868 research outputs found
Reheating in a Brane Monodromy Inflation Model
We study reheating in a recently proposed brane "monodromy inflation" model
in which the inflaton is the position of a D4 brane on a "twisted torus".
Specifically, we study the repeated collisions between the D4 brane and a D6
brane (on which the Standard Model fields are assumed to be localized) at a
fixed position along the monodromy direction as the D4 brane rolls down its
potential. We find that there is no trapping of the rolling D4 brane until it
reaches the bottom of its potential, and that reheating is entirely described
by the last brane encounter. Previous collisions have negligible effect on the
brane velocity and hence on the reheat temperature. In the context of our
setup, reheating is efficient and the reheat temperature is therefore high.Comment: 13 pages, reference adde
Cluster Approximation for the Farey Fraction Spin Chain
We consider the Farey fraction spin chain in an external field . Utilising
ideas from dynamical systems, the free energy of the model is derived by means
of an effective cluster energy approximation. This approximation is valid for
divergent cluster sizes, and hence appropriate for the discussion of the
magnetizing transition. We calculate the phase boundaries and the scaling of
the free energy. At we reproduce the rigorously known asymptotic
temperature dependence of the free energy. For , our results are
largely consistent with those found previously using mean field theory and
renormalization group arguments.Comment: 17 pages, 3 figure
Ramanujan sums for signal processing of low frequency noise
An aperiodic (low frequency) spectrum may originate from the error term in
the mean value of an arithmetical function such as M\"obius function or
Mangoldt function, which are coding sequences for prime numbers. In the
discrete Fourier transform the analyzing wave is periodic and not well suited
to represent the low frequency regime. In place we introduce a new signal
processing tool based on the Ramanujan sums c_q(n), well adapted to the
analysis of arithmetical sequences with many resonances p/q. The sums are
quasi-periodic versus the time n of the resonance and aperiodic versus the
order q of the resonance. New results arise from the use of this
Ramanujan-Fourier transform (RFT) in the context of arithmetical and
experimental signalsComment: 11 pages in IOP style, 14 figures, 2 tables, 16 reference
Symbolic dynamics for the -centre problem at negative energies
We consider the planar -centre problem, with homogeneous potentials of
degree -\a<0, \a \in [1,2). We prove the existence of infinitely many
collisions-free periodic solutions with negative and small energy, for any
distribution of the centres inside a compact set. The proof is based upon
topological, variational and geometric arguments. The existence result allows
to characterize the associated dynamical system with a symbolic dynamics, where
the symbols are the partitions of the centres in two non-empty sets
The Non-Trapping Degree of Scattering
We consider classical potential scattering. If no orbit is trapped at energy
E, the Hamiltonian dynamics defines an integer-valued topological degree. This
can be calculated explicitly and be used for symbolic dynamics of
multi-obstacle scattering.
If the potential is bounded, then in the non-trapping case the boundary of
Hill's Region is empty or homeomorphic to a sphere.
We consider classical potential scattering. If at energy E no orbit is
trapped, the Hamiltonian dynamics defines an integer-valued topological degree
deg(E) < 2. This is calculated explicitly for all potentials, and exactly the
integers < 2 are shown to occur for suitable potentials.
The non-trapping condition is restrictive in the sense that for a bounded
potential it is shown to imply that the boundary of Hill's Region in
configuration space is either empty or homeomorphic to a sphere.
However, in many situations one can decompose a potential into a sum of
non-trapping potentials with non-trivial degree and embed symbolic dynamics of
multi-obstacle scattering. This comprises a large number of earlier results,
obtained by different authors on multi-obstacle scattering.Comment: 25 pages, 1 figure Revised and enlarged version, containing more
detailed proofs and remark
Double exponential stability of quasi-periodic motion in Hamiltonian systems
We prove that generically, both in a topological and measure-theoretical
sense, an invariant Lagrangian Diophantine torus of a Hamiltonian system is
doubly exponentially stable in the sense that nearby solutions remain close to
the torus for an interval of time which is doubly exponentially large with
respect to the inverse of the distance to the torus. We also prove that for an
arbitrary small perturbation of a generic integrable Hamiltonian system, there
is a set of almost full positive Lebesgue measure of KAM tori which are doubly
exponentially stable. Our results hold true for real-analytic but more
generally for Gevrey smooth systems
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