学术报告

学术活动

学术报告
09/05 2022 Seminar
  • Title题目 SYK model with an extra diagonal perturbation: phase transition in the eigenvalue spectrum
  • Speaker报告人 吴双 (上海交通大学)
  • Date日期 2022年09月05日 15:30
  • Venue地点 南楼6520会议室
  • Abstract摘要

      In my talk, I will present how to study the SYK model with an extra constant source, i.e. a constant matrix or equivalently a diagonal matrix with only one non-zero entry λ by using methods from analytic combinatorics, we find exact expressions for the moments of this model. We further prove that the spectrum of this model can have a gap when λ1>λc1, thus exhibiting a phase transition in λ. In this case, a single isolated eigenvalue splits off from SYK's eigenvalues distribution. We located this single eigenvalue by analyzing the singular behavior of a supercritical functional composition scheme. In certain limit our results recover the ones of random matrices with non-zero mean entries. This talk is based on arXiv:2204.09998. 

      报告人简介:吴双,本科及研究生毕业于巴黎第六大学。博士毕业于巴黎萨克雷大学,博士阶段研究的课题为:Algebraic area distribution of two-dimensional random walks and the Hofstadter model。 

      在上海交通大学物理与天文学院担任博士后,研究课题:利用组合数学的方法研究SYK及其相关的模型。 

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