25,138 research outputs found
An open-system approach for the characterization of spatio-temporal chaos
We investigate the structure of the invariant measure of space-time chaos by
adopting an "open-system" point of view. We consider large but finite windows
of formally infinite one-dimensional lattices and quantify the effect of the
interaction with the outer region by mapping the problem on the dynamical
characterization of localized perturbations. This latter task is performed by
suitably generalizing the concept of Lyapunov spectrum to cope with
perturbations that propagate outside the region under investigation. As a
result, we are able to introduce a "volume"-propagation velocity, i.e. the
velocity with which ensembles of localized perturbations tend to fill volumes
in the neighbouring regions.Comment: Submitted to J.Stat.Phys. - 26 pages, 7 eps-figures included.
Keywords: High-dimensional Chaos; Fractals; Coupled map lattices; Numerical
simulations of chaotic model
Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops
We consider two coupled quantum tops with angular momentum vectors
and . The coupling Hamiltonian defines the
Feinberg-Peres model which is a known paradigm of quantum chaos. We show that
this model has a nonstandard symmetry with respect to the Altland-Zirnbauer
tenfold symmetry classification of quantum systems which extends the well-known
threefold way of Wigner and Dyson (referred to as `standard' symmetry classes
here). We identify that the nonstandard symmetry classes BD (chiral
orthogonal class with no zero modes), BD (chiral orthogonal class with one
zero mode) and C (antichiral orthogonal class) as well as the standard
symmetry class A (orthogonal class). We numerically analyze the specific
spectral quantum signatures of chaos related to the nonstandard symmetries. In
the microscopic density of states and in the distribution of the lowest
positive energy eigenvalue we show that the Feinberg-Peres model follows the
predictions of the Gaussian ensembles of random-matrix theory in the
appropriate symmetry class if the corresponding classical dynamics is chaotic.
In a crossover to mixed and near-integrable classical dynamics we show that
these signatures disappear or strongly change.Comment: 15 page
String compactifications on Calabi-Yau stacks
In this paper we study string compactifications on Deligne-Mumford stacks.
The basic idea is that all such stacks have presentations to which one can
associate gauged sigma models, where the group gauged need be neither finite
nor effectively-acting. Such presentations are not unique, and lead to
physically distinct gauged sigma models; stacks classify universality classes
of gauged sigma models, not gauged sigma models themselves. We begin by
defining and justifying a notion of ``Calabi-Yau stack,'' recall how one
defines sigma models on (presentations of) stacks, and calculate of physical
properties of such sigma models, such as closed and open string spectra. We
describe how the boundary states in the open string B model on a Calabi-Yau
stack are counted by derived categories of coherent sheaves on the stack. Along
the way, we describe numerous tests that IR physics is
presentation-independent, justifying the claim that stacks classify
universality classes. String orbifolds are one special case of these
compactifications, a subject which has proven controversial in the past;
however we resolve the objections to this description of which we are aware. In
particular, we discuss the apparent mismatch between stack moduli and physical
moduli, and how that discrepancy is resolved.Comment: 85 pages, LaTeX; v2: typos fixe
Bianchi Model CMB Polarization and its Implications for CMB Anomalies
We derive the CMB radiative transfer equation in the form of a multipole
hierarchy in the nearly-Friedmann-Robertson-Walker limit of homogeneous, but
anisotropic, universes classified via their Bianchi type. Compared with
previous calculations, this allows a more sophisticated treatment of
recombination, produces predictions for the polarization of the radiation, and
allows for reionization. Our derivation is independent of any assumptions about
the dynamical behaviour of the field equations, except that it requires
anisotropies to be small back to recombination; this is already demanded by
observations.
We calculate the polarization signal in the Bianchi VIIh case, with the
parameters recently advocated to mimic the several large-angle anomalous
features observed in the CMB. We find that the peak polarization signal is ~
1.2 micro K for the best-fit model to the temperature anisotropies, and is
mostly confined to multipoles l<10. Remarkably, the predicted large-angle EE
and TE power spectra in the Bianchi model are consistent with WMAP observations
that are usually interpreted as evidence of early reionization. However, the
power in B-mode polarisation is predicted to be similar to the E-mode power and
parity-violating correlations are also predicted by the model; the WMAP
non-detection of either of these signals casts further strong doubts on the
veracity of attempts to explain the large-angle anomalies with global
anisotropy. On the other hand, given that there exist further dynamical degrees
of freedom in the VIIh universes that are yet to be compared with CMB
observations, we cannot at this time definitively reject the anisotropy
explanation.Comment: Accepted for publication in MNRAS. Minor grammatical and
typographical changes to reflect version in press. 13 pages, 6 figure
Quantum cat maps with spin 1/2
We derive a semiclassical trace formula for quantized chaotic transformations
of the torus coupled to a two-spinor precessing in a magnetic field. The trace
formula is applied to semiclassical correlation densities of the quantum map,
which, according to the conjecture of Bohigas, Giannoni and Schmit, are
expected to converge to those of the circular symplectic ensemble (CSE) of
random matrices. In particular, we show that the diagonal approximation of the
spectral form factor for small arguments agrees with the CSE prediction. The
results are confirmed by numerical investigations.Comment: 26 pages, 3 figure
Entropy potential and Lyapunov exponents
According to a previous conjecture, spatial and temporal Lyapunov exponents
of chaotic extended systems can be obtained from derivatives of a suitable
function: the entropy potential. The validity and the consequences of this
hypothesis are explored in detail. The numerical investigation of a
continuous-time model provides a further confirmation to the existence of the
entropy potential. Furthermore, it is shown that the knowledge of the entropy
potential allows determining also Lyapunov spectra in general reference frames
where the time-like and space-like axes point along generic directions in the
space-time plane. Finally, the existence of an entropy potential implies that
the integrated density of positive exponents (Kolmogorov-Sinai entropy) is
independent of the chosen reference frame.Comment: 20 pages, latex, 8 figures, submitted to CHAO
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