（1+1）维双曲Heisenberg和Sigma模型

双曲O(N)线性σ模型及其均场极限

Hyperbolic $O (N)$ linear sigma model and its mean-field limit

本文研究了双曲O(N)线性σ模型在大N极限下的均场行为，证明了其在时间上的收敛性及收敛速率。

Asymptotic behaviors of governing equation of Gauged Sigma model for Heisenberg ferromagnet

In this note, we study weak solutions of equation \begin{equation}\label{eq 00.1} Δu =\frac{4e^u}{1+e^u} -4π\sum^{N}_{i=1}δ_{p_i}+4π\sum^{M}_{j=1}δ_{q_j} \quad{\rm in}\;\; \mathbb{R}^2, \end{equation} where $\{δ_{p_i}\}_{i=1}^N$ (resp. $\{δ_{q_j}\}_{j=1}^M$ ) are Dirac masses concentrated at the points $p_i, i=1,\cdots, N$, (resp. $q_j, i=1,\cdots, M$) %$δ_{p_j}$ is Dirac mass concentrated at the point $p_j$ and $N-M>1$. This equation presents a governing equation of Gauged Sigma model for Heisenberg ferromagnet and we prove that it has a sequence of solutions $u_β$ having behaviors as $-2πβ\l…

双曲空间上的尺度依赖Poincaré不等式、log-Sobolev不等式及海森堡不确定性原理的稳定性

Scale-Dependent Poincaré inequalities, log-Sobolev inequality and the stability of the Heisenberg Uncertainty Principle on the hyperbolic space

本文在双曲空间上建立尺度依赖的Poincaré-Hardy型恒等式，推导并改进多类不等式，获得海森堡不确定性原理的L2稳定性，并填补高斯测度对数Sobolev不等式的空白。

Liouville theorems for Kirchhoff-type hypoelliptic Partial Differential Equations and systems. I. Heisenberg group

In this paper, we show the nonexistence results for the Kirchhoff elliptic, parabolic, and hyperbolic type equations on the Heisenberg groups. Also, the pseudo-parabolic and pseudo-hyperbolic equations of the Kirchhoff-type are under consideration. To prove these results we use the test function method. In addition, the analogous results are transferred to the cases of systems. Also, we give some examples of non-local nonlinearities.

双曲 $O(N)$ 线性 sigma 模型的 Smoluchowski-Kramers 近似及其平均场极限

On the Smoluchowski-Kramers approximation for the hyperbolic $O(N)$ linear sigma model and its mean-field limit

研究二维环面上带耦合三次非线性的随机阻尼非线性波动方程系统，证明当阻尼系数趋于零且分量数趋于无穷时，系统收敛到平均场随机非线性热方程。

Sigma-convergence of semilinear stochastic wave equations

We address the homogenization of a semilinear hyperbolic stochastic partial differential equation with highly oscillating coefficients, in the context of ergodic algebras with mean value. To achieve our goal, we use a suitable variant of the sigma-convergence concept that takes into account both the random and deterministic behaviours of the phenomenon modelled by the underlying problem. We also provide an appropriate scheme for the approximation of the effective coefficients. To illustrate our approach, we work out some concrete problems such as the periodic homogenization problem, the almost…