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Phonon redshift and Hubble friction in an expanding BEC



Stephen Eckel, Ted Jacobson


We revisit the theoretical analysis of an expanding ring-shaped Bose-Einstein condensate. Starting from the action and integrating over dimensions orthogonal to the phonon's direction of travel, we derive an effective one-dimensional wave equation for azimuthally-travelling phonons. This wave equation shows that expansion redshifts the phonon frequency at a rate determined by the effective azimuthal sound speed, and damps the amplitude of the phonons at a rate given by $\dot\cal V}/\cal V}$, where $\calV}$ is the volume of the background condensate. This behavior is analogous to the redshifting and ''Hubble friction'' for quantum fields in the expanding universe and, given the scalings with radius determined by the shape of the ring potential, is consistent with recent experimental and theoretical results. The action-based dimensional reduction methods used here should be applicable in a variety of settings, and are well suited for systematic perturbation expansions.
SciPost Physics


Bose-Einstein condensation, quantum gasses, quantum simulation, cosmology


Eckel, S. and Jacobson, T. (2021), Phonon redshift and Hubble friction in an expanding BEC, SciPost Physics, [online],, (Accessed May 23, 2024)


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Created March 11, 2021, Updated April 22, 2021