4,866 research outputs found
Chiral Spin Textures of Strongly Interacting Particles in Quantum Dots
We probe for statistical and Coulomb induced spin textures among the
low-lying states of repulsively-interacting particles confined to potentials
that are both rotationally and time-reversal invariant. In particular, we focus
on two-dimensional quantum dots and employ configuration-interaction techniques
to directly compute the correlated many-body eigenstates of the system. We
produce spatial maps of the single-particle charge and spin density and verify
the annular structure of the charge density and the rotational invariance of
the spin field. We further compute two-point spin correlations to determine the
correlated structure of a single component of the spin vector field. In
addition, we compute three-point spin correlation functions to uncover chiral
structures. We present evidence for both chiral and quasi-topological spin
textures within energetically degenerate subspaces in the three- and
four-particle system.Comment: 13 pages, 17 figures, 1 tabl
Dynamics of circular arrangements of vorticity in two dimensions
The merger of two like-signed vortices is a well-studied problem, but in a
turbulent flow, we may often have more than two like-signed vortices
interacting. We study the merger of three or more identical co-rotating
vortices initially arranged on the vertices of a regular polygon. At low to
moderate Reynolds numbers, we find an additional stage in the merger process,
absent in the merger of two vortices, where an annular vortical structure is
formed and is long-lived. Vortex merger is slowed down significantly due to
this. Such annular vortices are known at far higher Reynolds numbers in studies
of tropical cyclones, which have been noticed to a break down into individual
vortices. In the pre-annular stage, vortical structures in a viscous flow are
found here to tilt and realign in a manner similar to the inviscid case, but
the pronounced filaments visible in the latter are practically absent in the
former. Interestingly at higher Reynolds numbers, the merger of an odd number
of vortices is found to proceed very differently from that of an even number.
The former process is rapid and chaotic whereas the latter proceeds more slowly
via pairing events. The annular vortex takes the form of a generalised
Lamb-Oseen vortex (GLO), and diffuses inwards until it forms a standard
Lamb-Oseen vortex. For lower Reynolds number, the numerical (fully nonlinear)
evolution of the GLO vortex follows exactly the analytical evolution until
merger. At higher Reynolds numbers, the annulus goes through instabilities
whose nonlinear stages show a pronounced difference between even and odd mode
disturbances. It is hoped that the present findings, that multiple vortex
merger is qualitatively different from the merger of two vortices, will
motivate studies on how multiple vortex interactions affect the inverse cascade
in two-dimensional turbulence.Comment: Abstract truncated. Paper to appear in Physical Review
Shape in an Atom of Space: Exploring quantum geometry phenomenology
A phenomenology for the deep spatial geometry of loop quantum gravity is
introduced. In the context of a simple model, an atom of space, it is shown how
purely combinatorial structures can affect observations. The angle operator is
used to develop a model of angular corrections to local, continuum flat-space
3-geometries. The physical effects involve neither breaking of local Lorentz
invariance nor Planck scale suppression, but rather reply on only the
combinatorics of SU(2) recoupling. Bhabha scattering is discussed as an example
of how the effects might be observationally accessible.Comment: 14 pages, 7 figures; v2 references adde
Annular Vortex Solutions to the Landau-Ginzburg Equations in Mesoscopic Superconductors
New vortex solutions to the Landau-Ginzburg equations are described. These
configurations, which extend the well known Abrikosov and giant magnetic vortex
ones, consist of a succession of ring-like supercurrent vortices organised in a
concentric pattern, possibly bound to a giant magnetic vortex then lying at
their center. The dynamical and thermodynamic stability of these annular
vortices is an important open issue on which hinges the direct experimental
observation of such configurations. Nevertheless, annular vortices should
affect indirectly specific dynamic properties of mesoscopic superconducting
devices amenable to physical observation.Comment: 12 pages, LaTeX, 2 Postscript figure
Hypotrochoids in conformal restriction systems and Virasoro descendants
A conformal restriction system is a commutative, associative, unital algebra
equipped with a representation of the groupoid of univalent conformal maps on
connected open sets of the Riemann sphere, and a family of linear functionals
on subalgebras, satisfying a set of properties including conformal invariance
and a type of restriction. This embodies some expected properties of
expectation values in conformal loop ensembles CLE. In the context of conformal
restriction systems, we study certain algebra elements associated with
hypotrochoid simple curves (including the ellipse). These have the CLE
interpretation of being "renormalized random variables" that are nonzero only
if there is at least one loop of hypotrochoid shape. Each curve has a center w,
a scale \epsilon\ and a rotation angle \theta, and we analyze the renormalized
random variable as a function of u=\epsilon e^{i\theta} and w. We find that it
has an expansion in positive powers of u and u*, and that the coefficients of
pure u (u*) powers are holomorphic in w (w*). We identify these coefficients
(the "hypotrochoid fields") with certain Virasoro descendants of the identity
field in conformal field theory, thereby showing that they form part of a
vertex operator algebraic structure. This largely generalizes works by the
author (in CLE), and the author with his collaborators V. Riva and J. Cardy (in
SLE 8/3 and other restriction measures), where the case of the ellipse, at the
order u^2, led to the stress-energy tensor of CFT. The derivation uses in an
essential way the Virasoro vertex operator algebra structure of conformal
derivatives established recently by the author. The results suggest in
particular the exact evaluation of CLE expectations of products of hypotrochoid
fields as well as non-trivial relations amongst them through the vertex
operator algebra, and further shed light onto the relationship between CLE and
CFT.Comment: 1 figure, 39 page
Mutual information and the F-theorem
Mutual information is used as a purely geometrical regularization of
entanglement entropy applicable to any QFT. A coefficient in the mutual
information between concentric circular entangling surfaces gives a precise
universal prescription for the monotonous quantity in the c-theorem for d=3.
This is in principle computable using any regularization for the entropy, and
in particular is a definition suitable for lattice models. We rederive the
proof of the c-theorem for d=3 in terms of mutual information, and check our
arguments with holographic entanglement entropy, a free scalar field, and an
extensive mutual information model.Comment: 80 pages, 16 figure
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