12,133 research outputs found
Delocalizing Entanglement of Anisotropic Black Branes
We study the mutual information between pairs of regions on the two
asymptotic boundaries of maximally-extended anisotropic black-brane solutions.
This quantity characterizes the local pattern of entanglement of thermofield
double states which are dual to these geometries. We analyse the disruption of
the mutual information in anisotropic shock wave geometries and show that the
entanglement velocity plays an important role in this phenomenon. Besides that
we compute several chaos-related properties of this system, like the
entanglement velocity, the butterfly velocity and the scrambling time. We find
that the butterfly velocity and the entanglement velocity violate the upper
bounds proposed in 1311.1200 and 1612.00082, but remain bounded by their
corresponding values in the infrared effective theory.Comment: 34 pages, 10 figures. V2: typos corrected and references added.
Analysis extended to higher anisotropies. Figures 3, 6(a) and 8(b) replaced
to include higher anisotropies. Figures 6(b), 7(a) and 7(b) replaced to
improve visualization. Minor changes in the end of the abstract and
introduction. Two figures added in App. C. Discussion and App.C expanded. V3:
Matches published versio
Definable henselian valuations
In this note we investigate the question whether a henselian valued field
carries a non-trivial 0-definable henselian valuation (in the language of
rings). It follows from the work of Prestel and Ziegler that there are
henselian valued fields which do not admit a 0-definable non-trivial henselian
valuation. We give conditions on the residue field which ensure the existence
of a parameter-free definiton. In particular, we show that a henselian valued
field admits a non-trivial 0-definable valuation when the residue field is
separably closed or sufficiently non-henselian, or when the absolute Galois
group of the (residue) field is non-universal.Comment: 14 pages, revised versio
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