Theory of the vortex-clustering transition in a confined two-dimensional quantum fluid

Abstract

Clustering of like-sign vortices in a planar bounded domain is known to occur at negative temperature, a phenomenon that Onsager demonstrated to be a consequence of bounded phase space. In a confined superfluid, quantized vortices can support such an ordered phase, provided they evolve as an almost isolated subsystem containing sufficient energy. A detailed theoretical understanding of the statistical mechanics of such states thus requires a microcanonical approach. Here we develop an analytical theory of the vortex clustering transition in a neutral system of quantum vortices confined to a two-dimensional disk geometry, within the microcanonical ensemble. The choice of ensemble is essential for identifying the correct thermodynamic limit of the system, enabling a rigorous description of clustering in the language of critical phenomena. As the system energy increases above a critical value, the system develops global order via the emergence of a macroscopic dipole structure from the homogeneous phase of vortices, spontaneously breaking the Z 2 symmetry associated with invariance under vortex circulation exchange, and the rotational SO(2) symmetry due to the disk geometry. The dipole structure emerges characterized by the continuous growth of the macroscopic dipole moment which serves as a global order parameter, resembling a continuous phase transition. The critical temperature of the transition, and the critical exponent associated with the dipole moment, are obtained exactly within mean-field theory. The clustering transition is shown to be distinct from the final state reached at high energy, known as supercondensation. The dipole moment develops via two macroscopic vortex clusters and the cluster locations are found analytically, both near the clustering transition and in the supercondensation limit. The microcanonical theory shows excellent agreement with Monte Carlo simulations, and signatures of the transition are apparent even for a modest system of 100 vortices, accessible in current Bose-Einstein condensate experiments.

Strongly anomalous non-thermal fixed point in a quenched two-dimensional Bose gas

“…For charge-neutral atoms in a closed trap without external fields, a potentially related clustering transition has been reported [88,89]. Onsager's point-vortex model [79] implies a maximum entropy state in which an equal number of elementary vortices and anti-vortices are randomly distributed in the system.…”

Einstein–Bose condensation of Onsager vortices

“…The successes of the recent experimental developments have also spawned novel theoretical investigations [13,[34][35][36][37][38][39][40][41][42][43][44][45]. In addition to visual inspection, the presence of Onsager vortices has been associated with indicators such as the vortex dipole moment [13,34], vortex clustering measures [7,8,36,37,40], or a peak in the power spectral density of incompressible kinetic energy [8,13,38,46].…”

Numerical Studies of Quantum Turbulence

“…This kind of vortex clustering is theoretically investigated by the GP equation and Monte Carlo calculation [145,146,148,149]. Recently, Simula et al found that such a negative temperature state is dynamically formed through the evaporative heating of vortex when the disk-shaped flat potential is used [146] 1 .…”

“…There are many studies for 2D QT [129,130,138,139,140,141,142,143,144,145,146,147,148,149], some of which discuss the possibility of the inverse cascade in QT. To our understanding, the existence of the inverse cascade in QT is controversial.…”