



01811nas a2200205   4500008004100000245005900041210005900100260001300159490000600172520120100178653002701379653003501406653003101441100001601472700002101488700001501509700001901524700002501543856003701568       2022                        eng d00aUniversal scattering with general dispersion relations0 aUniversal scattering with general dispersion relations  c4/6/20220 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 general spatial dimension D&ge;1 when the density of states diverges at a specific energy. To illustrate the underlying principles in an experimentally relevant setting, we focus on waveguide quantum electrodynamics (QED) problems (i.e. D=1) with dispersion relation ϵ(k)=&plusmn;|d|km, where m&ge;2 is an integer. For a large class of these problems for any positive integer m, 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 waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D&ge;1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.</p>10aFOS: Physical sciences10aMathematical Physics (math-ph)10aQuantum Physics (quant-ph)1 aWang, Yidan1 aGullans, Michael1 aNa, Xuesen1 aWhitsitt, Seth1 aGorshkov, Alexey, V.  uhttps://arxiv.org/abs/2103.09830