arXiv subjects

Hao-Xuan Sun

Publications and source records attributed to Hao-Xuan Sun.

3 recordsLinked to original sources

arXiv2026

Finding the stable mechanism of ring solitons in two-dimensional Fermi superfluids

We theoretically investigate the stable mechanism of a ring soliton in two-dimensional Fermi superfluids by solving the Bogoliubov-de Gennes equations and their time-dependent counterparts. In the uniform situation, we discover that the ring soliton is always driven away from its initial location, and moves towards the edge due to a curvature-induced effective potential. The ring soliton is impossible to remain static at any location in the uniform system. To balance the density difference between the ring soliton's two sides, a harmonic trap is introduced, which can exert an effect to counterbalances the curvature-induced effective potential. This enables the ring dark soliton to become a stable state at a particular equilibrium position r_s, where the free energy of the ring dark soliton just reaches the maximum value. Once ring soliton is slightly deviated from r_s, some stable periodic oscillations of ring soliton around r_s will turn out. Some dissipation will possibly occur to ring soliton once its minimum radius is comparable to the healing length of soliton's Friedel oscillation. This dissipation will increase the oscillation amplitude and finally make the ring soliton decay into sound ripples. Our research lays the groundwork for a more in-depth understanding of the stable mechanism of a ring dark soliton in the future.

cond-mat.quant-gas↗

arXiv2026

Localization Estimator for High Dimensional Tensor Covariance Matrices

This paper considers covariance matrix estimation of tensor data under high dimensionality. A multi-bandable covariance class is established to accommodate the need for complex covariance structures of multi-layer lattices and general covariance decay patterns. We propose a high dimensional covariance localization estimator for tensor data, which regulates the sample covariance matrix through a localization function. The statistical properties of the proposed estimator are studied by deriving the minimax rates of convergence under the spectral and the Frobenius norms. Numerical experiments and real data analysis on ocean eddy data are carried out to illustrate the utility of the proposed method in practice.

stat.ME↗

arXiv2025

High Dimensional Ensemble Kalman Filter

The Ensemble Kalman Filter (EnKF), as a fundamental data assimilation approach, has been widely used in many fields of the sciences and engineering. When the state variable is of high dimensional accompanied with high resolution observations of physical models, some key theoretical aspects of the EnKF are open for investigation. This paper proposes several high dimensional EnKF (HD-EnKF) methods equipped with consistent estimators for the important forecast error covariance and Kalman Gain matrices. It then studies the theoretical properties of the EnKF under both fixed and high dimensional state variables, which provides one-step and multiple-step mean square errors of the analysis states to the underlying oracle states offered by the Kalman Filter and gives the much needed insight to the roles played by the forecast error covariance on the accuracy of the EnKF. The accuracy of the data assimilation under the misspecified physical model is also considered. Numerical studies on the Lorenz-96 and the Shallow Water Equation models illustrate that the proposed HD-EnKF algorithms outperform the standard EnKF and widely used inflation methods.

stat.ME↗