Surface states and spectra

Vojkan Jakšić*, Yoram Last

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


Let ℤd+1+ = ℤd × ℤ+, let H0 be the discrete Laplacian on the Hilbert space l2(ℤd+1+) with a Dirichlet boundary condition, and let V be a potential supported on the boundary ∂ℤd+1+. We introduce the notions of surface states and surface spectrum of the operator H = H0+V and explore their properties. Our main result is that if the potential V is random and if the disorder is either large or small enough, then in dimension two H has no surface spectrum on σ(H0) with probability one. To prove this result we combine Aizenman-Molchanov theory with techniques of scattering theory.

Original languageAmerican English
Pages (from-to)459-477
Number of pages19
JournalCommunications in Mathematical Physics
Issue number3
StatePublished - 2001


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