429 research outputs found
The quantum to classical transition for random walks
We look at two possible routes to classical behavior for the discrete quantum
random walk on the line: decoherence in the quantum ``coin'' which drives the
walk, or the use of higher-dimensional coins to dilute the effects of
interference. We use the position variance as an indicator of classical
behavior, and find analytical expressions for this in the long-time limit; we
see that the multicoin walk retains the ``quantum'' quadratic growth of the
variance except in the limit of a new coin for every step, while the walk with
decoherence exhibits ``classical'' linear growth of the variance even for weak
decoherence.Comment: 4 pages RevTeX 4.0 + 2 figures (encapsulated Postscript). Trimmed for
length. Minor corrections + one new referenc
Quantum random walks with decoherent coins
The quantum random walk has been much studied recently, largely due to its
highly nonclassical behavior. In this paper, we study one possible route to
classical behavior for the discrete quantum walk on the line: the presence of
decoherence in the quantum ``coin'' which drives the walk. We find exact
analytical expressions for the time dependence of the first two moments of
position, and show that in the long-time limit the variance grows linearly with
time, unlike the unitary walk. We compare this to the results of direct
numerical simulation, and see how the form of the position distribution changes
from the unitary to the usual classical result as we increase the strength of
the decoherence.Comment: Minor revisions, especially in introduction. Published versio
Quantum Walks driven by many coins
Quantum random walks have been much studied recently, largely due to their
highly nonclassical behavior. In this paper, we study one possible route to
classical behavior for the discrete quantum random walk on the line: the use of
multiple quantum ``coins'' in order to diminish the effects of interference
between paths. We find solutions to this system in terms of the single coin
random walk, and compare the asymptotic limit of these solutions to numerical
simulations. We find exact analytical expressions for the time-dependence of
the first two moments, and show that in the long time limit the ``quantum
mechanical'' behavior of the one-coin walk persists. We further show that this
is generic for a very broad class of possible walks, and that this behavior
disappears only in the limit of a new coin for every step of the walk.Comment: 36 pages RevTeX 4.0 + 5 figures (encapsulated Postscript). Submitted
to Physical Review
Solar Magnetic Carpet I: Simulation of Synthetic Magnetograms
This paper describes a new 2D model for the photospheric evolution of the
magnetic carpet. It is the first in a series of papers working towards
constructing a realistic 3D non-potential model for the interaction of
small-scale solar magnetic fields. In the model, the basic evolution of the
magnetic elements is governed by a supergranular flow profile. In addition,
magnetic elements may evolve through the processes of emergence, cancellation,
coalescence and fragmentation. Model parameters for the emergence of bipoles
are based upon the results of observational studies. Using this model, several
simulations are considered, where the range of flux with which bipoles may
emerge is varied. In all cases the model quickly reaches a steady state where
the rates of emergence and cancellation balance. Analysis of the resulting
magnetic field shows that we reproduce observed quantities such as the flux
distribution, mean field, cancellation rates, photospheric recycle time and a
magnetic network. As expected, the simulation matches observations more closely
when a larger, and consequently more realistic, range of emerging flux values
is allowed (4e16 - 1e19 Mx). The model best reproduces the current observed
properties of the magnetic carpet when we take the minimum absolute flux for
emerging bipoles to be 4e16 Mx. In future, this 2D model will be used as an
evolving photospheric boundary condition for 3D non-potential modeling.Comment: 33 pages, 16 figures, 5 gif movies included: movies may be viewed at
http://www-solar.mcs.st-and.ac.uk/~karen/movies_paper1
An approximate renormalization-group transformation for Hamiltonian systems with three degrees of freedom
We construct an approximate renormalization transformation that combines
Kolmogorov-Arnold-Moser (KAM)and renormalization-group techniques, to analyze
instabilities in Hamiltonian systems with three degrees of freedom. This scheme
is implemented both for isoenergetically nondegenerate and for degenerate
Hamiltonians. For the spiral mean frequency vector, we find numerically that
the iterations of the transformation on nondegenerate Hamiltonians tend to
degenerate ones on the critical surface. As a consequence, isoenergetically
degenerate and nondegenerate Hamiltonians belong to the same universality
class, and thus the corresponding critical invariant tori have the same type of
scaling properties. We numerically investigate the structure of the attracting
set on the critical surface and find that it is a strange nonchaotic attractor.
We compute exponents that characterize its universality class.Comment: 10 pages typeset using REVTeX, 7 PS figure
Quantum random walks in optical lattices
We propose an experimental realization of discrete quantum random walks using
neutral atoms trapped in optical lattices. The random walk is taking place in
position space and experimental implementation with present day technology
--even using existing set-ups-- seems feasible. We analyze the influence of
possible imperfections in the experiment and investigate the transition from a
quantum random walk to the classical random walk for increasing errors and
decoherence.Comment: 8 pages, 4 figure
Plasma Wave Properties of the Schwarzschild Magnetosphere in a Veselago Medium
We re-formulate the 3+1 GRMHD equations for the Schwarzschild black hole in a
Veselago medium. Linear perturbation in rotating (non-magnetized and
magnetized) plasma is introduced and their Fourier analysis is considered. We
discuss wave properties with the help of wave vector, refractive index and
change in refractive index in the form of graphs. It is concluded that some
waves move away from the event horizon in this unusual medium. We conclude that
for the rotating non-magnetized plasma, our results confirm the presence of
Veselago medium while the rotating magnetized plasma does not provide any
evidence for this medium.Comment: 20 pages, 15 figures, accepted for publication in Astrophys. Space
Sc
Lubricating Bacteria Model for Branching growth of Bacterial Colonies
Various bacterial strains (e.g. strains belonging to the genera Bacillus,
Paenibacillus, Serratia and Salmonella) exhibit colonial branching patterns
during growth on poor semi-solid substrates. These patterns reflect the
bacterial cooperative self-organization. Central part of the cooperation is the
collective formation of lubricant on top of the agar which enables the bacteria
to swim. Hence it provides the colony means to advance towards the food. One
method of modeling the colonial development is via coupled reaction-diffusion
equations which describe the time evolution of the bacterial density and the
concentrations of the relevant chemical fields. This idea has been pursued by a
number of groups. Here we present an additional model which specifically
includes an evolution equation for the lubricant excreted by the bacteria. We
show that when the diffusion of the fluid is governed by nonlinear diffusion
coefficient branching patterns evolves. We study the effect of the rates of
emission and decomposition of the lubricant fluid on the observed patterns. The
results are compared with experimental observations. We also include fields of
chemotactic agents and food chemotaxis and conclude that these features are
needed in order to explain the observations.Comment: 1 latex file, 16 jpeg files, submitted to Phys. Rev.
Resonance- and Chaos-Assisted Tunneling
We consider dynamical tunneling between two symmetry-related regular islands
that are separated in phase space by a chaotic sea. Such tunneling processes
are dominantly governed by nonlinear resonances, which induce a coupling
mechanism between ``regular'' quantum states within and ``chaotic'' states
outside the islands. By means of a random matrix ansatz for the chaotic part of
the Hamiltonian, one can show that the corresponding coupling matrix element
directly determines the level splitting between the symmetric and the
antisymmetric eigenstates of the pair of islands. We show in detail how this
matrix element can be expressed in terms of elementary classical quantities
that are associated with the resonance. The validity of this theory is
demonstrated with the kicked Harper model.Comment: 25 pages, 5 figure
From chemical gardens to chemobrionics
Chemical gardens in laboratory chemistries ranging from silicates to polyoxometalates, in applications ranging from corrosion products to the hydration of Portland cement, and in natural settings ranging from hydrothermal vents in the ocean depths to brinicles beneath sea ice. In many chemical-garden experiments, the structure forms as a solid seed of a soluble ionic compound dissolves in a solution containing another reactive ion. In general any alkali silicate solution can be used due to their high solubility at high pH. The cation should not precipitate with the counterion of the metal salt used as seed. A main property of seed chemical-garden experiments is that initially, when the fluid is not moving under buoyancy or osmosis, the delivery of the inner reactant is diffusion controlled. Another experimental technique that isolates one aspect of chemical-garden formation is to produce precipitation membranes between different aqueous solutions by introducing the two solutions on either side of an inert carrier matrix. Chemical gardens may be grown upon injection of solutions into a so-called Hele-Shaw cell, a quasi-two-dimensional reactor consisting in two parallel plates separated by a small gap
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