慶應義塾大学 理工学部 数理科学科

タイトル One and two dimensional quasicrystal models
開催日時 2019年7月26日 17:00-18:00
主催者
講演者 高橋 悠樹 氏 (東北大学 AIMR)
場所 慶應義塾大学矢上キャンパス
14-631A/B
内容 We will first discuss the Fibonacci Hamiltonian, which is the most prominent one-dimensional quasicrystal model. The Fibonacci Hamiltonian has been studied intensively for the past thirty years and now it is known that the spectral properties of the Fibonacci Hamiltonian can be described by the so-called trace map. We then discuss the Square Fibonacci Hamiltonian and the Labyrinth model. They are two-dimensional quasicrystal models that are constructed by two copies of one-dimensional models. The spectra of the Square Fibonacci Hamiltonian and the Labyrinth model are given by sums and products of two Cantor sets, respectively. We will show that their spectra are intervals for sufficiently small coupling constants.
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