9,451 research outputs found
Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps
We develop a Melnikov method for volume-preserving maps with codimension one
invariant manifolds. The Melnikov function is shown to be related to the flux
of the perturbation through the unperturbed invariant surface. As an example,
we compute the Melnikov function for a perturbation of a three-dimensional map
that has a heteroclinic connection between a pair of invariant circles. The
intersection curves of the manifolds are shown to undergo bifurcations in
homologyComment: LaTex with 10 eps figure
Breathers in the weakly coupled topological discrete sine-Gordon system
Existence of breather (spatially localized, time periodic, oscillatory)
solutions of the topological discrete sine-Gordon (TDSG) system, in the regime
of weak coupling, is proved. The novelty of this result is that, unlike the
systems previously considered in studies of discrete breathers, the TDSG system
does not decouple into independent oscillator units in the weak coupling limit.
The results of a systematic numerical study of these breathers are presented,
including breather initial profiles and a portrait of their domain of existence
in the frequency-coupling parameter space. It is found that the breathers are
uniformly qualitatively different from those found in conventional spatially
discrete systems.Comment: 19 pages, 4 figures. Section 4 (numerical analysis) completely
rewritte
Extended Standard Map with Spatio-Temporal Asymmetry
We analyze the transport properties of a set of symmetry-breaking extensions
%, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and
temporal asymmetries result in the loss of periodicity in momentum direction in
the phase space dynamics, enabling the asymmetric diffusion which is the origin
of the unidirectional motion. The simplicity of the model makes the calculation
of the global dynamical properties of the system feasible both in phase space
and in controlling-parameter space. We present the results of numerical
experiments which show the intricate dependence of the asymmetric diffusion to
the controlling parameters.Comment: 6 pages latex 2e with 12 epsf fig
Quantum Breathers in a Nonlinear Lattice
We study nonlinear phonon excitations in a one-dimensional quantum nonlinear
lattice model using numerical exact diagonalization. We find that multi-phonon
bound states exist as eigenstates which are natural counterparts of breather
solutions of classical nonlinear systems. In a translationally invariant
system, these quantum breather states form particle-like bands and are
characterized by a finite correlation length. The dynamic structure factor has
significant intensity for the breather states, with a corresponding quenching
of the neighboring bands of multi-phonon extended states.Comment: 4 pages, RevTex, 4 postscript figures, Physical Relview Letters (in
press
Quantum affine Toda solitons
We review some of the progress in affine Toda field theories in recent years,
explain why known dualities cannot easily be extended, and make some
suggestions for what should be sought instead.Comment: 16pp, LaTeX. Minor revision
Cryptographical Properties of Ising Spin Systems
The relation between Ising spin systems and public-key cryptography is
investigated using methods of statistical physics. The insight gained from the
analysis is used for devising a matrix-based cryptosystem whereby the
ciphertext comprises products of the original message bits; these are selected
by employing two predetermined randomly-constructed sparse matrices. The
ciphertext is decrypted using methods of belief-propagation. The analyzed
properties of the suggested cryptosystem show robustness against various
attacks and competitive performance to modern cyptographical methods.Comment: 4 pages, 2 figure
Reconstructing the massive black hole cosmic history through gravitational waves
The massive black holes we observe in galaxies today are the natural
end-product of a complex evolutionary path, in which black holes seeded in
proto-galaxies at high redshift grow through cosmic history via a sequence of
mergers and accretion episodes. Electromagnetic observations probe a small
subset of the population of massive black holes (namely, those that are active
or those that are very close to us), but planned space-based gravitational-wave
observatories such as the Laser Interferometer Space Antenna (LISA) can measure
the parameters of ``electromagnetically invisible'' massive black holes out to
high redshift. In this paper we introduce a Bayesian framework to analyze the
information that can be gathered from a set of such measurements. Our goal is
to connect a set of massive black hole binary merger observations to the
underlying model of massive black hole formation. In other words, given a set
of observed massive black hole coalescences, we assess what information can be
extracted about the underlying massive black hole population model. For
concreteness we consider ten specific models of massive black hole formation,
chosen to probe four important (and largely unconstrained) aspects of the input
physics used in structure formation simulations: seed formation, metallicity
``feedback'', accretion efficiency and accretion geometry. For the first time
we allow for the possibility of ``model mixing'', by drawing the observed
population from some combination of the ``pure'' models that have been
simulated. A Bayesian analysis allows us to recover a posterior probability
distribution for the ``mixing parameters'' that characterize the fractions of
each model represented in the observed distribution. Our work shows that LISA
has enormous potential to probe the underlying physics of structure formation.Comment: 24 pages, 16 figures, submitted to Phys. Rev.
The Inhibition of Mixing in Chaotic Quantum Dynamics
We study the quantum chaotic dynamics of an initially well-localized wave
packet in a cosine potential perturbed by an external time-dependent force. For
our choice of initial condition and with small but finite, we find that
the wave packet behaves classically (meaning that the quantum behavior is
indistinguishable from that of the analogous classical system) as long as the
motion is confined to the interior of the remnant separatrix of the cosine
potential. Once the classical motion becomes unbounded, however, we find that
quantum interference effects dominate. This interference leads to a long-lived
accumulation of quantum amplitude on top of the cosine barrier. This pinning of
the amplitude on the barrier is a dynamic mechanism for the quantum inhibition
of classical mixing.Comment: 20 pages, RevTeX format with 6 Postscript figures appended in
uuencoded tar.Z forma
Chaos and Noise in a Truncated Toda Potential
Results are reported from a numerical investigation of orbits in a truncated
Toda potential which is perturbed by weak friction and noise. Two significant
conclusions are shown to emerge: (1) Despite other nontrivial behaviour,
configuration, velocity, and energy space moments associated with these
perturbations exhibit a simple scaling in the amplitude of the friction and
noise. (2) Even very weak friction and noise can induce an extrinsic diffusion
through cantori on a time scale much shorter than that associated with
intrinsic diffusion in the unperturbed system.Comment: 10 pages uuencoded PostScript (figures included), (A trivial
mathematical error leading to an erroneous conclusion is corrected
Piecewise Linear Models for the Quasiperiodic Transition to Chaos
We formulate and study analytically and computationally two families of
piecewise linear degree one circle maps. These families offer the rare
advantage of being non-trivial but essentially solvable models for the
phenomenon of mode-locking and the quasi-periodic transition to chaos. For
instance, for these families, we obtain complete solutions to several questions
still largely unanswered for families of smooth circle maps. Our main results
describe (1) the sets of maps in these families having some prescribed rotation
interval; (2) the boundaries between zero and positive topological entropy and
between zero length and non-zero length rotation interval; and (3) the
structure and bifurcations of the attractors in one of these families. We
discuss the interpretation of these maps as low-order spline approximations to
the classic ``sine-circle'' map and examine more generally the implications of
our results for the case of smooth circle maps. We also mention a possible
connection to recent experiments on models of a driven Josephson junction.Comment: 75 pages, plain TeX, 47 figures (available on request
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