Einstein–Bose condensation of Onsager vortices

Abstract

We have studied statistical mechanics of a gas of vortices in two dimensions. We introduce a new observable-a condensate fraction of Onsager vortices-to quantify the emergence of the vortex condensate. The condensation of Onsager vortices is most transparently observed in a single vortex species system and occurs due to a competition between solid body rotation (see vortex lattice) and potential flow (see multiple quantum vortex state). We propose an experiment to observe the condensation transition of the vortices in such a single vortex species system.

Vortex mass in a superfluid

“…Avalanches of anomalously heavy vortices in rotating neutron stars that glitch could perhaps result in a continuous gravitational wave signal detectable by future gravitational wave detectors [71]. In high-energy states of two-dimensional quantum turbulence the vortex particles may undergo condensation transition [72]-a phenomenon which may be influenced by the mass of the vortices. The ability to control the inertial mass of a vortex by varying the frequency of the kelvons has potential for applications.…”

2D quantum turbulence in a polariton quantum fluid

“…This approach allows not only to find the total incompressible energy spectrum, but also to consider the contributions of single vortices and clusters separately 38,51 , which turns out to be important in order to observe the Kolmogorov cascade at a large scale. The cluster selection algorithm was adopted from Refs.…”

“…We follow the cluster selection procedure described in section VI of Ref. 51 . We begin with the creating the list of vectors l i = (l(i, 1), l(i, 2), ..., l(i, NOS i )), consisting of the indices of the neighbors of i-th vortex sorted by increasing the distance (i = 1..N vort , where N vort it the total amount of vortices).…”

Origin of the inverse energy cascade in two-dimensional quantum turbulence

“…Onsager [9] predicted that these negative-T states correspond to spatial clustering of same-sign vortices, resulting in large-scale vortices. Recently, it has been proposed that the Onsager vortices in the strongly coupled regime undergo a condensation similar to the BoseEinstein condensation, but this requires much higher energies than those present in decaying turbulence or in the inverse energy cascade [18].…”