277 research outputs found
Transmission and Reflection in the Stadium Billiard: Time-dependent asymmetric transport
We investigate the transmission and reflection survival probabilities for the
chaotic stadium billiard with two holes placed asymmetrically. Classically,
these distributions are shown to have algebraic or exponential decays depending
on the choice of injecting hole and exact expressions are given for the first
time and confirmed numerically. As there is no reported quantum theoretical or
experimental analogue we propose a model for experimental observation of the
asymmetric transport using semiconductor nano-structures and comment on the
relevant quantum time-scales.Comment: 4 pages, 4 figure
Localized behavior in the Lyapunov vectors for quasi-one-dimensional many-hard-disk systems
We introduce a definition of a "localization width" whose logarithm is given
by the entropy of the distribution of particle component amplitudes in the
Lyapunov vector. Different types of localization widths are observed, for
example, a minimum localization width where the components of only two
particles are dominant. We can distinguish a delocalization associated with a
random distribution of particle contributions, a delocalization associated with
a uniform distribution and a delocalization associated with a wave-like
structure in the Lyapunov vector. Using the localization width we show that in
quasi-one-dimensional systems of many hard disks there are two kinds of
dependence of the localization width on the Lyapunov exponent index for the
larger exponents: one is exponential, and the other is linear. Differences, due
to these kinds of localizations also appear in the shapes of the localized
peaks of the Lyapunov vectors, the Lyapunov spectra and the angle between the
spatial and momentum parts of the Lyapunov vectors. We show that the Krylov
relation for the largest Lyapunov exponent as a
function of the density is satisfied (apart from a factor) in the same
density region as the linear dependence of the localization widths is observed.
It is also shown that there are asymmetries in the spatial and momentum parts
of the Lyapunov vectors, as well as in their and -components.Comment: 41 pages, 21 figures, Manuscript including the figures of better
quality is available from http://www.phys.unsw.edu.au/~gary/Research.htm
Plasma waves driven by gravitational waves in an expanding universe
In a Friedmann-Robertson-Walker (FRW) cosmological model with zero spatial
curvature, we consider the interaction of the gravitational waves with the
plasma in the presence of a weak magnetic field. Using the relativistic
hydromagnetic equations it is verified that large amplitude magnetosonic waves
are excited, assuming that both, the gravitational field and the weak magnetic
field do not break the homogeneity and isotropy of the considered FRW
spacetime.Comment: 14 page
Lyapunov instability for a periodic Lorentz gas thermostated by deterministic scattering
In recent work a deterministic and time-reversible boundary thermostat called
thermostating by deterministic scattering has been introduced for the periodic
Lorentz gas [Phys. Rev. Lett. {\bf 84}, 4268 (2000)]. Here we assess the
nonlinear properties of this new dynamical system by numerically calculating
its Lyapunov exponents. Based on a revised method for computing Lyapunov
exponents, which employs periodic orthonormalization with a constraint, we
present results for the Lyapunov exponents and related quantities in
equilibrium and nonequilibrium. Finally, we check whether we obtain the same
relations between quantities characterizing the microscopic chaotic dynamics
and quantities characterizing macroscopic transport as obtained for
conventional deterministic and time-reversible bulk thermostats.Comment: 18 pages (revtex), 7 figures (postscript
Spectral statistics of random geometric graphs
We use random matrix theory to study the spectrum of random geometric graphs,
a fundamental model of spatial networks. Considering ensembles of random
geometric graphs we look at short range correlations in the level spacings of
the spectrum via the nearest neighbour and next nearest neighbour spacing
distribution and long range correlations via the spectral rigidity Delta_3
statistic. These correlations in the level spacings give information about
localisation of eigenvectors, level of community structure and the level of
randomness within the networks. We find a parameter dependent transition
between Poisson and Gaussian orthogonal ensemble statistics. That is the
spectral statistics of spatial random geometric graphs fits the universality of
random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert
and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio
Chaos in the Einstein-Yang-Mills Equations
Yang-Mills color fields evolve chaotically in an anisotropically expanding
universe. The chaotic behaviour differs from that found in anisotropic
Mixmaster universes. The universe isotropizes at late times, approaching the
mean expansion rate of a radiation-dominated universe. However, small chaotic
oscillations of the shear and color stresses continue indefinitely. An
invariant, coordinate-independent characterisation of the chaos is provided by
means of fractal basin boundaries.Comment: 3 pages LaTeX + 3 pages of figure
Energy dissipation in wave propagation in general relativistic plasma
Based on a recent communication by the present authors the question of energy
dissipation in magneto hydrodynamical waves in an inflating background in
general relativity is examined. It is found that the expanding background
introduces a sort of dragging force on the propagating wave such that unlike
the Newtonnian case energy gets dissipated as it progresses. This loss in
energy having no special relativistic analogue is, however, not mechanical in
nature as in elastic wave. It is also found that the energy loss is model
dependent and also depends on the number of dimensions.Comment: 12 page
Open Mushrooms: Stickiness revisited
We investigate mushroom billiards, a class of dynamical systems with sharply
divided phase space. For typical values of the control parameter of the system
, an infinite number of marginally unstable periodic orbits (MUPOs) exist
making the system sticky in the sense that unstable orbits approach regular
regions in phase space and thus exhibit regular behaviour for long periods of
time. The problem of finding these MUPOs is expressed as the well known problem
of finding optimal rational approximations of a real number, subject to some
system-specific constraints. By introducing a generalized mushroom and using
properties of continued fractions, we describe a zero measure set of control
parameter values for which all MUPOs are destroyed and therefore
the system is less sticky. The open mushroom (billiard with a hole) is then
considered in order to quantify the stickiness exhibited and exact leading
order expressions for the algebraic decay of the survival probability function
are calculated for mushrooms with triangular and rectangular stems.Comment: 21 pages, 11 figures. Includes discussion of a three-dimensional
mushroo
Chaos, Fractals and Inflation
In order to draw out the essential behavior of the universe, investigations
of early universe cosmology often reduce the complex system to a simple
integrable system. Inflationary models are of this kind as they focus on simple
scalar field scenarios with correspondingly simple dynamics. However, we can be
assured that the universe is crowded with many interacting fields of which the
inflaton is but one. As we describe, the nonlinear nature of these interactions
can result in a complex, chaotic evolution of the universe. Here we illustrate
how chaotic effects can arise even in basic models such as homogeneous,
isotropic universes with two scalar fields. We find inflating universes which
act as attractors in the space of initial conditions. These universes display
chaotic transients in their early evolution. The chaotic character is reflected
by the fractal border to the basin of attraction. The broader implications are
likely to be felt in the process of reheating as well as in the nature of the
cosmic background radiation.Comment: 16 pages, RevTeX. See published version for fig
On the statistical and transport properties of a non-dissipative Fermi-Ulam model
The transport and diffusion properties for the velocity of a Fermi-Ulam model were characterized using the decay rate of the survival probability. The system consists of an ensemble of non-interacting particles confined to move along and experience elastic collisions with two infinitely heavy walls. One is fixed, working as a returning mechanism of the colliding particles, while the other one moves periodically in time. The diffusion equation is solved, and the diffusion coefficient is numerically estimated by means of the averaged square velocity. Our results show remarkably good agreement of the theory and simulation for the chaotic sea below the first elliptic island in the phase space. From the decay rates of the survival probability, we obtained transport properties that can be extended to other nonlinear mappings, as well to billiard problems.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES
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