Bloch varieties and quantum ergodicity for periodic graph operators Institutional Repository Document uri icon


  • For periodic graph operators, we establish criteria to determine the overlaps of spectral band functions based on Bloch varieties. One criterion states that for a large family of periodic graph operators, the irreducibility of Bloch varieties implies no non-trivial periods for spectral band functions. This particularly shows that spectral band functions of discrete periodic Schr"odinger operators on $mathbb{Z}^d$ have no non-trivial periods, answering a question asked by Mckenzie and Sabri [Quantum ergodicity for periodic graphs. arXiv preprint arXiv:2208.12685 (2022)].

author list (cited authors)

  • Liu, W.

complete list of authors

  • Liu, Wencai

Book Title

  • arXiv

publication date

  • October 2022