200 citations · 1k across the 51 of their papers we have counts for
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Analytic and algebraic properties of dispersion relations (Bloch varieties) and Fermi surfaces. What is known and unknown
Peter Kuchment
The article surveys the known results and conjectures about the analytic properties of dispersion relations and Fermi surfaces for periodic equations of mathematical physics and th…
Dispersion relations and spectra of periodically perforated structures
Peter Kuchment, Jari Taskinen
We establish absolute continuity of the spectrum of a periodic Schrödiner operator in R^n with periodic perforations. We also prove analytic dependece of the dispersion relation on…
Generic properties of dispersion relations for discrete periodic operators
Ngoc T. Do, Peter Kuchment, Frank Sottile
An old problem in mathematical physics deals with the structure of the dispersion relation of the Schrödinger operator in with periodic potential near the edges of…
Spectra of "fattened" open book structures
James E. Corbin, Peter Kuchment
We establish convergence of spectra of Neumann Laplacian in a thin neighborhood of a branching 2D structure in 3D to the spectrum of an appropriately defined operator on the struct…
Analyticity of the spectrum and Dirichlet-to-Neumann operator technique for quantum graphs
Peter Kuchment, Jia Zhao
In some previous works, the analytic structure of the spectrum of a quantum graph operator as a function of the vertex conditions and other parameters of the graph was established.…
On Parseval frames of exponentially decaying composite Wannier functions
David Auckly, Peter Kuchment
Let be a periodic self-adjoint linear elliptic operator in with coefficients periodic with respect to a lattice $\G$, e.g. Schrödinger operator $(i^{-1}\partial/\partial…