15:30 - 16:30, November 13, 2025 (Thursday) Room 505, Cosmology Building, National Taiwan University + Cisco WebEx, Physical+Online Seminar
(實體+線上演講 台灣大學次震宇宙館505研討室+ Cisco WebEx)
Statistical Properties of Various Quantum Disordered Systems Fumihiko Nakano (Tohoku University)
Abstract
Quantum disordered system is one of the most important topics in mathematical physics, and related to various interesting phenomena, such as Anderson localization, quantum Hall effect, topological insulator, etc. A typical characteristics is densely distributed point spectrum with exponentially localized eigenfunctions, but recently its statistical properties are drawing much attention. In this talk, we first overview the developments on the 1-dimensional decaying models which exhibits continuous transitions for various properties, and then discuss some of the recent topics :
(1) -dimensional decaying models : we have a phase transition on the spectrum, depending on the tail of the on-site distribution. Extremal value statistics is also observed.
(2) models with critical energies : some special models (e.g., polymer-model, mosaic-model) have finite set of critical energies embedded in the localized regime, because of which they have non-vanishing transport. We see a "sharp" transition for the local eigenvalue statistics: from clock to Poisson with no intermediate ones.
(3)-model : this is a 1-dimensional random Schrödinger operator with explicit connection to VRJP, a RWRE, and non-linear -model. In this model, transition of spectral properties is linked to the recurrence-transience of RWRE, and behavior of correlation functions of the -model.
