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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：量子算法及相关研究介绍
量子算法 量子纠缠 量子测不准关系
2023/4/23
我们介绍近期在量子算法、量子纠缠及其物理实现、斜信息及量子测不准关系方面的有关研究工作。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Many-body localization and quantum many-body scars: The strong and weak form of ergodicity breaking
多体定位 量子多体疤痕 遍历性断裂 强弱形式
2023/4/23
The fate of an isolated quantum many-body system has attracted much attention in the past decade. One of the most important issues is whether such a system can reach thermalization under its own dynam...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：流模型：计算物理视角
流模型 计算物理 最优输运理论
2023/4/24
我将结合一些个人的研究体会，介绍与流模型(flow-based generative model)相关的科学问题与科学应用。从计算物理的视角出发，我们将看到流模型与最优输运理论、流体力学、辛几何算法、重正化群、蒙特卡罗采样与分子分子模拟等领域的关联。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Dispersion Analysis of CIP–FEM for Helmholtz Equation
亥姆霍兹方程 CIP-FEM 色散分析
2023/4/24
When solving the Helmholtz equation numerically, the accuracy of numerical solution deteriorates as the wave number k increases, known as `pollution effect' which is directly related to the phase diff...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：等离子体物理中的机器学习问题与应用
等离子体物理 机器学习 等离子体系统
2023/4/24
等离子体物理在聚变能研究、深空探测、工业加工与材料处理等众多关键领域具有重要应用，而等离子体系统因自身具有多尺度、非线性、多组分、开放性等复杂性特点，为传统的实验、理论与模拟研究方法带来大量困难。机器学习方法通过利用来自实验与模拟等多种来源的科学数据训练算法，得到更加灵活而有效的工具，在数据处理、模拟、预测、反演等问题中逐步发挥出特有的优势。同时，利用机器学习手段来简化物理模型、降低模型维度、挖掘...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Global unique solutions for the inhomogeneous Navier-Stokes equation with only bounded density, in critical regularity spaces
临界正则性空间 界密度 非齐次 纳维-斯托克斯方程 全局唯一解
2023/4/25
Our work is to prove the global existence and uniqueness of solutions to the inhomogeneous incompressible Navier-Stokes system in the case where the initial density $\rho_0$ is discontinuous and the i...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Almost periodic function and rotation number of the Schrodinger operator
薛定谔算子 几乎周期函数 旋转数
2023/4/25
The concept of almost periodic functions is due to H. Bohr. The concept of rotation number is due to H. Poincaré. The Schr?dinger operator is named after E. Schr?dinger. I will present our work relate...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On constructions of Lax representations: some examples
松弛表示 构造 非线性数学物理方程 KdV方程
2023/4/24
著名数学家Peter Lax 在1968年将重要的非线性数学物理方程---KdV方程表示为一个算子方程， 即给出了KdV方程的Lax表示或Lax对。Lax对在孤立子理论的发展中扮演者重要角色，可以看成是研究可积系统的出发点。但如何构造一个给定非线性系统的Lax表示却是非常困难的问题。本报告在概述Lax表示历史的基础上，以Boris Kupershmidt提出的两个非线性发展型方程为具体例子，介绍L...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：On nonlinear Schrodinger-type equations with nonlinear damping
非线性阻尼 非线性 薛定谔型方程
2023/4/25
In this talk，I will introduce equations of nonlinear Schrodinger-type augmented by nonlinear damping terms. The nonlinear damping can prevent finite time blow-up in several situations. The solution of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：最大纠缠态集合的局部区分性
最大纠缠态 集合 局部区分性 正交量子态
2023/4/26
正交量子态集合的局部不可区分性是量子非局域性的一种体现，关于正交量子态集合局部区分性的研究是量子非局域性的重要内容，并且在量子数据隐藏、量子秘密共享和量子私有查询等方面有许多应用。这里主要介绍最大纠缠态（尤其是广义贝尔态）集合的局部区分性的基本理论以及近期的一些研究进展。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Wave scattering in anisotropic media
各向异性介质 波散射 数学
2023/4/26
In this talk, I will report some recent progress regarding wave scattering problems in anisotropic media.
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Splitting Numerical Schemes for Two-dimensional Maxwell-Debye Equations
二维 麦克斯韦-德拜方程组 拆分数值方案
2023/4/27
In this talk, we are interested in designing some efficient numerical methods for Maxwell-Debye equations in metamaterials with negative refractive index. Dimensional splitting method is used to reduc...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Survey of Stability of Peaked Solitons II: Multicomponent Case
峰值孤子 稳定性 多组分案例
2023/4/27
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A Survey of Stability of Peaked Solitons I: Scalar Case
峰值孤子 稳定性 标量案例
2023/4/27
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：非厄米量子行走的理论和实验研究
非厄米 量子行走 理论 实验研究
2023/4/27
通常对量子物理和量子信息的研究集中在封闭系统，但真实的系统往往是开放的，与环境之间存在相互耦合。通过对非厄米物理的研究可以获得对开放系统更深刻的认识。本次报告中，我将介绍非厄米体系展现出极其丰富的物理性质，例如非厄米趋肤效应；非厄米拓扑半金属中存在对称性无关的拓扑奇异线；非厄米准晶中存在多重拓扑相变和迁移率边，这些都在厄米体系中完全没有对应。实验中我们可利用量子行走模型展现并观测这些物性。利用这些...