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

Abstract

We study the massive point-vortex model introduced in Ref. [1], 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-Pitiavskii (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.

Instabilities of vortex-ring-bright soliton in trapped binary 3D Bose-Einstein condensates

“…Another important dynamical effect not covered by the Lagrangian ( 9) is the transverse inertia of the vortex core. For two-dimensional flows, this effect has been considered in recent works [45,46]. The three-dimensional case studied here is more complicated.…”

“…Earlier work of different subsets of the present au-thors [36][37][38][39] has explored the instabilities of chiefly onecomponent, three-dimensional structures, such as vortex lines and vortex rings, as well as multi-line/ring variants thereof. The last few years have led to a deeper and intensified consideration of vortical patterns bearing a second component that fills the relevant vortex core [40][41][42], as well as their dynamics and instabilities [43,44], and interactions with each other [45,46] and with defects [47]. Most of these above studies have been centered around the somewhat less computationally intensive, yet still quite interesting 2d realm.…”

Phase diagram, stability and magnetic properties of nonlinear excitations in spinor Bose–Einstein condensates

“…Additionally, exploring the interaction effects of vortex lattices as well as their stability and dynamics in spinor setups is of direct relevance, due to the potential of inclusion of external rotation [2,10]. Indeed, it is already of significant recent interest to explore the interaction of two multi-component vortical patterns, as has been explored recently in two-component settings, e.g., in [81,82] (see also references therein). Moreover, in the current setup the inclusion of three-body recombination processes as a dissipative mechanism in selective spin-channels constitutes a situation that accounts for possible experimental imperfections [7].…”

Bubbles with attached quantum vortices in trapped binary Bose-Einstein condensates

“…In particular, with a sufficiently strong cross-repulsion between two components, phase separation occurs [11,12]. It lies in the base of many related configurations and phenomena of high interest, such as domain walls and surface tension between segregated condensates [4,13], the dynamics of bubbles [14], the quantum counterparts of classical hydrodynamic instabilities (Kelvin-Helmholtz [15,16], Rayleigh-Taylor [17][18][19], Plateau-Rayleigh [20], the parametric instability of capillary waves at the interface [21]), complex textures in rotating binary condensates [22][23][24], vortices with filled cores [3,[25][26][27][28][29][30], three-dimensional topological structures [31][32][33][34][35], etc.…”