2020/09/30 by Stephen Eckel, Ted Jacobson, Theodore Jacobson · 11 citations
Physics and Astronomy · #Action (physics) #Amplitude #Classical mechanics #Cosmology #Dark energy #Hubble volume #Hubble's law #Mechanical and Optical Resonators #Metric expansion of space #Perturbation (astronomy) #Phonon #Physics #Quantum Electrodynamics and Casimir Effect #Quantum electrodynamics #Quantum mechanics #Quantum, superfluid, helium dynamics #RADIUS #Redshift #cond-mat.quant-gas #gr-qc #hep-th #physics.atom-ph
paper · pdf · doi:10.21468/scipostphys.10.3.064
published in SciPost Physics 10(3) (SciPost.org) · Typos fixed, minor clarifications, version published in SciPost
openalex publication_date 2021/03/11 · arxiv created 2021/03/14 · arxiv updated 2021/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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 V/V <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mover> <mml:mstyle mathvariant="script"> <mml:mi>𝒱</mml:mi> </mml:mstyle> <mml:mo accent="true">̇</mml:mo> </mml:mover> <mml:mi>/</mml:mi> <mml:mstyle mathvariant="script"> <mml:mi>𝒱</mml:mi> </mml:mstyle> </mml:mrow> </mml:math> , where V <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mstyle mathvariant="script"> <mml:mi>𝒱</mml:mi> </mml:mstyle> </mml:math> 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.