Quantum scattering by intersecting {\delta}-potential barriers: from Gaudin's kaleidoscope to quantum Galperin billiards

Abstract:We develop a general framework for the scattering of a plane wave by a class of Gaudin kaleidoscope models: straight $\delta$-potential barriers intersecting at a common point. The projected Lippmann-Schwinger equations split into a singular part, a finite pole closure generated by a geometric moving rule, and a regular remainder, the outgoing state being an atomic measure on the circle. At the special angles $\pi/N$, where the intersecting barriers generate the dihedral group $D_N$, the number of channels stays fixed, whereas at generic angles channels are created and destroyed, opening smoothly from zero weight as a critical direction is crossed. This leaves no singular trace in the probabilities, being carried instead by the phase shifts, a quantum-classical correspondence beyond the reach of the coordinate Bethe ansatz. The same equations solve the quantum Galperin billiards exactly, the method of images reducing them to a single linear system whose phase shifts follow in closed form.

arXiv:2609.23406 [quant-ph]

(or arXiv:2609.23406v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2609.23406 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.