Spectral Properties of Periodic Elastic Beam Hamiltonians on Hexagonal Lattices

Math Physics Seminar
Thursday, October 13, 2022 - 4:00pm for 1 hour (actually 50 minutes)
Skiles Room 005
Burak Hatinoglu – School of Mathematics, Georgia Tech – bhatinoglu3@gatech.edu
Michael Loss

Elastic beam Hamiltonians on single-layer graphs are constructed out of Euler-Bernoulli beams, each governed by a scalar valued fourth-order Schrödinger operator equipped with a real symmetric potential. Unlike the second-order Schrödinger operator commonly applied in quantum graph literature, here the self-adjoint vertex conditions encode geometry of the graph by their dependence on angles at which edges are met. In this talk, I will first consider spectral properties of this Hamiltonian with periodic potentials on a special equal-angle lattice, known as graphene or honeycomb lattice. I will also discuss spectral properties for the same operator on lattices in the geometric neighborhood of graphene. This talk is based on a joint work with Mahmood Ettehad (University of Minnesota),https://arxiv.org/pdf/2110.05466.pdf.