We analyze the motion of quantum vortices in a two-dimensional spinless superfluid within Popov's hydrodynamic description. In the long healing length limit (where a large number of particles are inside the vortex core) the superfluid dynamics is determined by saddle points of Popov's action, which, in particular, allows for weak solutions of the Gross-Pitaevskii equation. We solve the resulting equations of motion for a vortex moving with respect to the superfluid and find the reconstruction of the vortex core to be a non-analytic function of the force applied on the vortex. This response produces an anomalously large dipole moment of the vortex and, as a result, the spectrum associated with the vortex motion exhibits narrow resonances lying within the phonon part of the spectrum, contrary to traditional view.
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We are grateful to V. Cheianov for valuable discussions on the initial stage of this work and to R. Fattal and D. Klein for help and advice on the numerical work in this paper. We also thank A. Abanov, Y. Galperin, N. Prokofiev, and L. Radzihovsky for reading the manuscript and remarks, and to L. Glazman and A. Kitaev for a discussion of the results. This research has been supported by the United States-Israel Binational Science Foundation (BSF) grant No. 2012134 (O.A. and A.K.) and Simons foundation (O.A. and I.A.).
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- Gross-Pitaevskii equations
- Popov's equations
- Quantum vortices
- Two dimensional superfluid