36 citations · 389 across the 48 of their papers we have counts for
6 papers · 1 filter
Power law logarithmic bounds of moments for long range operators in arbitrary dimension
Wencai Liu
We show that the sublinear bound of the bad Green's functions implies explicit logarithmic bounds of moments for long range operators in arbitrary dimension.
Bloch varieties and quantum ergodicity for periodic graph operators
Wencai Liu
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 p…
Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on
Wencai Liu
Let with and . Let be the discrete periodic Schrödinger operator on , where $Δ…
Distributions of resonances of supercritical quasi-periodic operators
Wencai Liu
We discover that the distribution of (frequency and phase) resonances plays a role in determining the spectral type of supercritical quasi-periodic Schrödinger operators. In partic…
One dimensional discrete Schrödinger operators with resonant embedded eigenvalues
Wencai Liu, Kang Lyu
In this paper, we introduce a new family of functions to construct Schrödinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schrödinger op…
Small denominators and large numerators of quasiperiodic Schrödinger operators
Wencai Liu
We initiate an approach to simultaneously treat numerators and denominators of Green's functions arising from quasi-periodic Schrödinger operators, which in particular allows us to…