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Mathematical Physics Seminar

Spectral Properties of Continuum Fibonacci Schrodinger Operators

May Mei - Denison University

Location:  Hill 705
Date & time: Thursday, 05 December 2019 at 12:00PM - 1:00PM

Abstract:   The Nobel Prize-winning discovery of quasicrystals irrevocably changed the paradigm of crystalline structure. From the standpoint of theoretical physics, questions about the time evolution of quantum particles lead to the study of a Schrodinger operator that depends on parameters that we will refer to as the potential, which corresponds to the potential energy of the system, and the coupling constant which encodes interaction strength. In particular, we are interested in potentials that are generated by ergodic transformations. Discrete Schrodinger operators with potentials generated by aperiodic subshifts over a finite alphabet have been studied since the mid 1980’s. More specifically, the Fibonacci Hamiltonian has been a particularly well-studied example. Several continuum analogues have also been considered. In this talk, we will offer a brief survey of discrete ergodic Schrodinger operators and discuss spectral properties of one particular continuum Fibonacci Schrodinger operator in which each letter of the subshift sequence is replaced with a function.