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PRODID:-//prob.tw//NTU Seminars V2//EN
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UID:2025-11-13-fumihiko-nakano-statistical-properties-of-various-quantum-disordered-systems@seminars.prob.tw
DTSTAMP:20261014T103741Z
DTSTART:20251113T073000Z
DTEND:20251113T083000Z
SUMMARY:Statistical properties of various quantum disordered systems
DESCRIPTION:Fumihiko Nakano\nQuantum 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 :\n(1) $d$-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.\n(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.\n(3) $H_{2|2}$-model : this is a 1-dimensional random Schr¨odinger operator with explicit connection to VRJP\, a RWRE\, and non-linear $\\\\sigma$-model. In this model\, transition of spectral properties is linked to the recurrence-transience of RWRE\, and behavior of correlation functions of the $\\\\sigma$-model.
LOCATION:台大次震宇宙館 505 室
URL:http://127.0.0.1:8123/?event=2025-11-13-fumihiko-nakano-statistical-properties-of-various-quantum-disordered-systems
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