequency noise summation method, the three-cornered hat (TCH) method, and the optical clock transition detection method, are used to evaluate the clock laser performance. The summation result of various frequency noise terms is compared with the result of the TCH method. In addition, the $\rm ^{27}Al^+$ ion optical clock transition with ultra-narrow linewidth is also used to detect the frequency noise of the laser at lower Fourier frequencies. The results of the three methods show good agreements, showing a frequency instability level of $1.3\times10^{-16}$, and giving us confidence that these evaluation methods may provides guidance for accurate evaluations of high stability laser sources.

We consider the time-dependent Schr\"odinger equation that is generated on the bosonic Fock space by a long-range quantum many-body Hamiltonian. We derive the first bound on the maximal speed of particle transport in these systems that is thermodynamically stable and holds all the way down to microscopic length scales. For this, we develop a novel multiscale rendition of the ASTLO (adiabatic spacetime localization observables) method. Our result opens the door to deriving the first thermodynamically stable Lieb-Robinson bounds on general local operators for these long-range interacting bosonic systems., Comment: 28 pages, 5 figures; v1->v2: relaxed decay assumption in main result

Overcoming diffraction limit is crucial for obtaining high-resolution image and observing fine microstructure. With this conventional difficulty still puzzling us and the prosperous development of wave dynamics of light interacting with gravitational fields in recent years, how spatial curvature affect the diffraction limit is an attractive and important question. Here we investigate the issue of diffraction limit and optical resolution on two-dimensional curved spaces - surfaces of revolution (SORs) with constant or variable spatial curvature. We show that the diffraction limit decreases and resolution is improved on SORs with positive Gaussian curvature, opening a new avenue to super-resolution. The diffraction limit is also influenced by propagation direction, as well as the propagation distance in curved space with variable spatial curvature. These results provide a possible method to control optical resolution in curved space or equivalent waveguides with varying refractive index distribution and may allow one to detect the presence of non-uniform strong gravitational effect by probing locally the optical resolution.

We consider Markovian open quantum dynamics (MOQD). We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed in any finite-energy subspace. More precisely, we prove that if the initial quantum state is localized in space, then any finite-energy part of the solution of the von Neumann-Lindblad equation is approximately localized inside an energy-dependent light cone. We also obtain an explicit upper bound for the slope of this light cone., Comment: 43 pages

We study general lattice bosons with long-range hopping and long-range interactions decaying as $|x-y|^{-\alpha} $ with $\alpha\in (d+2,2d+1)$. We find a linear light cone for the information propagation starting from suitable initial states. We apply these bounds to estimate the minimal time needed for quantum messaging, for the propagation of quantum correlations, and for quantum state control. The proofs are based on the ASTLO method (adiabatic spacetime localization observables). Our results pose previously unforeseen limitations on the applicability of fast-transfer and entanglement-generation protocols developed for breaking linear light cones in long-range and/or bosonic systems., Comment: 29 pages, 1 figure; see arXiv:2212.14472 for additional details

Cryogenic ultra-stable lasers have extremely low thermal noise limits and frequency drifts, but they are more seriously affected by vibration noise from cryostats. Main material candidates for cryogenic ultra-stable cavities include silicon and sapphire. Although sapphire has many excellent properties at low temperature, the development of sapphire-based cavities is less advanced than that of silicon-based. Using a homemade cryogenic sapphire cavity, we develop an ultra-stable laser source with a frequency instability of $1.9\times10^{-16}$. This is the best frequency instability level among similar systems using cryogenic sapphire cavities reported so far. Low vibration performance of the cryostat is demonstrated with a two-stage vibration isolation, and the vibration suppression is further improved by different mixing ratio of the gas-liquid helium. With this technique, vibrations at frequencies higher than tens of hertz are greatly suppressed., Comment: 4 pages, 4 figures

We prove bounds on the minimal time for quantum messaging, propagation/creation of correlations, and control of states for general lattice quantum many-body systems. The proofs are based on a maximal velocity bound, which states that the many-body evolution stays, up to small leaking probability tails, within a light cone of the support of the initial conditions. This estimate is used to prove the light-cone approximation of dynamics and Lieb-Robinson-type bound, which in turn yield the results above. Our conditions cover long-range interactions. The main results of this paper as well as some key steps of the proofs were first presented in [36]., Comment: updated reference [36] M. Lemm, C. Rubiliani, I. M. Sigal, and J. Zhang, Information propagation in long-range quantum many-body systems, Phys. Rev. A, To appear (2023)

We study the Ginzburg-Landau equations on line bundles over non-compact Riemann surfaces with constant negative curvature. We prove existence of solutions with energy strictly less than that of the constant curvature (magnetic field) one. These solutions are the non-commutative generalizations of the Abrikosov vortex lattice of superconductivity. Conjecturally, they are (local) minimizers of the Ginzburg-Landau energy. We obtain precise asymptotic expansions of these solutions and their energies in terms of the curvature of the underlying Riemann surface. Among other things, our result shows the spontaneous breaking of the gauge-translational symmetry of the Ginzburg-Landau equations., Comment: added Section 7 on extension to degenerate case; reformulated main result; minor changes

In this paper, we continue the development of a generic adiabatic scheme for nonlinear evolutions. We consider an abstract gradient flow of some energy functional, together with a given manifold of static solutions arising from broken symmetries. First, we list a number of explicit and generic conditions on the energy functional that ensures the validity of our adiabatic scheme. Then, we construct some explicit low-energy but no necessarily static configurations, which form a stable manifold with finite codimensions for the given gradient flow. Thirdly, we show that the gradient flow is globally well-posed with initial configuration from the stable manifold. Finally, we show that any solution to the full gradient flow starting from the stable manifold is essentially governed by an effective equation on the manifold of static solutions, up to a uniformly small and dissipating error term., Comment: 27pp. Part I has appeared in arxiv.org:2103.05932

We study the rescaled mean curvature flow (MCF) of hypersurfaces that are global graphs over a fixed cylinder of arbitrary dimensions. We construct an explicit stable manifold for the rescaled MCF of finite codimensions in a suitable configuration space. For any initial hypersurface from this stable manifold, we construct a unique global solution to the rescaled MCF, and derive precise asymptotics for these solutions that are valid for all time. Using these asymptotics, we prove asymptotic stability of cylindrical singularities of arbitrary dimensions under generic initial perturbations. As a by-product, for any flow of hypersurfaces evolving according to the MCF that enters this stable manifold at any time and first develops a singularity at a subsequent time, we give a simple proof of the uniqueness of tangent flow, first established by Colding and Minicozzi. Moreover, in this case we show the unique singularity profile is determined by the hypersurface profile when the flow enters the stable manifold. For all results in this paper, there is no symmetry or solitonic assumption., Comment: 38 pp

In this paper, we develop an adiabatic theory for the evolution of large closed surfaces under the area-constrained Willmore (ACW) flow in a three-dimensional asymptotically Schwarzschild manifold. We construct explicitly a map, defined on a certain four-dimensional manifold of barycenters, which characterizes key static and dynamical properties of the ACW flow. In particular, using this map, we find an explicit four-dimensional effective dynamics of barycenters, which serves as a uniform asymptotic approximation for the (infinite-dimensional) ACW flow, so long as the initial surface satisfies certain mild geometric constraints (which determine the validity interval). Conversely, given any prescribed flow of barycenters evolving according to this effective dynamics, we construct a family of surfaces evolving by the ACW flow, whose barycenters are uniformly close to the prescribed ones on a large time interval (whose size depends on the geometric constraints of initial configurations)., Comment: 25 pp

In this paper, we consider the concentration property of solutions to the dispersive Ginzburg-Landau (or Gross-Pitaevskii) equation in three dimensions. On a spatial domain, it has long been conjectured that such a solution concentrates near some curve evolving according to the binormal curvature flow, and conversely, that a curve moving this way can be realized in a suitable sense by some solution to the dispersive Ginzburg-Landau equation. Some partial results are known with rather strong symmetry assumptions. Our main theorems here provide affirmative answer to both conjectures under certain small curvature assumption. The results are valid for small but fixed material parameter in the equation, in contrast to the general practice to take this parameter to its zero limit. The advantage is that we can retain precise description of the vortex filament structure. The results hold on a long but finite time interval, depending on the curvature assumption., Comment: 26 pp

In the study of evolution equations, the method of adiabatic approximation is an essential tool to reduce an infinite-dimensional dynamical system to a simpler, possibly finite-dimensional one. In this paper, we formulate a generic scheme of adiabatic approximation that is valid for an abstract nonlinear evolution under mild regularity assumptions. The key prerequisite for the scheme is the existence of what we call approximate solitons. These are some low energy but not necessarily stationary configurations. The approximate solitons are characterized by a number of parameters (possibly infinitely many), and have a manifold structure. The adiabatic scheme reduces the given abstract evolution equation to an effective equation on the manifold of approximate solitons. We give sufficient conditions for the approximate solitons so that the reduction scheme is valid up to a large time. The validity is determined by the energy property of the original evolution as well as the adiabaticity of the approximate solitons., Comment: 32 pp