## The 1D Anderson Model: From Furstenberg's Theorem to Spectral and Dynamical Localization via Large Deviation Estimates

**题目：**The 1D Anderson Model: From Furstenberg's Theorem to Spectral and Dynamical Localization via Large Deviation Estimates

**报告人：**Rice大学David Damanik教授

**时间：**2017年5月8日（周一）下午4:00-5:00

**地点：**理科楼B203

**摘要：**Anderson's Nobel Prize-winning work showed that a random environment can localize a quantum state for all times. In general dimensions, and without assuming sufficient regularity of the single-site distribution, this can be rigorously shown only via an intricate multi-scale analysis.

In one dimension, the positivity of the Lyapunov exponent that can be shown using Furstenberg's Theorem has for a long time been expected to imply Anderson localization rather directly. However, for singular distributions such as the Bernoulli case, no direct proof was available and a multi-scale analysis was still necessary. This talk will explain the history of this problem and its proof, the obstacles in finding a direct path from Furstenberg to Anderson, and recent work that does in fact find the desired direct path and opens the door for new results that were previously inaccessible in situations where no multi-scale analysis is available.

**联系人：**瞿燕辉