3,884 research outputs found
Constructive spherical codes on layers of flat tori
A new class of spherical codes is constructed by selecting a finite subset of
flat tori from a foliation of the unit sphere S^{2L-1} of R^{2L} and designing
a structured codebook on each torus layer. The resulting spherical code can be
the image of a lattice restricted to a specific hyperbox in R^L in each layer.
Group structure and homogeneity, useful for efficient storage and decoding, are
inherited from the underlying lattice codebook. A systematic method for
constructing such codes are presented and, as an example, the Leech lattice is
used to construct a spherical code in R^{48}. Upper and lower bounds on the
performance, the asymptotic packing density and a method for decoding are
derived.Comment: 9 pages, 5 figures, submitted to IEEE Transactions on Information
Theor
Fast Scrambling of mutual information in Kerr-AdS
We compute the disruption of mutual information in a TFD state dual to a Kerr
black hole with equal angular momenta in due to an equatorial
shockwave. The shockwave respects the axi-symmetry of the Kerr geometry with
specific angular momenta & . The
sub-systems considered are hemispheres in the and the dual CFTs
with the equator of the as their boundary. We compute the change in the
mutual information by determining the growth of the HRT surface at late times.
We find that at late times leading upto the scrambling time the minimum value
of the instantaneous Lyapunov index is bounded by
and is found to be greater
than in certain regimes with and denoting the black
hole's temperature and the horizon angular velocity respectively while
. We also find that
for non-extremal geometries the null perturbation obeys
for it to reach the outer horizon from the
boundary. The scrambling time at very late times is given by
where is the Kerr entropy.
We also find that the onset of scrambling is delayed due to a term proportional
to which is not extensive and does not scale
with the entropy of Kerr black hole.Comment: 18-pages, 4-figure
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