53,863 research outputs found
Constraints on Macroscopic Realism Without Assuming Non-Invasive Measurability
Macroscopic realism is the thesis that macroscopically observable properties
must always have definite values. The idea was introduced by Leggett and Garg
(1985), who wished to show a conflict with the predictions of quantum theory.
However, their analysis required not just the assumption of macroscopic realism
per se, but also that the observable properties could be measured
non-invasively. In recent years there has been increasing interest in
experimental tests of the violation of the Leggett-Garg inequality, but it has
remained a matter of controversy whether this second assumption is a reasonable
requirement for a macroscopic realist view of quantum theory. In a recent
critical assessment Maroney and Timpson (2017) identified three different
categories of macroscopic realism, and argued that only the simplest category
could be ruled out by Leggett-Garg inequality violations. Allen, Maroney, and
Gogioso (2016) then showed that the second of these approaches was also
incompatible with quantum theory in Hilbert spaces of dimension 4 or higher.
However, we show that the distinction introduced by Maroney and Timpson between
the second and third approaches is not noise tolerant, so unfortunately Allen's
result, as given, is not directly empirically testable. In this paper we
replace Maroney and Timpson's three categories with a parameterization of
macroscopic realist models, which can be related to experimental observations
in a noise tolerant way, and recover the original definitions in the noise-free
limit. We show how this parameterization can be used to experimentally rule out
classes of macroscopic realism in Hilbert spaces of dimension 3 or higher,
including the category tested by the Leggett-Garg inequality, without any use
of the non-invasive measurability assumption.Comment: 20 pages, 10 figure
Exact expression for the diffusion propagator in a family of time-dependent anharmonic potentials
We have obtained the exact expression of the diffusion propagator in the
time-dependent anharmonic potential . The
underlying Euclidean metric of the problem allows us to obtain analytical
solutions for a whole family of the elastic parameter a(t), exploiting the
relation between the path integral representation of the short time propagator
and the modified Bessel functions. We have also analyzed the conditions for the
appearance of a non-zero flow of particles through the infinite barrier located
at the origin (b<0).Comment: RevTex, 19 pgs. Accepted in Physical Review
Generalization of coloring linear transformation
The paper is focused on the technique of linear
transformation between correlated and uncorrelated
Gaussian random vectors, which is more or less commonly
used in the reliability analysis of structures. These linear
transformations are frequently needed to transform
uncorrelated random vectors into correlated vectors with
a prescribed covariance matrix (coloring transformation),
and also to perform an inverse (whitening) transformation,
i.e. to decorrelate a random vector with a non-identity
covariance matrix. Two well-known linear transformation
techniques, namely Cholesky decomposition and eigendecomposition
(also known as principal component
analysis, or the orthogonal transformation of a covariance
matrix), are shown to be special cases of the generalized
linear transformation presented in the paper. The proposed
generalized linear transformation is able to rotate the
transformation randomly, which may be desired in order
to remove unwanted directional bias. The conclusions
presented herein may be useful for structural reliability
analysis with correlated random variables or random
fields
Thermal ratchet effects in ferrofluids
Rotational Brownian motion of colloidal magnetic particles in ferrofluids
under the influence of an oscillating external magnetic field is investigated.
It is shown that for a suitable time dependence of the magnetic field, a noise
induced rotation of the ferromagnetic particles due to rectification of thermal
fluctuations takes place. Via viscous coupling, the associated angular momentum
is transferred from the magnetic nano-particles to the carrier liquid and can
then be measured as macroscopic torque on the fluid sample. A thorough
theoretical analysis of the effect in terms of symmetry considerations,
analytical approximations, and numerical solutions is given which is in
accordance with recent experimental findings.Comment: 18 pages, 6 figure
The Renormalization-Group peculiarities of Griffiths and Pearce: What have we learned?
We review what we have learned about the "Renormalization-Group
peculiarities" which were discovered about twenty years ago by Griffiths and
Pearce, and which questions they asked are still widely open. We also mention
some related developments.Comment: Proceedings Marseille meeting on mathematical results in statistical
mechanic
Snake states and their symmetries in graphene
Snake states are open trajectories for charged particles propagating in two
dimensions under the influence of a spatially varying perpendicular magnetic
field. In the quantum limit they are protected edge modes that separate
topologically inequivalent ground states and can also occur when the particle
density rather than the field is made nonuniform. We examine the correspondence
of snake trajectories in single-layer graphene in the quantum limit for two
families of domain walls: (a) a uniform doped carrier density in an
antisymmetric field profile and (b) antisymmetric carrier distribution in a
uniform field. These families support different internal symmetries but the
same pattern of boundary and interface currents. We demonstrate that these
physically different situations are gauge equivalent when rewritten in a Nambu
doubled formulation of the two limiting problems. Using gauge transformations
in particle-hole space to connect these problems, we map the protected
interfacial modes to the Bogoliubov quasiparticles of an interfacial
one-dimensional p-wave paired state. A variational model is introduced to
interpret the interfacial solutions of both domain wall problems
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