applied math seminar
Numerically approximating the bulk spectrum of a quasiperiodic Hamiltonian on an infinite system
The bulk spectrum of a certain insulator on a quasicrystalline lattice cannot directly be computed from finite systems. No choice of boundary conditions gives a Hamiltonian whose spectrum is close to the spectrum of the full Hamiltonian. Augmenting the system, to a model reminiscent of the system being probed by a scanning tunnelling microscope, creates a finite system whose pseudospectrum is related to the spectrum of the full Hamiltonian. Mathematically, the larger system is easily described using the Pauli spin matrices. A numerical study of the spectrum and associated approximate eigenvectors will be discussed. The approximate eigenvectors on the quasicyrstal have unusual, perhaps beautiful, patterns. These will be used to punctuate the math and physics.
Contact Name: Pavel Lushnikov