201 research outputs found
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 , (ii) the localization length of eigenstates
vanishes as , (iii) the density of states
diverges logarithmically (particle-hole symmetry) and algebraically (no
particle-hole symmetry), (iv) mobility edge curves show algebraic singularities
at . 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 and the rotation
frequency , which are the conjugate variables of energy and angular
momentum . 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 symmetry and breaks
symmetry. We find that, near the uniform state, the rotation free state
() emerges at particular values of and . At large
energies, we obtain asymptotically exact vortex density distributions, whose
validity condition gives rise the lower bound of 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
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