Fermi isospectrality for discrete periodic Schrodinger operators Academic Article uri icon

abstract

  • AbstractLet , where , , are pairwise coprime. Let be the discrete Schrdinger operator, where is the discrete Laplacian on and the potential is periodic. We prove three rigidity theorems for discrete periodic Schrdinger operators in any dimension : If at some energy level, Fermi varieties of two realvalued periodic potentials V and Y are the same (this feature is referred to as Fermi isospectrality of V and Y), and Y is a separable function, then V is separable; If two complexvalued periodic potentials V and Y are Fermi isospectral and both and are separable functions, then, up to a constant, lower dimensional decompositions and are Floquet isospectral, ; If a realvalued potential V and the zero potential are Fermi isospectral, then V is zero. In particular, all conclusions in (1), (2) and (3) hold if we replace the assumption Fermi isospectrality with a stronger assumption Floquetisospectrality.

published proceedings

  • COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS

author list (cited authors)

  • Liu, W.

citation count

  • 3

complete list of authors

  • Liu, Wencai

publication date

  • February 2023

publisher