arXiv subjects

Yidong Wu

Publications and source records attributed to Yidong Wu.

4 recordsLinked to original sources

arXiv2026

Optimal Asynchronous Stochastic Nonconvex Optimization under Heavy-Tailed Noise

This paper considers the problem of asynchronous stochastic nonconvex optimization with heavy-tailed gradient noise and arbitrarily heterogeneous computation times across workers. We propose an asynchronous normalized stochastic gradient descent algorithm with momentum. The analysis show that our method achieves the optimal time complexity under the assumption of bounded $p$th-order central moment with $p\in(1,2]$. We also provide numerical experiments to show the effectiveness of proposed method.

math.OC↗

arXiv2022

Fractional Charges in the Su-Schrieffer-Heeger Model

The Su-Schrieffer-Heeger(SSH) model has been widely used to study the topological property of 1D systems. It is claimed that there is fractional charge at the boundary of the nontrivial phase while none at that of trivial phase. However, this conclusion is in direct contradiction to the modern theory of polarization(MTP). We solve this paradox by showing that the polarization of SSH model depends only on the distribution of the positive charges and is irrelevant to the Zak phase defined in previous works. Thus the distribution of positive charges alone determines whether the SSH chain is topological or not. Similarly, we show the polarization defined by Berry connection can not be used to characterize topological property of a 2D generalization of SSH model.

cond-mat.str-el↗

arXiv2018

The impacts of the quantum-dot confining potential on the spin-orbit effect

For a nanowire quantum dot with the confining potential modeled by both the infinite and the finite square wells, we obtain exactly the energy spectrum and the wave functions in the strong spin-orbit coupling regime. We find that regardless of how small the well height is, there are at least two bound states in the finite square well: one has the $σ^{x}\mathcal{P}=-1$ symmetry and the other has the $σ^{x}\mathcal{P}=1$ symmetry. When the well height is slowly tuned from large to small, the position of the maximal probability density of the first excited state moves from the center to $x\ne0$, while the position of the maximal probability density of the ground state is always at the center. A strong enhancement of the spin-orbit effect is demonstrated by tuning the well height. In particular, there exists a critical height $V^{c}_{0}$, at which the spin-orbit effect is enhanced to maximal.

cond-mat.mes-hall↗

arXiv2011

A Scheme to Classify Topological Property of Band Insulator Based On One-band U(1) Chern Number

Topological insulator(TI) is a phase of matter discovered recently. Kane and Mele proposed this phase is distinguished from the ordinary band insulator by a Z2 topological invariant.2 Several authors have try to related this Z2 invariant to Chern numbers. Roy find a way to calculate Z2 by Chern Number of one of the two degenerate Bands or one-band Chern number(OBChN). However, he give no concrete concrete proof of the equivalence of his Z2 and the Z2 in ref[2] beside \from the topological considerations of K theory". So the importance of OBChN hasn't been recognized by the community. In this letter we prove OBChN determines the Z2 in ref[2]. Then we illustrate OBChN is not only an useful tool to identify TI but also a natural criterion to classify topological property of all time-reversal invariant band insulators. More importantly we find a field in three dimensional TI can be identified with magnetic field with magnetic monopole.

cond-mat.mtrl-sci↗