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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Monotonicity of the second Neumann eigenfunction in symmetry domain
对称域 第二个 诺依曼特征函数 单调性
2023/4/18
In 1974, Jeffrey Rauch proposed the hot spot conjecture for the second eigenfunctions of the Neumann eigenvalue problems. We will recall some of its development and related studies in recent years. We...
Exact solution for eigenfunction statistics at the center-of-band anomaly in the Anderson localization model
Exact solution for eigenfunction statistics Anderson localization model
2010/11/24
An exact solution is found for the problem of the center-of-band (E = 0) anomaly in the one-
dimensional (1D) Anderson model of localization. By deriving and solving an equation for the
generating f...
Commensurability effects in one-dimensional Anderson localization: anomalies in eigenfunction statistics
Commensurability effects eigenfunction statistics
2010/11/18
The one-dimensional (1d) Anderson model (AM), i.e. a tight-binding chain with uncorrelated Gaussian disorder in the on-site energies, has statistical anomalies at any rational point f = 2a E , where ...
Eigenfunction localization for the 2D periodic Schrödinger operator
Eigenfunction localization 2D periodic Schrö dinger operator
2010/11/30
We prove that for any fixed trigonometric polynomial potential satisfying a genericity condition, the spectrum of the two dimension periodic Schr¨odinger operator has finite multiplicity and the Fouri...
The nodal line of the second eigenfunction of the Robin Laplacian in $\mathbb{R}^2$ can be closed
Laplacian eigenfunction nodal line Robin boundary
2010/12/13
We construct a multiply connected domain in R2 for which the second eigenfunction of the Laplacian with Robin boundary condi-tions has an interior nodal line. In the process, we adapt a bound of Donne...