arXiv subjects

Jingxuan Zhang

Publications and source records attributed to Jingxuan Zhang.

51 records · Page 3Linked to original sources

arXiv2023

Characterization of an $\rm ^{27}Al^+$ ion optical clock laser with three independent methods

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.

physics.atom-ph↗

arXiv2023

On the microscopic propagation speed of long-range quantum many-body systems

We consider the time-dependent Schrödinger 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.

math-ph↗

arXiv2023

Diffraction limit of light in curved space

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.

physics.optics↗

arXiv2023

Ginzburg-Landau Equations on Non-compact Riemann Surfaces

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.

math.AP↗

arXiv2023

Light cones for open quantum systems

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.

quant-ph↗

arXiv2023

An ultra-stable cryogenic sapphire cavity laser with an instability of $1.9\times10^{-16}$ based on a low vibration level cryostat

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.

physics.ins-det↗

arXiv2022

A generic framework of adiabatic approximation for nonlinear evolutions II

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.

math.AP↗

arXiv2022

A generic framework of adiabatic approximation for evolutions with focusing nonlinearity

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.

math.AP↗

arXiv2022

Adiabatic theory for the area-constrained Willmore flow

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).

math.DG↗

arXiv2021

On the Stability of Cylindrical Singularities of the Mean Curvature Flow

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.

math.DG↗

arXiv2021

Adiabatic approximation for the motion of Ginzburg-Landau vortex filament

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.

math.AP↗

arXiv2018

Deep Learning in Software Engineering

Recent years, deep learning is increasingly prevalent in the field of Software Engineering (SE). However, many open issues still remain to be investigated. How do researchers integrate deep learning into SE problems? Which SE phases are facilitated by deep learning? Do practitioners benefit from deep learning? The answers help practitioners and researchers develop practical deep learning models for SE tasks. To answer these questions, we conduct a bibliography analysis on 98 research papers in SE that use deep learning techniques. We find that 41 SE tasks in all SE phases have been facilitated by deep learning integrated solutions. In which, 84.7% papers only use standard deep learning models and their variants to solve SE problems. The practicability becomes a concern in utilizing deep learning techniques. How to improve the effectiveness, efficiency, understandability, and testability of deep learning based solutions may attract more SE researchers in the future.

cs.SE↗

arXiv2017

What Makes a Good App Description?

In the Google Play store, an introduction page is associated with every mobile application (app) for users to acquire its details, including screenshots, description, reviews, etc. However, it remains a challenge to identify what items influence users most when downloading an app. To explore users' perspective, we conduct a survey to inquire about this question. The results of survey suggest that the participants pay most attention to the app description which gives users a quick overview of the app. Although there exist some guidelines about how to write a good app description to attract more downloads, it is hard to define a high quality app description. Meanwhile, there is no tool to evaluate the quality of app description. In this paper, we employ the method of crowdsourcing to extract the attributes that affect the app descriptions' quality. First, we download some app descriptions from Google Play, then invite some participants to rate their quality with the score from one (very poor) to five (very good). The participants are also requested to explain every score's reasons. By analyzing the reasons, we extract the attributes that the participants consider important during evaluating the quality of app descriptions. Finally, we train the supervised learning models on a sample of 100 app descriptions. In our experiments, the support vector machine model obtains up to 62% accuracy. In addition, we find that the permission, the number of paragraphs and the average number of words in one feature play key roles in defining a good app description.

cs.HC↗

arXiv2017

An Unsupervised Approach for Discovering Relevant Tutorial Fragments for APIs

Developers increasingly rely on API tutorials to facilitate software development. However, it remains a challenging task for them to discover relevant API tutorial fragments explaining unfamiliar APIs. Existing supervised approaches suffer from the heavy burden of manually preparing corpus-specific annotated data and features. In this study, we propose a novel unsupervised approach, namely Fragment Recommender for APIs with PageRank and Topic model (FRAPT). FRAPT can well address two main challenges lying in the task and effectively determine relevant tutorial fragments for APIs. In FRAPT, a Fragment Parser is proposed to identify APIs in tutorial fragments and replace ambiguous pronouns and variables with related ontologies and API names, so as to address the pronoun and variable resolution challenge. Then, a Fragment Filter employs a set of nonexplanatory detection rules to remove non-explanatory fragments, thus address the non-explanatory fragment identification challenge. Finally, two correlation scores are achieved and aggregated to determine relevant fragments for APIs, by applying both topic model and PageRank algorithm to the retained fragments. Extensive experiments over two publicly open tutorial corpora show that, FRAPT improves the state-of-the-art approach by 8.77% and 12.32% respectively in terms of F-Measure. The effectiveness of key components of FRAPT is also validated.

cs.SE↗

arXiv2017

A More Accurate Model for Finding Tutorial Segments Explaining APIs

Developers prefer to utilize third-party libraries when they implement some functionalities and Application Programming Interfaces (APIs) are frequently used by them. Facing an unfamiliar API, developers tend to consult tutorials as learning resources. Unfortunately, the segments explaining a specific API scatter across tutorials. Hence, it remains a challenging issue to find the relevant segments. In this study, we propose a more accurate model to find the exact tutorial fragments explaining APIs. This new model consists of a text classifier with domain specific features. More specifically, we discover two important indicators to complement traditional text based features, namely co-occurrence APIs and knowledge based API extensions. In addition, we incorporate Word2Vec, a semantic similarity metric to enhance the new model. Extensive experiments over two publicly available tutorial datasets show that our new model could find up to 90% fragments explaining APIs and improve the state-of-the-art model by up to 30% in terms of F-measure.

cs.SE↗