报告时间：2024年06月20日 15:30开始
报 告 人：Dr. Shiwen Zhang (University of Massachusetts Lowell, USA)
报告地点：博彩导航
9号楼113报告厅
报告题目： Approximate Eigenvalues via the Landscape Function in Disordered Media
报告摘要：
Schrödinger operators with random potentials are very important models in quantum mechanics, in the study of transport properties of electrons in solids. In this talk, we study the approximation of eigenvalues via landscape theory for some random Schrödinger operators. The localization landscape theory, introduced in 2012 by Filoche and Mayboroda, considers the landscape function u solving Hu=1 for an operator H. Landscape theory has remarkable power in studying the eigenvalue problems for a large class of operators and has led to numerous “landscape baked” results in mathematics, as well as in theoretical and experimental physics. We first give a brief review of the localization landscape theory. Then we focus on some recent progress of the landscape-eigenvalue approximation for operators on general graphs. We show that the maximum of the landscape function is comparable to the reciprocal of the ground state eigenvalue, for Anderson or random hopping models on certain graphs with growth and heat kernel conditions, as well as on some fractal-like graphs such as the Sierpinski gasket graph. There will be precise asymptotic behavior of the ground state energy for some 1D chain models, as well as numerical stimulations for excited states energies. We will also show estimates of the integrated density of states in terms of a counting function based upon the landscape function. The talk is based on recent joint work with L. Shou (UMD) and W. Wang (ICMSEC).
报告人简介：
Dr. Zhang joined the Department of Mathematics & Statistics at University of Massachusetts Lowell in 2022. He obtained PhD from University of California, Irvine in 2016, under the supervision of Svetlana Jitomirskaya. After that, he get postdoctoral position at Michigan State University and University of Minnesota. His research field is Mathematical Physics and spectral theory. In particular, he is interested in quantum localization in disordered medium.
