58,969 research outputs found
Properties of Persistent Mutual Information and Emergence
The persistent mutual information (PMI) is a complexity measure for
stochastic processes. It is related to well-known complexity measures like
excess entropy or statistical complexity. Essentially it is a variation of the
excess entropy so that it can be interpreted as a specific measure of system
internal memory. The PMI was first introduced in 2010 by Ball, Diakonova and
MacKay as a measure for (strong) emergence. In this paper we define the PMI
mathematically and investigate the relation to excess entropy and statistical
complexity. In particular we prove that the excess entropy is an upper bound of
the PMI. Furthermore we show some properties of the PMI and calculate it
explicitly for some example processes. We also discuss to what extend it is a
measure for emergence and compare it with alternative approaches used to
formalize emergence.Comment: 45 pages excerpt of Diploma-Thesi
Semiclassical Virasoro Blocks from AdS Gravity
We present a unified framework for the holographic computation of Virasoro
conformal blocks at large central charge. In particular, we provide bulk
constructions that correctly reproduce all semiclassical Virasoro blocks that
are known explicitly from conformal field theory computations. The results
revolve around the use of geodesic Witten diagrams, recently introduced in
arXiv:1508.00501, evaluated in locally AdS geometries generated by
backreaction of heavy operators. We also provide an alternative computation of
the heavy-light semiclassical block -- in which two external operators become
parametrically heavy -- as a certain scattering process involving higher spin
gauge fields in AdS; this approach highlights the chiral nature of Virasoro
blocks. These techniques may be systematically extended to compute corrections
to these blocks and to interpolate amongst the different semiclassical regimes.Comment: 32 pages + refs. v2: fixed figure glitc
Lifting SU(2) Spin Networks to Projected Spin Networks
Projected spin network states are the canonical basis of quantum states of
geometry for the most recent EPR-FK spinfoam models for quantum gravity. They
are functionals of both the Lorentz connection and the time normal field. We
analyze in details the map from these projected spin networks to the standard
SU(2) spin networks of loop quantum gravity. We show that this map is not
one-to-one and that the corresponding ambiguity is parameterized by the Immirzi
parameter. We conclude with a comparison of the scalar products between
projected spin networks and SU(2) spin network states.Comment: 14 page
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