864 research outputs found
Inherited crustal deformation along the East Gondwana margin revealed by seismic anisotropy tomography
Acknowledgments We thank Mallory Young for providing phase velocity measurements in mainland Australia and Tasmania. Robert Musgrave is thanked for making available his tilt-filtered magnetic intensity map. In the short term, data may be made available by contacting the authors (S.P. or N.R.). A new database of passive seismic data recorded in Australia is planned as part of a national geophysics data facility for easy access download. Details on the status of this database may be obtained from the authors (S.P., N.R., or A.M.R.). There are no restrictions on access for noncommercial use. Commercial users should seek written permission from the authors (S.P. or N.R.). Ross Cayley publishes with the permission of the Director of the Geological Survey of Victoria.Peer reviewedPublisher PD
Hyperdeterminants as integrable discrete systems
We give the basic definitions and some theoretical results about
hyperdeterminants, introduced by A. Cayley in 1845. We prove integrability
(understood as 4d-consistency) of a nonlinear difference equation defined by
the 2x2x2-hyperdeterminant. This result gives rise to the following hypothesis:
the difference equations defined by hyperdeterminants of any size are
integrable.
We show that this hypothesis already fails in the case of the
2x2x2x2-hyperdeterminant.Comment: Standard LaTeX, 11 pages. v2: corrected a small misprint in the
abstrac
Octonionic Representations of GL(8,R) and GL(4,C)
Octonionic algebra being nonassociative is difficult to manipulate. We
introduce left-right octonionic barred operators which enable us to reproduce
the associative GL(8,R) group. Extracting the basis of GL(4,C), we establish an
interesting connection between the structure of left-right octonionic barred
operators and generic 4x4 complex matrices. As an application we give an
octonionic representation of the 4-dimensional Clifford algebra.Comment: 14 pages, Revtex, J. Math. Phys. (submitted
E_7 and the tripartite entanglement of seven qubits
In quantum information theory, it is well known that the tripartite
entanglement of three qubits is described by the group [SL(2,C)]^3 and that the
entanglement measure is given by Cayley's hyperdeterminant. This has provided
an analogy with certain N=2 supersymmetric black holes in string theory, whose
entropy is also given by the hyperdeterminant. In this paper, we extend the
analogy to N=8. We propose that a particular tripartite entanglement of seven
qubits, encoded in the Fano plane, is described by the exceptional group E_7(C)
and that the entanglement measure is given by Cartan's quartic E_7 invariant.Comment: Minor improvements. 15 page late
Qubits from extra dimensions
We link the recently discovered black hole-qubit correspondence to the
structure of extra dimensions. In particular we show that for toroidal
compactifications of type IIB string theory simple qubit systems arise
naturally from the geometrical data of the tori parametrized by the moduli. We
also generalize the recently suggested idea of the attractor mechanism as a
distillation procedure of GHZ-like entangled states on the event horizon, to
moduli stabilization for flux attractors in F-theory compactifications on
elliptically fibered Calabi-Yau four-folds. Finally using a simple example we
show that the natural arena for qubits to show up is an embedded one within the
realm of fermionic entanglement of quantum systems with indistinguishable
constituents.Comment: 32 pages Late
The frequency map for billiards inside ellipsoids
The billiard motion inside an ellipsoid Q \subset \Rset^{n+1} is completely
integrable. Its phase space is a symplectic manifold of dimension , which
is mostly foliated with Liouville tori of dimension . The motion on each
Liouville torus becomes just a parallel translation with some frequency
that varies with the torus. Besides, any billiard trajectory inside
is tangent to caustics , so the
caustic parameters are integrals of the
billiard map. The frequency map is a key tool to
understand the structure of periodic billiard trajectories. In principle, it is
well-defined only for nonsingular values of the caustic parameters. We present
four conjectures, fully supported by numerical experiments. The last one gives
rise to some lower bounds on the periods. These bounds only depend on the type
of the caustics. We describe the geometric meaning, domain, and range of
. The map can be continuously extended to singular values of
the caustic parameters, although it becomes "exponentially sharp" at some of
them. Finally, we study triaxial ellipsoids of \Rset^3. We compute
numerically the bifurcation curves in the parameter space on which the
Liouville tori with a fixed frequency disappear. We determine which ellipsoids
have more periodic trajectories. We check that the previous lower bounds on the
periods are optimal, by displaying periodic trajectories with periods four,
five, and six whose caustics have the right types. We also give some new
insights for ellipses of \Rset^2.Comment: 50 pages, 13 figure
- âŠ