71 research outputs found
Non Hamiltonian Chaos from Nambu Dynamics of Surfaces
We discuss recent work with E.Floratos (JHEP 1004:036,2010) on Nambu Dynamics
of Intersecting Surfaces underlying Dissipative Chaos in . We present
our argument for the well studied Lorenz and R\"{o}ssler strange attractors. We
implement a flow decomposition to their equations of motion. Their volume
preserving part preserves in time a family of two intersecting surfaces, the so
called {\em Nambu Hamiltonians}. For dynamical systems with linear dissipative
sector such as the Lorenz system, they are specified in terms of Intersecting
Quadratic Surfaces. For the case of the R\"{o}ssler system, with nonlinear
dissipative part, they are given in terms of a Helicoid intersected by a
Cylinder. In each case they foliate the entire phase space and get deformed by
Dissipation, the irrotational component to their flow. It is given by the
gradient of a surface in specified in terms of a scalar function. All
three intersecting surfaces reproduce completely the dynamics of each strange
attractor.Comment: 10 pages, Invited Talks at the International Conferences on:
Nonlinear Dynamics and Complexity; Theory, Methods and Applications, 12-16
July 2010, Thessaloniki, Greece; Second Greek-Turkish Conference on
Statistical Mechanics and Dynamical Systems, Turunc-Symi, 5-12 September 201
Charged Cosmic String Nucleation in de Sitter Space
We investigate the quantum nucleation of pairs of charged circular cosmic
strings in de Sitter space. By including self-gravity we obtain the classical
potential energy barrier and compute the quantum mechanical tunneling
probability in the semiclassical approximation. We also discuss the classical
evolution of charged circular strings after their nucleation.Comment: 12 pages Latex + 3 figures (not included), Nordita 94/38
The Omega-Infinity Limit of Single Spikes
A new infinite-size limit of strings in RxS2 is presented. The limit is
obtained from single spike strings by letting by letting the angular velocity
parameter omega become infinite. We derive the energy-momenta relation of
omega-infinity single spikes as their linear velocity v-->1 and their angular
momentum J-->1. Generally, the v-->1, J-->1 limit of single spikes is singular
and has to be excluded from the spectrum and be studied separately. We discover
that the dispersion relation of omega-infinity single spikes contains
logarithms in the limit J-->1. This result is somewhat surprising, since the
logarithmic behavior in the string spectra is typically associated with their
motion in non-compact spaces such as AdS. Omega-infinity single spikes seem to
completely cover the surface of the 2-sphere they occupy, so that they may
essentially be viewed as some sort of "brany strings". A proof of the
sphere-filling property of omega-infinity single spikes is given in the
appendix.Comment: 35 pages, 14 figures. Matches published version; Contains equation
(4.21) that gives the first few finite-size corrections to the energy of
omega-infinity single spike
Chaotic Information Processing by Extremal Black Holes
We review an explicit regularization of the AdS/CFT correspondence,
that preserves all isometries of bulk and boundary degrees of freedom. This
scheme is useful to characterize the space of the unitary evolution operators
that describe the dynamics of the microstates of extremal black holes in four
spacetime dimensions. Using techniques from algebraic number theory to evaluate
the transition amplitudes, we remark that the regularization scheme expresses
the fast quantum computation capability of black holes as well as its chaotic
nature.Comment: 8 pages, 2 JPEG figues. Contribution to the VII Black Holes Workshop,
Aveiro PT, Decemeber 201
The quantum cat map on the modular discretization of extremal black hole horizons
Based on our recent work on the discretization of the radial AdS geometry
of extremal BH horizons,we present a toy model for the chaotic unitary
evolution of infalling single particle wave packets.
We construct explicitly the eigenstates and eigenvalues for the single
particle dynamics for an observer falling into the BH horizon, with time
evolution operator the quantum Arnol'd cat map (QACM).
Using these results we investigate the validity of the eigenstate
thermalization hypothesis (ETH), as well as that of the fast scrambling time
bound (STB).
We find that the QACM, while possessing a linear spectrum, has eigenstates,
which are random and satisfy the assumptions of the ETH.
We also find that the thermalization of infalling wave packets in this
particular model is exponentially fast, thereby saturating the STB, under the
constraint that the finite dimension of the single--particle Hilbert space
takes values in the set of Fibonacci integers.Comment: 28 pages LaTeX2e, 8 jpeg figures. Clarified certain issues pertaining
to the relation between mixing time and scrambling time; enhanced discussion
of the Eigenstate Thermalization Hypothesis; revised figures and updated
references. Typos correcte
Exact Multiparticle Amplitudes at Threshold in Theories with Softly Broken Symmetry
We consider the problem of multiparticle production at threshold in a
-theory with an symmetry softly broken down to
by nonequal masses. We derive the set of recurrence
relations between the multiparticle amplitudes which sums all relevant diagrams
with arbitrary number of loops in the large- limit with fixed number of
produced particles. We transform it into a quantum mechanical problem and show
how it can be obtained directly from the operator equations of motion by
applying the factorization at large . We find the exact solutions to the
problem by using the Gelfand--Diki\u{\i} representation of the diagonal
resolvent of the Schr\"{o}dinger operator. The result coincides with the tree
amplitudes while the effect of loops is the renormalization of the coupling
constant and masses. The form of the solution is due to the fact that the exact
amplitude of the process \ra vanishes at on mass shell when
averaged over the -indices of incoming particles. We discuss what
dynamical symmetry is behind this property. We also give an exact solution in
the large- limit for the model of the scalar particle
with the spontaneous breaking of a reflection symmetry.Comment: Latex, 33 pages, NBI-HE-94-3
M2-brane Dynamics in the Classical Limit of the BMN Matrix Model
We investigate the large-N limit of the BMN matrix model by analyzing the
dynamics of ellipsoidal M2-branes that spin in the 11-dimensional maximally
supersymmetric SO(3)xSO(6) plane-wave background. We identify finite-energy
solutions by specifying the local minima of the corresponding energy
functional. These configurations are static in SO(3) due to the Myers effect
and rotate in SO(6) with an angular momentum that is bounded from above. As a
first step towards studying their chaotic properties, we evaluate the Lyapunov
exponents of their radial fluctuations.Comment: 7 pages, 8 figure
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