1,293 research outputs found
A role of constraint in self-organization
In this paper we introduce a neural network model of self-organization. This
model uses a variation of Hebb rule for updating its synaptic weights, and
surely converges to the equilibrium status. The key point of the convergence is
the update rule that constrains the total synaptic weight and this seems to
make the model stable. We investigate the role of the constraint and show that
it is the constraint that makes the model stable. For analyzing this setting,
we propose a simple probabilistic game that models the neural network and the
self-organization process. Then, we investigate the characteristics of this
game, namely, the probability that the game becomes stable and the number of
the steps it takes.Comment: To appear in the Proc. RANDOM'98, Oct. 199
Introduction of the Translational Operator in Frequency Domain and Treatment of Certain Linear Differential Equations (II)
Introduction of the Translational Operator in Frequency Domain and Treatment of Certain Linear Differential Equations (I)
Notes on Entanglement Entropy in String Theory
In this paper, we study the entanglement entropy in string theory in the
simplest setup of dividing the nine dimensional space into two halves. This
corresponds to the leading quantum correction to the horizon entropy in string
theory on the Rindler space. This entropy is also called the conical entropy
and includes surface term contributions. We first derive a new simple formula
of the conical entropy for any free higher spin fields. Then we apply this
formula to computations of conical entropy in open and closed superstring. In
our analysis of closed string, we study the twisted conical entropy defined by
making use of string theory on Melvin backgrounds. This quantity is easier to
calculate owing to the folding trick. Our analysis shows that the entanglement
entropy in closed superstring is UV finite owing to the string scale cutoff.Comment: 27 pages, no figures, latex, v2: typos corrected, references adde
EPR Pairs, Local Projections and Quantum Teleportation in Holography
In this paper we analyze three quantum operations in two dimensional
conformal field theories (CFTs): local projection measurements, creations of
partial entanglement between two CFTs, and swapping of subsystems between two
CFTs. We also give their holographic duals and study time evolutions of
entanglement entropy. By combining these operations, we present an analogue of
quantum teleportation between two CFTs and give its holographic realization. We
introduce a new quantity to probe tripartite entanglement by using local
projection measurement.Comment: 61 pages, 24 figures. v2: comments and refs added. v3: minor
correction
Quantum Dimension as Entanglement Entropy in 2D CFTs
We study entanglement entropy of excited states in two dimensional conformal
field theories (CFTs). Especially we consider excited states obtained by acting
primary operators on a vacuum. We show that under its time evolution,
entanglement entropy increases by a finite constant when the causality
condition is satisfied. Moreover, in rational CFTs, we prove that this
increased amount of (both Renyi and von-Neumann) entanglement entropy always
coincides with the log of quantum dimension of the primary operator.Comment: 5 pages, 3 eps figures, Revte
Out-of-Time-Ordered Correlators in
In this note we continue analysing the non-equilibrium dynamics in the
orbifold conformal field theory. We compute the
out-of-time-ordered four-point correlators with twist operators. For rational
which is the square of the compactification radius, we find
that the correlators approach non-trivial constants at late time. For
they are expressed in terms of the modular matrices and for higher
orbifolds are functions of and . For irrational , we find a new
polynomial decay of the correlators that is a signature of an intermediate
regime between rational and chaotic models.Comment: 20 pages, 3 figure
Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories
We introduce a new optimization procedure for Euclidean path integrals which
compute wave functionals in conformal field theories (CFTs). We optimize the
background metric in the space on which the path integration is performed.
Equivalently this is interpreted as a position-dependent UV cutoff. For
two-dimensional CFT vacua, we find the optimized metric is given by that of a
hyperbolic space and we interpret this as a continuous limit of the conjectured
relation between tensor networks and Anti--de Sitter (AdS)/conformal field
theory (CFT) correspondence. We confirm our procedure for excited states, the
thermofield double state, the Sachdev-Ye-Kitaev model and discuss its extension
to higher-dimensional CFTs. We also show that when applied to reduced density
matrices, it reproduces entanglement wedges and holographic entanglement
entropy. We suggest that our optimization prescription is analogous to the
estimation of computational complexity.Comment: 7 pages, Revtex, 2 figures, Version 2 : The version published in PRL,
title expanded and typos correcte
cMERA as Surface/State Correspondence in AdS/CFT
We present how the surface/state correspondence, conjectured in
arXiv:1503.03542, works in the setup of AdS3/CFT2 by generalizing the
formulation of cMERA. The boundary states in conformal field theories play a
crucial role in our formulation and the bulk diffeomorphism is naturally taken
into account. We give an identification of bulk local operators which
reproduces correct scalar field solutions on AdS3 and bulk scalar propagators.
We also calculate the information metric for a locally excited state and show
that it is given by that of 2d hyperbolic manifold, which is argued to describe
the time slice of AdS3.Comment: 8 pages, Revtex, 3 figures; comments added, a derivation of bulk
propagators is adde
- …