Nonlocal field theory of quasiparticle scattering in dipolar Bose-Einstein condensates

Abstract

We consider the propagation of quasiparticle excitations in a dipolar Bose-Einstein condensate, and derive a nonlocal field theory of quasiparticle scattering at a stepwise inhomogeneity of the sound speed, obtained by tuning the contact coupling part of the interaction on one side of the barrier. To solve this problem $ab$ $initio$, i.e., without prior assumptions on the form of the solutions, we reformulate the dipolar Bogoliubov-de Gennes equation as a singular integral equation. The latter is of a $novel$ $hypersingular$ type, in having a kernel which is hypersingular at only two isolated points. Deriving its solution, we show that the integral equation reveals a continuum of evanescent channels at the sound barrier which is absent for a purely contact-interaction condensate. We furthermore demonstrate that by performing a discrete approximation for the kernel, one achieves an excellent solution accuracy for already a moderate number of discretization steps. Finally, we show that the non-monotonic nature of the system dispersion, corresponding to the emergence of a roton minimum in the excitation spectrum, results in peculiar features of the transmission and reflection at the sound barrier which are nonexistent for contact interactions.

arXiv comment19 pages, 10 figures

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Cited by in corpus (5)

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• Quasiparticle solutions for the nonlocal NLSE with an anti-Hermitian term in semiclassical approximation
• Phonons mimicking doubly special relativity kinematics
• Harvesting entanglement from the Lorentz-violating quantum field vacuum in a dipolar Bose-Einstein condensate
• Semiclassical states localized on a one-dimensional manifold and governed by the nonlocal NLSE with an anti-Hermitian term