



@article {3030,
	title = {Universal scattering with general dispersion relations},
	journal = {Phys. Rev. Research},
	volume = {4},
	year = {2022},
	month = {4/6/2022},
	chapter = {023014},
	abstract = {<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\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to waveguide QED scattering for these more general dispersion relations. We then extend these results to general integer dimensions D\&ge;1, dispersion relations ϵ(k)=|k|a for a D-dimensional momentum vector k with any real positive a, and separable potential scattering.</p>},
	keywords = {FOS: Physical sciences, Mathematical Physics (math-ph), Quantum Physics (quant-ph)},
	doi = {https://doi.org/10.1103/PhysRevResearch.4.023014},
	url = {https://arxiv.org/abs/2103.09830},
	author = {Wang, Yidan and Michael Gullans and Na, Xuesen and Whitsitt, Seth and Alexey V. Gorshkov}
}
@article {2760,
	title = {Universality in one-dimensional scattering with general dispersion relations},
	journal = {Phys. Rev. Res.},
	volume = {4},
	year = {2022},
	month = {3/17/2021},
	chapter = {023014},
	abstract = {<p>Many synthetic quantum systems allow particles to have dispersion relations that are neither linear nor quadratic functions. Here, we explore single-particle scattering in one dimension when the dispersion relation is ϵ(k)=\&plusmn;|d|km, where m\&ge;2 is an integer. We study impurity scattering problems in which a single-particle in a one-dimensional waveguide scatters off of an inhomogeneous, discrete set of sites locally coupled to the waveguide. For a large class of these problems, we rigorously prove that when there are no bright zero-energy eigenstates, the S-matrix evaluated at an energy E\&rarr;0 converges to a universal limit that is only dependent on m. We also give a generalization of a key index theorem in quantum scattering theory known as Levinson\&$\#$39;s theorem -- which relates the scattering phases to the number of bound states -- to impurity scattering for these more general dispersion relations.</p>},
	doi = {https://doi.org/10.48550/arXiv.2103.09830},
	url = {https://arxiv.org/abs/2103.09830},
	author = {Yidan Wang and Michael Gullans and Xuesen Na and Alexey V. Gorshkov}
}
