  Brillouin-zone (BZ) definition in a class of non-reciprocal Willis monatomic
lattices (WMLs) is analytically quantified. It is shown that BZ boundaries only
shift in response to non-reciprocity in one-dimensional WMLs, implying a
constant BZ width, with asymmetric dispersion diagrams exhibiting unequal
wavenumber ranges for forward and backward going waves. An extension to square
WMLs is briefly discussed, analogously demonstrating the emergence of shifted
and irregularly shaped BZs, which maintain constant areas regardless of
non-reciprocity strength.
