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Exact Boundary Controllability for a Coupled System of Wave Equations with Neumann Boundary Controls(Dedicated to Professor Haim Brezis on the occasion of his 70th birthday)

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Chinese Annals of Mathematics,Series B 2017年第2期38卷 473-488页

作者： Tatsien LI Bopeng RAO school of mathematical sciences fudan universityShanghai 200433China/shanghai key laboratory for contemporary applied mathematics/nonlinear mathematical modeling and methods laboratory institut de recherche mathmatique avancée universite de strasbourgFrance

This paper first shows the exact boundary controllability for a coupled system of wave equations with Neumann boundary controls. In order to establish the corresponding observability inequality, the authors introduce a compact perturbation method which does not depend on the Riesz basis property, but depends only on the continuity of projection with respect to a weaker norm, which is obviously true in many cases of application. Next,in the case of fewer Neumann boundary controls, the non-exact boundary controllability for the initial data with the same level of energy is shown.

关键词： Compactness-uniqueness perturbation, Boundary observability, Exactboundary controllability, Non-exact boundary controllability, Coupledsystem of wave equations, Neumann boundary condition

Nonlinear Maps Preserving the Jordan Triple ＊-Product on Factor von Neumann Algebras

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Chinese Annals of Mathematics,Series B 2018年第4期39卷 633-642页

作者： Changjing LI Quanyuan CHEN Ting WANG School of Mathematical Sciences Shandong Normal University Jinan 250014 China. College of Information Jingdezhen Ceramic Institute Jingdezhen 333403 Jiangxi China. Department of Mathematics and Statistics Nanyang Normal University Nanyang 473061 Henan China

Let A and B be two factor von Neumann algebras. For A, B ∈ A, define by [A, B]_*= AB-BA~*the skew Lie product of A and B. In this article, it is proved that a bijective map Φ : A → B satisfies Φ([[A, B]_*, C]_*) = [[Φ(A), Φ(B)]_*, Φ(C)]_*for all A, B, C ∈ A if and only if Φ is a linear *-isomorphism, or a conjugate linear *-isomorphism, or the negative of a linear *-isomorphism, or the negative of a conjugate linear *-isomorphism.

关键词： Neumann 非线性代数学产品地图约旦保存晶型

Well-posedness for the Cahn-Hilliard Equation with Neumann Boundary Condition on the Half Space

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Journal of Partial Differential Equations 2017年第4期30卷 344-380页

作者： WANG Ling-Jun College of Science Wuhan University of Science and Technology Wuhan 430065 China

In this paper, we investigate the Cahn-Hilliard equation defined on the halfspace and subject to the Neumann boundary and initial condition. For given initialdata in some sobolev space, we prove the existence and anal... 详细信息

关键词： Neumann 半空间边界方程 sobolev

The Neumann Problem of Complex Special Lagrangian Equations with Supercritical Phase

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Analysis in Theory and Applications 2019年第2期35卷 144-162页

作者： Chuanqiang Chen Xinan Ma Wei Wei Department of Applied Mathematics Zhejiang Unioersity of TechnologyHangzhou310023ZhejiangChina School of Mathematical Sciences University of Science and Technology of ChinaHefei230026AnhuiChina School of Mathematical Sciences University of Science and Technology of ChinaHefei230026AnhuiChina

nspired by the Neumann problem of real special Lagrangian equations with supercritical phase,we consider the Neumann problem of complex special Lagrangian equations with supercritical phase in this paper,and establish... 详细信息

关键词： Special Lagrangian equation Neumann problem supercritical phase

包含临界Sobolev-Hardy指数的奇异椭圆方程的Neumann问题

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山东农业大学学报（自然科学版） 2019年第5期50卷 913-917页

作者：公艳山东农业大学信息科学与工程学院

在0∈■Ω的情况下,解决了一类包含临界 Sobolev-Hardy 指数的奇异椭圆方程解的存在性,它与0∈Ω是不同的.根据笔者已证的一个广义存在性定理,得到了这类奇异椭圆方程的一个正解的存在性结论.

关键词： Sobolev-Hardy 指数椭圆方程 Neumann 问题

Quantitative conditions for time evolution in terms of the von Neumann equation

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Science China(Physics,Mechanics & Astronomy) 2018年第7期61卷 54-60页

作者： WenHua Wang HuaiXin Cao ZhengLi Chen Lie Wang School of Ethnic Education Shaanxi Normal University Xi'an 710062 China School of Mathematics and In Cbrmatton Sctence Shaanxi Normal University Xi 'an 710062 China

The adiabatic theorem describes the time evolution of the pure state and gives an adiabatic approximate solution to the Schr ¨odinger equation by choosing a single eigenstate of the Hamiltonian as the initial state. In quantum systems, states are divided into pure states(unite vectors) and mixed states(density matrices, i.e., positive operators with trace one). Accordingly, mixed states have their own corresponding time evolution, which is described by the von Neumann equation. In this paper, we discuss the quantitative conditions for the time evolution of mixed states in terms of the von Neumann equation. First, we introduce the definitions for uniformly slowly evolving and δ-uniformly slowly evolving with respect to mixed states, then we present a necessary and sufficient condition for the Hamiltonian of the system to be uniformly slowly evolving and we obtain some upper bounds for the adiabatic approximate error. Lastly, we illustrate our results in an example.

关键词： Neumann Hamiltonian 进化时间方程混合状态状态演变密度矩阵

Enhancing von Neumann entropy by chaos in spin–orbit entanglement

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Chinese Physics B 2019年第10期28卷 153-159页

作者：刘郴荣喻佩陈宪章徐洪亚黄亮来颖诚 School of Physical Science and Technology and Key Laboratory for Magnetism and Magnetic Materials of MOELanzhou UniversityLanzhou 730000China School of Electrical Computerand Energy EngineeringArizona State UniversityTempeAZ 85287USA Department of Physics Arizona State UniversityTempeAZ 85287USA

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin-orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin-orbit coupling regime, we find that classical chaos can significantly enhance spin-orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.

关键词： spin-orbit entanglement chaos von Neumann entropy spin decoherence

COMPLEX INTERPOLATION OF NONCOMMUTATIVE HARDY SPACES ASSOCIATED WITH SEMIFINITE VON Neumann ALGEBRAS

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Acta Mathematica Scientia 2020年第1期40卷 245-260页

作者：吐尔德·别克 Kordan NOSPANOV College of Mathematics and Systems Science Xinjiang UniversityUrumqi 830046China Faculty of Mechanics and Mathematics L.N.Gumilyov Eurasian National UniversityAstana 010008Kazakhstan

We proved a complex interpolation theorem of noncommutative Hardy spaces associated with semi-finite von Neumann algebras and extend the Riesz type factorization to the semi-finite case.

关键词： subdiagonal algebra complex interpolation noncommutative Hardy space semi-finite von Neumann algebra

Singularly perturbed Neumann problem for fractional Schrdinger equations

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Science China Mathematics 2018年第4期61卷 695-708页

作者： Guoyuan Chen School of Data Sciences Zhejiang University of Finance & Economics

This paper is concerned with a Neumann type problem for singularly perturbed fractional nonlinear Schrdinger equations with subcritical exponent. For some smooth bounded domain ?  R^n, our boundary condition is given by∫_?u(x)-u(y)/|x-y|^(n+2s)dy = 0 for x ∈ R^n\?.We establish existence of non-negative small energy solutions, and also investigate the integrability of the solutions on Rn.

关键词： Neumann inger 方程边界条件非线性