23,073 research outputs found
Covariant fuzzy observables and coarse-graining
A fuzzy observable is regarded as a smearing of a sharp observable, and the
structure of covariant fuzzy observables is studied. It is shown that the
covariant coarse-grainings of sharp observables are exactly the covariant fuzzy
observables. A necessary and sufficient condition for a covariant fuzzy
observable to be informationally equivalent to the corresponding sharp
observable is given.Comment: 19 page
Sharp thresholds for Gibbs-non-Gibbs transition in the fuzzy Potts model with a Kac-type interaction
We investigate the Gibbs properties of the fuzzy Potts model on the
d-dimensional torus with Kac interaction. We use a variational approach for
profiles inspired by that of Fernandez, den Hollander and Mart{\i}nez for their
study of the Gibbs-non-Gibbs transitions of a dynamical Kac-Ising model on the
torus. As our main result, we show that the mean-field thresholds dividing
Gibbsian from non-Gibbsian behavior are sharp in the fuzzy Kac-Potts model with
class size unequal two. On the way to this result we prove a large deviation
principle for color profiles with diluted total mass densities and use
monotocity arguments.Comment: 20 page
Stochastic domination for the Ising and fuzzy Potts models
We discuss various aspects concerning stochastic domination for the Ising
model and the fuzzy Potts model. We begin by considering the Ising model on the
homogeneous tree of degree , \Td. For given interaction parameters ,
and external field h_1\in\RR, we compute the smallest external field
such that the plus measure with parameters and dominates
the plus measure with parameters and for all .
Moreover, we discuss continuity of with respect to the three
parameters , , and also how the plus measures are stochastically
ordered in the interaction parameter for a fixed external field. Next, we
consider the fuzzy Potts model and prove that on \Zd the fuzzy Potts measures
dominate the same set of product measures while on \Td, for certain parameter
values, the free and minus fuzzy Potts measures dominate different product
measures. For the Ising model, Liggett and Steif proved that on \Zd the plus
measures dominate the same set of product measures while on \T^2 that
statement fails completely except when there is a unique phase.Comment: 22 pages, 5 figure
On Vague Computers
Vagueness is something everyone is familiar with. In fact, most people think
that vagueness is closely related to language and exists only there. However,
vagueness is a property of the physical world. Quantum computers harness
superposition and entanglement to perform their computational tasks. Both
superposition and entanglement are vague processes. Thus quantum computers,
which process exact data without "exploiting" vagueness, are actually vague
computers
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