Note on quantum unique ergodicity

Steve Zelditch*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


We prove that (near) off-diagonal matrix elements script A sign ψi, ψ j (i ≠ j) of pseudodifferential operators relative to eigenfunctions of quantum uniquely ergodic Laplacians vanish as the eigenvalues tend to infinity. It follows that QUE systems cannot have quasi-modes with singular limits and a bounded number of essential frequencies, as is believed to occur for the stadium and other examples.

Original languageEnglish (US)
Pages (from-to)1869-1872
Number of pages4
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - Jun 2004

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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