螺旋约化波动方程的对称正系统

带Sommerfeld边界条件的螺旋约化波动方程解的唯一性

Uniqueness of Solutions to the Helically Reduced Wave Equation with Sommerfeld Boundary Conditions

本文考虑$(n+1)$维Minkowski空间$n\geq2$上具有任意源的波动方程的螺旋约化.约化方程是${\bf R}^n$上的混合椭圆-双曲型方程。我们得到了一个由$n$ -维球$B$组成的区域上的解的唯一性定理，该区域以螺旋对称轴的约化为中心，并满足$\partial B\approx S^{n-1}$上的进出Sommerfeld条件。在广义相对论中，这种边值问题的非线性推广（使用$n=3$）出现在双星螺旋的中间阶段。

A reduced model for domain walls in soft ferromagnetic films at the cross-over from symmetric to asymmetric wall types

We study the Landau-Lifshitz model for the energy of multi-scale transition layers -- called "domain walls" -- in soft ferromagnetic films. Domain walls separate domains of constant magnetization vectors $m^\pm \in \mathbb{S}^2$ that differ by an angle $2α$. Assuming translation invariance tangential to the wall, our main result is the rigorous derivation of a reduced model for the energy of the optimal transition layer, which in a certain parameter regime confirms the experimental, numerical and physical predictions: The minimal energy splits into a contribution from an asymmetric, divergence…

A short note on simplified pseudospectral methods for computing ground state and dynamics of spherically symmetric Schrodinger--Poisson--Slater system

In a recent paper we proposed and compared various approaches to compute the ground state and dynamics of the Schrödinger--Poisson--Slater (SPS) system for general external potential and initial condition, concluding that the methods based on sine pseudospectral discretization in space are the best candidates. This note is concerned with the case that the external potential and initial condition are spherically symmetric. For the SPS system with spherical symmetry, via applying a proper change of variables into the reduced quasi-1D model we simplify the methods proposed for the general 3D case…

Symmetric Criticality in Classical Field Theory

This is a brief overview of work done by Ian Anderson, Mark Fels, and myself on symmetry reduction of Lagrangians and Euler-Lagrange equations, a subject closely related to Palais' Principle of Symmetric Criticality. After providing a little history, I describe necessary and sufficient conditions on a group action such that reduction of a group-invariant Lagrangian by the symmetry group yields the correct symmetry-reduced Euler-Lagrange equations.

Reduced density matrix of nonlocal identical particles

We probe the theoretical connection among three different approaches to analyze the entanglement of identical particles, i.e., the first quantization language (1QL), elementary-symmetric/exterior products (which has the mathematical equivalence to no-labeling approaches), and the algebraic approach based on the GNS construction. Among several methods to quantify the entanglement of identical particles, we focus on the computation of reduced density matrices, which can be achieved by the concept of \emph{symmetrized partial trace} defined in 1QL. We show that the symmetrized partial trace corre…

纳米线中对称与反对称交换相互作用的约化理论

Reduced theory of symmetric and antisymmetric exchange interactions in nanowires

本文研究线支撑的扰动 Dirichlet 能量极小值，证明其在 $Γ$-收敛下约化为曲线上的简化能量泛函，揭示反对称交换相互作用贡献的各向异性项取决于曲率，并阐述其对含 DMI 的铁磁纳米线研究的意义。