Onsager vortex clusters on a sphere

We study Onsager vortex clustered states in a shell-shaped superfluid containing a large number of quantum vortices. In the incompressible limit and at low temperatures, the relevant problem can be boiled down to the statistical mechanics of neutral point vortices confined on a sphere. We analyze rotation free vortex clustered states within the mean field theory in the microcanonical ensemble. We find that the sandwich state, which involves the separating of vortices with opposite circulation and the clustering of vortices with same circulation around the poles and the equator, is the maximum entropy vortex distribution, subject to zero angular momentum constraint. The dipole momentum vanishes for the sandwich state and the quadrupole tensor serves as an order parameter to characterize the vortex cluster structure. For given finite angular momentum, the equilibrium vortex distribution forms a dipole structure, i.e., vortices with opposite sign are separated and are accumulated around the south and north pole, respectively. The conditions for the onset of clustering, and the exponents associated with the quadrupole moment and the dipole moment as functions of energy, are obtained within the mean field theory. At large energies, we obtain asymptotically exact vortex density distributions using the stereographic projection method, which give rise the parameter bounds for the vortex clustered states. The analytical predictions are in excellent agreement with microcanonical Monte Carlo simulations.Comment: 10 pages,10 figure

Flat Bands Under Correlated Perturbations

Flat band networks are characterized by coexistence of dispersive and flat bands. Flat bands (FB) are generated by compact localized eigenstates (CLS) with local network symmetries, based on destructive interference. Correlated disorder and quasiperiodic potentials hybridize CLS without additional renormalization, yet with surprising consequencies: (i) states are expelled from the FB energy $E_{FB}$, (ii) the localization length of eigenstates vanishes as $\xi \sim 1 / \ln (E- E_{FB})$, (iii) the density of states diverges logarithmically (particle-hole symmetry) and algebraically (no particle-hole symmetry), (iv) mobility edge curves show algebraic singularities at $E_{FB}$. Our analytical results are based on perturbative expansions of the CLS, and supported by numerical data in one and two lattice dimensions

Snell's Law for a vortex dipole in a Bose-Einstein condensate

A quantum vortex dipole, comprised of a closely bound pair of vortices of equal strength with opposite circulation, is a spatially localized travelling excitation of a planar superfluid that carries linear momentum, suggesting a possible analogy with ray optics. We investigate numerically and analytically the motion of a quantum vortex dipole incident upon a step-change in the background superfluid density of an otherwise uniform two-dimensional Bose-Einstein condensate. Due to the conservation of fluid momentum and energy, the incident and refracted angles of the dipole satisfy a relation analogous to Snell's law, when crossing the interface between regions of different density. The predictions of the analogue Snell's law relation are confirmed for a wide range of incident angles by systematic numerical simulations of the Gross-Piteavskii equation. Near the critical angle for total internal reflection, we identify a regime of anomalous Snell's law behaviour where the finite size of the dipole causes transient capture by the interface. Remarkably, despite the extra complexity of the surface interaction, the incoming and outgoing dipole paths obey Snell's law.Comment: 16 pages, 7 figures, Scipost forma

Core structure of static ferrodark solitons in a spin-1 Bose-Einstein condensate

We develop an analytical description of static ferrodark solitons in the easy-plane phase of ferromagnetic spin-1 Bose-Einstein condensates. We find that the type-I ferrodark soliton has a single width while the type-II ferrodark soliton exhibits two characteristic length scales. The proposed ansatzes show excellent agreement with numerical results. We demonstrate that the ferrodark solitons are the lowest energy transverse magnetic kinks that connect the oppositely magnetized magnetic domains. Spin-singlet amplitudes, nematic tensor densities and nematic currents of ferrodark solitons are also discussed.Comment: 8 pages, 9 figure

Axis-symmetric Onsager Clustered States of Point Vortices in a Bounded Domain

We study axis-symmetric Onsager clustered states of a neutral point vortex system confined to a two-dimensional disc. Our analysis is based on the mean field of bounded point vortices in the microcanonical ensemble. The clustered vortex states are specified by the inverse temperature $\beta$ and the rotation frequency $\omega$, which are the conjugate variables of energy $E$ and angular momentum $L$. The formation of the axis-symmetric clustered vortex states (azimuthal angle independent) involves the separating of vortices with opposite circulation and the clustering of vortices with same circulation around origin and edge. The state preserves $\rm SO(2)$ symmetry and breaks $\mathbb Z_2$ symmetry. We find that, near the uniform state, the rotation free state ($\omega=0$) emerges at particular values of $L^2/E$ and $\beta$. At large energies, we obtain asymptotically exact vortex density distributions, whose validity condition gives rise the lower bound of $\beta$ for the rotation free states. Noticeably, the obtained vortex density distribution near the edge at large energies provides a novel exact vortex density distribution for the corresponding chiral vortex system.Comment: 6 pages, 4 figure