The force-based QC spectral equivalence conjecture

Let $N\geq4$, let $1\leq K\leq N-2$, and let $F>0$. Denote by $L^{{\rm qcf}}_F$ and $L^{{\rm qnl}}_F$ the force-based and quasinonlocal QC operators, respectively. Spectral equivalence conjecture. The operator $L^{{\rm qcf}}_F$ is diagonalizable and has the same spectrum as $L^{{\rm qnl}}_F$. This conjecture concerns the spectral structure underlying iterative methods for the force-based QC approximation; the paper presents numerical evidence but does not establish the assertion analytically.