9,930 research outputs found
Fine structure of distributions and central limit theorem in diffusive billiards
We investigate deterministic diffusion in periodic billiard models, in terms
of the convergence of rescaled distributions to the limiting normal
distribution required by the central limit theorem; this is stronger than the
usual requirement that the mean square displacement grow asymptotically
linearly in time. The main model studied is a chaotic Lorentz gas where the
central limit theorem has been rigorously proved. We study one-dimensional
position and displacement densities describing the time evolution of
statistical ensembles in a channel geometry, using a more refined method than
histograms. We find a pronounced oscillatory fine structure, and show that this
has its origin in the geometry of the billiard domain. This fine structure
prevents the rescaled densities from converging pointwise to gaussian
densities; however, demodulating them by the fine structure gives new densities
which seem to converge uniformly. We give an analytical estimate of the rate of
convergence of the original distributions to the limiting normal distribution,
based on the analysis of the fine structure, which agrees well with simulation
results. We show that using a Maxwellian (gaussian) distribution of velocities
in place of unit speed velocities does not affect the growth of the mean square
displacement, but changes the limiting shape of the distributions to a
non-gaussian one. Using the same methods, we give numerical evidence that a
non-chaotic polygonal channel model also obeys the central limit theorem, but
with a slower convergence rate.Comment: 16 pages, 19 figures. Accepted for publication in Physical Review E.
Some higher quality figures at http://www.maths.warwick.ac.uk/~dsander
Chaos in cylindrical stadium billiards via a generic nonlinear mechanism
We describe conditions under which higher-dimensional billiard models in
bounded, convex regions are fully chaotic, generalizing the Bunimovich stadium
to dimensions above two. An example is a three-dimensional stadium bounded by a
cylinder and several planes; the combination of these elements may give rise to
defocusing, allowing large chaotic regions in phase space. By studying families
of marginally-stable periodic orbits that populate the residual part of phase
space, we identify conditions under which a nonlinear instability mechanism
arises in their vicinity. For particular geometries, this mechanism rather
induces stable nonlinear oscillations, including in the form of
whispering-gallery modes.Comment: 4 pages, 4 figure
Occurrence of normal and anomalous diffusion in polygonal billiard channels
From extensive numerical simulations, we find that periodic polygonal
billiard channels with angles which are irrational multiples of pi generically
exhibit normal diffusion (linear growth of the mean squared displacement) when
they have a finite horizon, i.e. when no particle can travel arbitrarily far
without colliding. For the infinite horizon case we present numerical tests
showing that the mean squared displacement instead grows asymptotically as t
log t. When the unit cell contains accessible parallel scatterers, however, we
always find anomalous super-diffusion, i.e. power-law growth with an exponent
larger than 1. This behavior cannot be accounted for quantitatively by a simple
continuous-time random walk model. Instead, we argue that anomalous diffusion
correlates with the existence of families of propagating periodic orbits.
Finally we show that when a configuration with parallel scatterers is
approached there is a crossover from normal to anomalous diffusion, with the
diffusion coefficient exhibiting a power-law divergence.Comment: 9 pages, 15 figures. Revised after referee reports: redrawn figures,
additional comments. Some higher quality figures available at
http://www.fis.unam.mx/~dsander
Invasive Wild pigs as primary nest predators for Wild turkeys
Depredation of wild turkey (Meleagris gallopavo) nests is a leading cause of reduced recruitment for the recovering and iconic game species. invasive wild pigs (Sus scrofa) are known to depredate nests, and have been expanding throughout the distributed range of wild turkeys in north America. We sought to gain better insight on the magnitude of wild pigs depredating wild turkey nests. We constructed simulated wild turkey nests throughout the home ranges of 20 GPS-collared wild pigs to evaluate nest depredation relative to three periods within the nesting season (i.e., early, peak, and late) and two nest densities (moderate = 12.5-25 nests/km2, high = 25-50 nests/km2) in south-central Texas, USA during March–June 2016. Overall, the estimated probability of nest depredation by wild pigs was 0.3, equivalent to native species of nest predators in the study area (e.g., gray fox [Urocyon cinereoargenteus], raccoon [Procyon lotor], and coyote [Canis latrans]). female wild pigs exhibited a constant rate of depredation regardless of nesting period or density of nests. However, male wild pigs increased their rate of depredation in areas with higher nest densities. Management efforts should remove wild pigs to reduce nest failure in wild turkey populations especially where recruitment is low
Topological graph states and quantum error correction codes
Deciding if a given family of quantum states is topologically ordered is an
important but nontrivial problem in condensed matter physics and quantum
information theory. We derive necessary and sufficient conditions for a family
of graph states to be in TQO-1, which is a class of quantum error correction
code states whose code distance scales macroscopically with the number of
physical qubits. Using these criteria, we consider a number of specific graph
families, including the star and complete graphs, and the line graphs of
complete and completely bipartite graphs, and discuss which are topologically
ordered and how to construct the codewords. The formalism is then employed to
construct several codes with macroscopic distance, including a
three-dimensional topological code generated by local stabilizers that also has
a macroscopic number of encoded logical qubits. The results indicate that graph
states provide a fruitful approach to the construction and characterization of
topological stabilizer quantum error correction codes.Comment: 21 pages, 7 figures
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