141 research outputs found
Matrix Quantization of Turbulence
Based on our recent work on Quantum Nambu Mechanics \cite{af2}, we provide
an explicit quantization of the Lorenz chaotic attractor through the
introduction of Non-commutative phase space coordinates as Hermitian matrices in . For the volume preserving part, they satisfy the
commutation relations induced by one of the two Nambu Hamiltonians, the second
one generating a unique time evolution. Dissipation is incorporated quantum
mechanically in a self-consistent way having the correct classical limit
without the introduction of external degrees of freedom. Due to its volume
phase space contraction it violates the quantum commutation relations. We
demonstrate that the Heisenberg-Nambu evolution equations for the Matrix Lorenz
system develop fast decoherence to N independent Lorenz attractors. On the
other hand there is a weak dissipation regime, where the quantum mechanical
properties of the volume preserving non-dissipative sector survive for long
times.Comment: 14 pages, Based on invited talks delivered at: Fifth Aegean Summer
School, "From Gravity to Thermal Gauge theories and the AdS/CFT
Correspondance", September 2009, Milos, Greece; the Intern. Conference on
Dynamics and Complexity, Thessaloniki, Greece, 12 July 2010; Workshop on
"AdS4/CFT3 and the Holographic States of Matter", Galileo Galilei Institute,
Firenze, Italy, 30 October 201
Symmetries within domain walls
The comparison of symmetries in the interior and the exterior of a domain
wall is relevant when discussing the correspondence between domain walls and
branes, and also when studying the interaction of walls and magnetic monopoles.
I discuss the symmetries in the context of an SU(N) times Z_2 model (for odd N)
with a single adjoint scalar field. Situations in which the wall interior has
less symmetry than the vacuum are easy to construct while the reverse situation
requires significant engineering of the scalar potential.Comment: 5 pages. Added reference
Modular discretization of the AdS2/CFT1 Holography
We propose a finite discretization for the black hole geometry and dynamics.
We realize our proposal, in the case of extremal black holes, for which the
radial and temporal near horizon geometry is known to be
AdS. We implement its discretization by
replacing the set of real numbers with the set of integers modulo
, with AdS going over to the finite geometry
AdS.
We model the dynamics of the microscopic degrees of freedom by generalized
Arnol'd cat maps, , which are isometries of the
geometry at both the classical and quantum levels.
These exhibit well studied properties of strong arithmetic chaos, dynamical
entropy, nonlocality and factorization in the cutoff discretization , which
are crucial for fast quantum information processing.
We construct, finally, a new kind of unitary and holographic correspondence,
for AdS/CFT, via coherent states of both the bulk and boundary
geometries.Comment: 33 pages LaTeX2e, 1 JPEG figure. Typos corrected, references added.
Clarification of several points in the abstract and the tex
Metastability of Spherical Membranes in Supermembrane and Matrix Theory
Motivated by recent work we study rotating ellipsoidal membranes in the
framework of the light-cone supermembrane theory. We investigate stability
properties of these classical solutions which are important for the
quantization of super membranes. We find the stability modes for all sectors of
small multipole deformations. We exhibit an isomorphism of the linearized
membrane equation with that of the SU(N) matrix model for every value of .
The boundaries of the linearized stability region are at a finite distance and
they appear for finite size perturbations.Comment: 7 pages (two column
On sphaleron deformations induced by Yukawa interactions
Due to the presence of the chiral anomaly sphalerons with Chern-Simons number
a half (CS=1/2) are the only static configurations that allow for a fermion
level crossing in the two-dimensional Abelian-Higgs model with massless
fermions, i.e. in the absence of Yukawa interactions. In the presence of
fermion-Higgs interactions we demonstrate the existence of zero energy
solutions to the one-dimensional Dirac equation at deformed sphalerons with
CS Induced level crossing due to Yukawa interactions illustrates a
non-trivial generalization of the Atiyah-Patodi-Singer index theorem and of the
equivalence between parity anomaly in odd and the chiral anomaly in even
dimensions. We discuss a subtle manifestation of this effect in the standard
electroweak theory at finite temperatures.Comment: 14 pages, Latex, NBI-HE-93-7
Phase Space Geometry and Chaotic Attractors in Dissipative Nambu Mechanics
Following the Nambu mechanics framework we demonstrate that the
non-dissipative part of the Lorenz system can be generated by the intersection
of two quadratic surfaces that form a doublet under the group SL(2,R). All
manifolds are classified into four dinstict classes; parabolic, elliptical,
cylindrical and hyperbolic. The Lorenz attractor is localized by a specific
infinite set of one parameter family of these surfaces. The different classes
correspond to different physical systems. The Lorenz system is identified as a
charged rigid body in a uniform magnetic field with external torque and this
system is generalized to give new strange attractors.Comment: 22 pages, 13 figure
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