



01418nas a2200157   4500008004100000245008100041210006900122260001400191490000600205520093500211100001601146700002101162700001501183700002501198856003701223       2022                        eng d00aUniversality in one-dimensional scattering with general dispersion relations0 aUniversality in onedimensional scattering with general dispersio  c3/17/20210 v43 a<p>Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in one dimension when the dispersion relation is ϵ(k)=&plusmn;|d|km, where m&ge;2 is an integer. We study impurity scattering problems in which a single-particle in a one-dimensional waveguide scatters off of an inhomogeneous, discrete set of sites locally coupled to the waveguide. For a large class of these problems, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E&rarr;0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson&#39;s theorem -- which relates the scattering phases to the number of bound states -- to impurity scattering for these more general dispersion relations.</p>1 aWang, Yidan1 aGullans, Michael1 aNa, Xuesen1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2103.09830