2024年02月23日 星期五 登录 EN

学术活动
A Landscape View of Eigenvalues Approximation
首页 - 学术活动
报告人:
Wei Wang, University of Minnesota
邀请人:
Weiying Zheng, Professor
题目:
A Landscape View of Eigenvalues Approximation
时间地点:
9:00-10:00 February 2(Thursday),Tencent Meeting ID: 910 434 196
摘要:
Waves of all sorts, including electromagnetic waves, acoustic waves, and mechanical vibrations, play a role in shaping our world. In disordered systems, the transport of waves is hindered, resulting in a suppression of their motion. Building on the recent theoretical progress, the 'localization landscape' enables the solution of some of the most compelling puzzles of wave localizations in disordered media. In this talk, we will discuss random Schrödinger operators. Using the effective potential, we show that the ratio between the eigenvalues and the local minima of the effective potential approaches constants as the domain size approaches infinity. By counting the local minima points of the effective potential, we introduce the landscape law to establish non-asymptotic estimates from above and below on the integrated density of states (IDOS). Further, we will discuss various improved approximations to the IDOS between energy ranges.