20,874 research outputs found
Continuity of symplectically adjoint maps and the algebraic structure of Hadamard vacuum representations for quantum fields on curved spacetime
We derive for a pair of operators on a symplectic space which are adjoints of
each other with respect to the symplectic form (that is, they are sympletically
adjoint) that, if they are bounded for some scalar product on the symplectic
space dominating the symplectic form, then they are bounded with respect to a
one-parametric family of scalar products canonically associated with the
initially given one, among them being its ``purification''. As a typical
example we consider a scalar field on a globally hyperbolic spacetime governed
by the Klein-Gordon equation; the classical system is described by a symplectic
space and the temporal evolution by symplectomorphisms (which are
symplectically adjoint to their inverses). A natural scalar product is that
inducing the classical energy norm, and an application of the above result
yields that its ``purification'' induces on the one-particle space of the
quantized system a topology which coincides with that given by the two-point
functions of quasifree Hadamard states. These findings will be shown to lead to
new results concerning the structure of the local (von Neumann)
observable-algebras in representations of quasifree Hadamard states of the
Klein-Gordon field in an arbitrary globally hyperbolic spacetime, such as local
definiteness, local primarity and Haag-duality (and also split- and type
III_1-properties). A brief review of this circle of notions, as well as of
properties of Hadamard states, forms part of the article.Comment: 42 pages, LaTeX. The Def. 3.3 was incomplete and this has been
corrected. Several misprints have been removed. All results and proofs remain
unchange
Spatio-Temporal Patterns act as Computational Mechanisms governing Emergent behavior in Robotic Swarms
open access articleOur goal is to control a robotic swarm without removing its swarm-like nature. In other words, we aim to intrinsically control a robotic swarm emergent behavior. Past attempts at governing robotic swarms or their selfcoordinating emergent behavior, has proven ineffective, largely due to the swarm’s inherent randomness (making it difficult to predict) and utter simplicity (they lack a leader, any kind of centralized control, long-range communication, global knowledge, complex internal models and only operate on a couple of basic, reactive rules). The main problem is that emergent phenomena itself is not fully understood, despite being at the forefront of current research. Research into 1D and 2D Cellular Automata has uncovered a hidden computational layer which bridges the micromacro gap (i.e., how individual behaviors at the micro-level influence the global behaviors on the macro-level). We hypothesize that there also lie embedded computational mechanisms at the heart of a robotic swarm’s emergent behavior. To test this theory, we proceeded to simulate robotic swarms (represented as both particles and dynamic networks) and then designed local rules to induce various types of intelligent, emergent behaviors (as well as designing genetic algorithms to evolve robotic swarms with emergent behaviors). Finally, we analysed these robotic swarms and successfully confirmed our hypothesis; analyzing their developments and interactions over time revealed various forms of embedded spatiotemporal patterns which store, propagate and parallel process information across the swarm according to some internal, collision-based logic (solving the mystery of how simple robots are able to self-coordinate and allow global behaviors to emerge across the swarm)
Correction of non-linearity effects in detectors for electron spectroscopy
Using photoemission intensities and a detection system employed by many
groups in the electron spectroscopy community as an example, we have
quantitatively characterized and corrected detector non-linearity effects over
the full dynamic range of the system. Non-linearity effects are found to be
important whenever measuring relative peak intensities accurately is important,
even in the low-countrate regime. This includes, for example, performing
quantitative analyses for surface contaminants or sample bulk stoichiometries,
where the peak intensities involved can differ by one or two orders of
magnitude, and thus could occupy a significant portion of the detector dynamic
range. Two successful procedures for correcting non-linearity effects are
presented. The first one yields directly the detector efficiency by measuring a
flat-background reference intensity as a function of incident x-ray flux, while
the second one determines the detector response from a least-squares analysis
of broad-scan survey spectra at different incident x-ray fluxes. Although we
have used one spectrometer and detection system as an example, these
methodologies should be useful for many other cases.Comment: 13 pages, 12 figure
Hadamard States and Adiabatic Vacua
Reversing a slight detrimental effect of the mailer related to TeXabilityComment: 10pages, LaTeX (RevTeX-preprint style
Natural three-qubit interactions in one-way quantum computing
We address the effects of natural three-qubit interactions on the
computational power of one-way quantum computation (\QC). A benefit of using
more sophisticated entanglement structures is the ability to construct compact
and economic simulations of quantum algorithms with limited resources. We show
that the features of our study are embodied by suitably prepared optical
lattices, where effective three-spin interactions have been theoretically
demonstrated. We use this to provide a compact construction for the Toffoli
gate. Information flow and two-qubit interactions are also outlined, together
with a brief analysis of relevant sources of imperfection.Comment: 4 pages, 3 figures, RevTeX
Limits of sensing temporal concentration changes by single cells
Berg and Purcell [Biophys. J. 20, 193 (1977)] calculated how the accuracy of
concentration sensing by single-celled organisms is limited by noise from the
small number of counted molecules. Here we generalize their results to the
sensing of concentration ramps, which is often the biologically relevant
situation (e.g. during bacterial chemotaxis). We calculate lower bounds on the
uncertainty of ramp sensing by three measurement devices: a single receptor, an
absorbing sphere, and a monitoring sphere. We contrast two strategies, simple
linear regression of the input signal versus maximum likelihood estimation, and
show that the latter can be twice as accurate as the former. Finally, we
consider biological implementations of these two strategies, and identify
possible signatures that maximum likelihood estimation is implemented by real
biological systems.Comment: 11 pages, 2 figure
Generating quantum states through spin chain dynamics
Spin chains can realise perfect quantum state transfer between the two ends
via judicious choice of coupling strengths. In this paper, we study what other
states can be created by engineering a spin chain. We conclude that, up to
local phases, all single excitation quantum states with support on every site
of the chain can be created. We pay particular attention to the generation of
W-states that are superposed over every site of the chain.Comment: 9 pages, 1 figur
Fisher-information condition for enhanced signal detection via stochastic resonance
Various situations where a signal is enhanced by noise through stochastic resonance are now known. This paper contributes to determining general conditions under which improvement by noise can be a priori decided as feasible or not. We focus on the detection of a known signal in additive white noise. Under the assumptions of a weak signal and a sufficiently large sample size, it is proved, with an inequality based on the Fisher information, that improvement by adding noise is never possible, generically, in these conditions. However, under less restrictive conditions, an example of signal detection is shown with favorable action of adding noise.Fabing Duan, François Chapeau-Blondeau, Derek Abbot
Quantum Communication in Spin Systems With Long-Range Interactions
We calculate the fidelity of transmission of a single qubit between distant
sites on semi-infinite and finite chains of spins coupled via the magnetic
dipole interaction. We show that such systems often perform better than their
Heisenberg nearest-neighbour coupled counterparts, and that fidelities closely
approaching unity can be attained between the ends of finite chains without any
special engineering of the system, although state transfer becomes slow in long
chains. We discuss possible optimization methods, and find that, for any
length, the best compromise between the quality and the speed of the
communication is obtained in a nearly uniform chain of 4 spins.Comment: 15 pages, 8 eps figures, updated references, corrected text and
corrected figs. 1, 4 and
Distributional Modes for Scalar Field Quantization
We propose a mode-sum formalism for the quantization of the scalar field
based on distributional modes, which are naturally associated with a slight
modification of the standard plane-wave modes. We show that this formalism
leads to the standard Rindler temperature result, and that these modes can be
canonically defined on any Cauchy surface.Comment: 15 pages, RevTe
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