We study the massive point-vortex model introduced in Richaud et al. [A. Richaud, V. Penna, R. Mayol, and M. Guilleumas, Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.

Dynamics of massive point vortices in a binary mixture of Bose-Einstein condensates / Richaud, Andrea; Penna, Vittorio; Fetter, Alexander. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - STAMPA. - 103:023311(2021). [10.1103/PhysRevA.103.023311]

Dynamics of massive point vortices in a binary mixture of Bose-Einstein condensates

Richaud, Andrea;Penna, Vittorio;
2021

Abstract

We study the massive point-vortex model introduced in Richaud et al. [A. Richaud, V. Penna, R. Mayol, and M. Guilleumas, Phys. Rev. A 101, 013630 (2020)], which describes two-dimensional point vortices of one species that have small cores of a different species. We derive the relevant Lagrangian itself, based on the time-dependent variational method with a two-component Gross-Pitaevskii (GP) trial function. The resulting Lagrangian resembles that of charged particles in a static electromagnetic field, where the canonical momentum includes an electromagnetic term. The simplest example is a single vortex with a rigid circular boundary, where a massless vortex can only precess uniformly. In contrast, the presence of a sufficiently large filled vortex core renders such precession unstable. A small core mass can also lead to small radial oscillations, which are, in turn, clear evidence of the associated inertial effect. Detailed numerical analysis of coupled two-component GP equations with a single vortex and small second-component core confirms the presence of such radial oscillations, implying that this more realistic GP vortex also acts as if it has a small massive core.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2873272