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arXiv · 2212.08671

Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate

Yi-Hsien Du·Sergej Moroz·Dung Xuan Nguyen·Dam Thanh Son
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Abstract

We construct an effective field theory describing the collective Tkachenko oscillation mode of a vortex lattice in a two-dimensional rotating Bose-Einstein condensate in the long-wavelength regime. The theory has the form of a noncommutative field theory of a Nambu-Goldstone boson, which exhibits a noncommutative version of dipole symmetry. From the effective field theory, we show that, at zero temperature, the decay width $\Gamma$ of the Tkachenko mode scales with its energy $E$ as $\Gamma\sim E^3$ in the low-energy limit. We also discuss the width of the Tkachenko mode at a small temperature.

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Yi-Hsien Du, Sergej Moroz, Dung Xuan Nguyen, Dam Thanh Son. 2022-12-16. Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate. https://doi.org/10.1103/physrevresearch.6.l012040

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