Multivariate pseudospectrum and topological physics

Applied Math And Analysis Seminar

Terry Loring (University of New Mexico)

Wednesday, March 21, 2018 -
12:00pm to 1:00pm
Location: 
119 Physics

The usual pseudospectrum acquires an additional feature when restricted to matrices with a certain symmetry. The new feature is a simple form of K-theory which can be used to compute the index of some one-dimensional topological insulators. The usual pseudospectrum applies to a single matrix, or equivalently to two Hermitian matrices. Generalized to apply to more Hermitian matrices, the nature of the pseudospectrum changes radically, often having interesting geometry. Examples come from D-branes and higher-dimensional topological insulators. The algorithm to compute the pseudospectrum also produces common approximate eigenvectors for a collection of almost commuting Hermitian matrices. Applied to a basic model of a finite volume topological insulator it produces vectors that are approximately stationary and somewhat localized in position.

Last updated: 2018/05/21 - 12:02am