16,011 research outputs found
Noncontextuality, Finite Precision Measurement and the Kochen-Specker Theorem
Meyer recently queried whether non-contextual hidden variable models can,
despite the Kochen-Specker theorem, simulate the predictions of quantum
mechanics to within any fixed finite experimental precision. Clifton and Kent
have presented constructions of non-contextual hidden variable theories which,
they argued, indeed simulate quantum mechanics in this way. These arguments
have evoked some controversy. One aim of this paper is to respond to and rebut
criticisms of the MCK papers. We thus elaborate in a little more detail how the
CK models can reproduce the predictions of quantum mechanics to arbitrary
precision. We analyse in more detail the relationship between classicality,
finite precision measurement and contextuality, and defend the claims that the
CK models are both essentially classical and non-contextual. We also examine in
more detail the senses in which a theory can be said to be contextual or
non-contextual, and in which an experiment can be said to provide evidence on
the point. In particular, we criticise the suggestion that a decisive
experimental verification of contextuality is possible, arguing that the idea
rests on a conceptual confusion.Comment: 27 pages; published version; minor changes from previous versio
Design and Evaluation of a Probabilistic Music Projection Interface
We describe the design and evaluation of a probabilistic
interface for music exploration and casual playlist generation.
Predicted subjective features, such as mood and
genre, inferred from low-level audio features create a 34-
dimensional feature space. We use a nonlinear dimensionality
reduction algorithm to create 2D music maps of
tracks, and augment these with visualisations of probabilistic
mappings of selected features and their uncertainty.
We evaluated the system in a longitudinal trial in users’
homes over several weeks. Users said they had fun with the
interface and liked the casual nature of the playlist generation.
Users preferred to generate playlists from a local
neighbourhood of the map, rather than from a trajectory,
using neighbourhood selection more than three times more
often than path selection. Probabilistic highlighting of subjective
features led to more focused exploration in mouse
activity logs, and 6 of 8 users said they preferred the probabilistic
highlighting mode
Random Tilings: Concepts and Examples
We introduce a concept for random tilings which, comprising the conventional
one, is also applicable to tiling ensembles without height representation. In
particular, we focus on the random tiling entropy as a function of the tile
densities. In this context, and under rather mild assumptions, we prove a
generalization of the first random tiling hypothesis which connects the maximum
of the entropy with the symmetry of the ensemble. Explicit examples are
obtained through the re-interpretation of several exactly solvable models. This
also leads to a counterexample to the analogue of the second random tiling
hypothesis about the form of the entropy function near its maximum.Comment: 32 pages, 42 eps-figures, Latex2e updated version, minor grammatical
change
Topological quantum field theory and invariants of graphs for quantum groups
On basis of generalized 6j-symbols we give a formulation of topological
quantum field theories for 3-manifolds including observables in the form of
coloured graphs. It is shown that the 6j-symbols associated with deformations
of the classical groups at simple even roots of unity provide examples of this
construction. Calculational methods are developed which, in particular, yield
the dimensions of the state spaces as well as a proof of the relation,
previously announced for the case of by V.Turaev, between these
models and corresponding ones based on the ribbon graph construction of
Reshetikhin and Turaev.Comment: 38 page
Two-dimensional O(n) model in a staggered field
Nienhuis' truncated O(n) model gives rise to a model of self-avoiding loops
on the hexagonal lattice, each loop having a fugacity of n. We study such loops
subjected to a particular kind of staggered field w, which for n -> infinity
has the geometrical effect of breaking the three-phase coexistence, linked to
the three-colourability of the lattice faces. We show that at T = 0, for w > 1
the model flows to the ferromagnetic Potts model with q=n^2 states, with an
associated fragmentation of the target space of the Coulomb gas. For T>0, there
is a competition between T and w which gives rise to multicritical versions of
the dense and dilute loop universality classes. Via an exact mapping, and
numerical results, we establish that the latter two critical branches coincide
with those found earlier in the O(n) model on the triangular lattice. Using
transfer matrix studies, we have found the renormalisation group flows in the
full phase diagram in the (T,w) plane, with fixed n. Superposing three
copies of such hexagonal-lattice loop models with staggered fields produces a
variety of one or three-species fully-packed loop models on the triangular
lattice with certain geometrical constraints, possessing integer central
charges 0 <= c <= 6. In particular we show that Benjamini and Schramm's RGB
loops have fractal dimension D_f = 3/2.Comment: 40 pages, 17 figure
On the causal Barrett--Crane model: measure, coupling constant, Wick rotation, symmetries and observables
We discuss various features and details of two versions of the Barrett-Crane
spin foam model of quantum gravity, first of the Spin(4)-symmetric Riemannian
model and second of the SL(2,C)-symmetric Lorentzian version in which all
tetrahedra are space-like. Recently, Livine and Oriti proposed to introduce a
causal structure into the Lorentzian Barrett--Crane model from which one can
construct a path integral that corresponds to the causal (Feynman) propagator.
We show how to obtain convergent integrals for the 10j-symbols and how a
dimensionless constant can be introduced into the model. We propose a `Wick
rotation' which turns the rapidly oscillating complex amplitudes of the Feynman
path integral into positive real and bounded weights. This construction does
not yet have the status of a theorem, but it can be used as an alternative
definition of the propagator and makes the causal model accessible by standard
numerical simulation algorithms. In addition, we identify the local symmetries
of the models and show how their four-simplex amplitudes can be re-expressed in
terms of the ordinary relativistic 10j-symbols. Finally, motivated by possible
numerical simulations, we express the matrix elements that are defined by the
model, in terms of the continuous connection variables and determine the most
general observable in the connection picture. Everything is done on a fixed
two-complex.Comment: 22 pages, LaTeX 2e, 1 figur
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