4,927 research outputs found
Matrix product states for anyonic systems and efficient simulation of dynamics
Matrix product states (MPS) have proven to be a very successful tool to study
lattice systems with local degrees of freedom such as spins or bosons.
Topologically ordered systems can support anyonic particles which are labeled
by conserved topological charges and collectively carry non-local degrees of
freedom. In this paper we extend the formalism of MPS to lattice systems of
anyons. The anyonic MPS is constructed from tensors that explicitly conserve
topological charge. We describe how to adapt the time-evolving block decimation
(TEBD) algorithm to the anyonic MPS in order to simulate dynamics under a local
and charge-conserving Hamiltonian. To demonstrate the effectiveness of anyonic
TEBD algorithm, we used it to simulate (i) the ground state (using imaginary
time evolution) of an infinite 1D critical system of (a) Ising anyons and (b)
Fibonacci anyons both of which are well studied, and (ii) the real time
dynamics of an anyonic Hubbard-like model of a single Ising anyon hopping on a
ladder geometry with an anyonic flux threading each island of the ladder. Our
results pertaining to (ii) give insight into the transport properties of
anyons. The anyonic MPS formalism can be readily adapted to study systems with
conserved symmetry charges, as this is equivalent to a specialization of the
more general anyonic case.Comment: 18 pages, 15 figue
Hamilton Geometry - Phase Space Geometry from Modified Dispersion Relations
Quantum gravity phenomenology suggests an effective modification of the
general relativistic dispersion relation of freely falling point particles
caused by an underlying theory of quantum gravity. Here we analyse the
consequences of modifications of the general relativistic dispersion on the
geometry of spacetime in the language of Hamilton geometry. The dispersion
relation is interpreted as the Hamiltonian which determines the motion of point
particles. It is a function on the cotangent bundle of spacetime, i.e. on phase
space, and determines the geometry of phase space completely, in a similar way
as the metric determines the geometry of spacetime in general relativity. After
a review of the general Hamilton geometry of phase space we discuss two
examples. The phase space geometry of the metric Hamiltonian
and the phase space geometry of the first order q-de
Sitter dispersion relation of the form which is suggested from quantum gravity phenomenology. We
will see that for the metric Hamiltonian the geometry of phase space is
equivalent to the standard metric spacetime geometry from general relativity.
For the q-de Sitter Hamiltonian the Hamilton equations of motion for
point particles do not become autoparallels but contain a force term, the
momentum space part of phase space is curved and the curvature of spacetime
becomes momentum dependent.Comment: 6 page
Hamilton geometry: Phase space geometry from modified dispersion relations
We describe the Hamilton geometry of the phase space of particles whose
motion is characterised by general dispersion relations. In this framework
spacetime and momentum space are naturally curved and intertwined, allowing for
a simultaneous description of both spacetime curvature and non-trivial momentum
space geometry. We consider as explicit examples two models for Planck-scale
modified dispersion relations, inspired from the -de Sitter and
-Poincar\'e quantum groups. In the first case we find the expressions
for the momentum and position dependent curvature of spacetime and momentum
space, while for the second case the manifold is flat and only the momentum
space possesses a nonzero, momentum dependent curvature. In contrast, for a
dispersion relation that is induced by a spacetime metric, as in General
Relativity, the Hamilton geometry yields a flat momentum space and the usual
curved spacetime geometry with only position dependent geometric objects.Comment: 32 pages, section on quantisation of the theory added, comments on
additin of momenta on curved momentum spaces extende
Simulation of braiding anyons using Matrix Product States
Anyons exist as point like particles in two dimensions and carry braid
statistics which enable interactions that are independent of the distance
between the particles. Except for a relatively few number of models which are
analytically tractable, much of the physics of anyons remain still unexplored.
In this paper, we show how U(1)-symmetry can be combined with the previously
proposed anyonic Matrix Product States to simulate ground states and dynamics
of anyonic systems on a lattice at any rational particle number density. We
provide proof of principle by studying itinerant anyons on a one dimensional
chain where no natural notion of braiding arises and also on a two-leg ladder
where the anyons hop between sites and possibly braid. We compare the result of
the ground state energies of Fibonacci anyons against hardcore bosons and
spinless fermions. In addition, we report the entanglement entropies of the
ground states of interacting Fibonacci anyons on a fully filled two-leg ladder
at different interaction strength, identifying gapped or gapless points in the
parameter space. As an outlook, our approach can also prove useful in studying
the time dynamics of a finite number of nonabelian anyons on a finite
two-dimensional lattice.Comment: Revised version: 20 pages, 14 captioned figures, 2 new tables. We
have moved a significant amount of material concerning symmetric tensors for
anyons --- which can be found in prior works --- to Appendices in order to
streamline our exposition of the modified Anyonic-U(1) ansat
Posterior Capsule Opacification After Piggyback Intraocular Lens Implantation
This is a case report on piggyback lens implantation with late hyperopic shift occurrence
associated with Elschnig pearl formation in the peripheral interface between two
lenses
Position-squared coupling in a tunable photonic crystal optomechanical cavity
We present the design, fabrication, and characterization of a planar silicon
photonic crystal cavity in which large position-squared optomechanical coupling
is realized. The device consists of a double-slotted photonic crystal structure
in which motion of a central beam mode couples to two high-Q optical modes
localized around each slot. Electrostatic tuning of the structure is used to
controllably hybridize the optical modes into supermodes which couple in a
quadratic fashion to the motion of the beam. From independent measurements of
the anti-crossing of the optical modes and of the optical spring effect, the
position-squared vacuum coupling rate is measured to be as large as 245 Hz to
the fundamental in-plane mechanical resonance of the structure at 8.7MHz, which
in displacement units corresponds to a coupling coefficient of 1 THz/nm.
This level of position-squared coupling is approximately five orders of
magnitude larger than in conventional Fabry-Perot cavity systems.Comment: 11 pages, 6 figure
GUARD DOGS AND GAS EXPLODERS AS COYOTE DEPREDATION CONTROL TOOLS IN NORTH DAKOTA
Guard dogs and gas exploders have been successfully used in North Dakota to protect sheep from coyote (Canis latrans) depredation since the mid-1970s. They have been used in addition to other lethal and nonlethal control tools. The U.S. Fish and Wildlife Service gathered information from field testing and landowner interviews to measure their effectiveness. Guard dogs reduced the rate of depredation by 93 percent on the 36 ranches surveyed. Gas exploders deterred coyotes from depredating on 30 ranches an average of 31 days during the 1980 and 1981 grazing seasons. An increasing number of sheep producers are using these control methods to reduce losses and become less dependent on a publicly funded damage control program
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