20,104 research outputs found
A THEORY OF QUALITATIVE SIMILARITY
The central result of this paper establishes an isomorphism between two types of mathematical structures: ""ternary preorders"" and ""convex topologies."" The former are characterized by reflexivity, symmetry and transitivity conditions, and can be interpreted geometrically as ordered betweenness relations; the latter are defined as intersection-closed families of sets satisfying an ""abstract convexity"" property. A large range of examples is given. As corollaries of the main result we obtain a version of Birkhoff''s representation theorem for finite distributive lattices, and a qualitative version of the representation of ultrametric distances by indexed taxonomic hierarchies.
Universal dynamical decoupling of a single solid-state spin from a spin bath
Controlling the interaction of a single quantum system with its environment
is a fundamental challenge in quantum science and technology. We dramatically
suppress the coupling of a single spin in diamond with the surrounding spin
bath by using double-axis dynamical decoupling. The coherence is preserved for
arbitrary quantum states, as verified by quantum process tomography. The
resulting coherence time enhancement is found to follow a general scaling with
the number of decoupling pulses. No limit is observed for the decoupling action
up to 136 pulses, for which the coherence time is enhanced more than 25 times
compared to spin echo. These results uncover a new regime for experimental
quantum science and allow to overcome a major hurdle for implementing quantum
information protocols.Comment: submitted 24 May 2010; published online 9 September 201
Malmquist Bias and the Distance to the Virgo Cluster
This paper investigates the impact of Malmquist bias on the distance to the
Virgo cluster determined by the H_0 Key Project using M100, and consequently on
the derived value of H_0. Malmquist bias is a volume-induced statistical effect
which causes the most probable distance to be different from the raw distance
measured. Consideration of the bias in the distance to the Virgo cluster raises
this distance and lowers the calculated value of H_0. Monte Carlo simulations
of the cluster have been run for several possible distributions of spirals
within the cluster and of clusters in the local universe. Simulations
consistent with known information regarding the cluster and the errors of
measurement result in a bias of about 6.5%-8.5%. This corresponds to an
unbiased distance of 17.2-17.4 Mpc and a value of H_0 in the range 80-82
km/s/Mpc.
The problem of determining the bias to Virgo illustrates several key points
regarding Malmquist bias. Essentially all conventional astronomical distance
measurements are subject to this bias. In addition, the bias accumulates when
an attempt is made to construct "distance ladders" from measurements which are
individually biased. As will be shown in the case of Virgo, the magnitude and
direction of the bias are sensitive to the spatial distribution of the parent
poputation from which the observed object is drawn - a distribution which is
often poorly known. This leads to uncertainty in the magnitude of the bias, and
adds to the importance of minimizing the number of steps in "distance ladders".Comment: 19 pages, 3 figures, Latex, To appear in Ap
Comparison of the STI NIPIP tracking dynamics identification with the on-line Fourier analyzer DFA results including a time varying case
The Non-Intrusive Pilot Identification Procedure (NIPIP) recently developed at STI and described at the 1981 Annual Manual was used to identify operators who were compensatory tracking a sub-critical-instability task. NIPIP uses a time domain least squares procedure converting to frequency domain coefficients. The forcing function was a sum of sinusoids supplied by the STI Mark II Describing Function Analyzer, which computes on-line Fourier coefficients of the operator's error/input describing function. The resulting open-loop and operator dynamics computed by each procedure are compared, and they are shown to be reasonably close when there is reasonable power in the error signal at the measurement frequencies. A special run was made in which the operator abruptly reduced gain within 1 sec, and the ability of the NIPIP to identify this step time variation in the operator is illustrated
Nanopositioning of a diamond nanocrystal containing a single NV defect center
Precise control over the position of a single quantum object is important for
many experiments in quantum science and nanotechnology. We report on a
technique for high-accuracy positioning of individual diamond nanocrystals. The
positioning is done with a home-built nanomanipulator under real-time scanning
electron imaging, yielding an accuracy of a few nanometers. This technique is
applied to pick up, move and position a single NV defect center contained in a
diamond nanocrystal. We verify that the unique optical and spin properties of
the NV center are conserved by the positioning process.Comment: 3 pages, 3 figures; high-resolution version available at
http://www.ns.tudelft.nl/q
Spin filling of a quantum dot derived from excited-state spectroscopy
We study the spin filling of a semiconductor quantum dot using excited-state
spectroscopy in a strong magnetic field. The field is oriented in the plane of
the two-dimensional electron gas in which the dot is electrostatically defined.
By combining the observation of Zeeman splitting with our knowledge of the
absolute number of electrons, we are able to determine the ground state spin
configuration for one to five electrons occupying the dot. For four electrons,
we find a ground state spin configuration with total spin S=1, in agreement
with Hund's first rule. The electron g-factor is observed to be independent of
magnetic field and electron number.Comment: 11 pages, 7 figures, submitted to New Journal of Physics, focus issue
on Solid State Quantum Informatio
Zero Temperature Phase Transition in Spin-ladders: Phase Diagram and Dynamical studies of Cu(Hp)Cl
In a magnetic field, spin-ladders undergo two zero-temperature phase
transitions at the critical fields Hc1 and Hc2. An experimental review of
static and dynamical properties of spin-ladders close to these critical points
is presented. The scaling functions, universal to all quantum critical points
in one-dimension, are extracted from (a) the thermodynamic quantities
(magnetization) and (b) the dynamical functions (NMR relaxation). A simple
mapping of strongly coupled spin ladders in a magnetic field on the exactly
solvable XXZ model enables to make detailed fits and gives an overall
understanding of a broad class of quantum magnets in their gapless phase
(between Hc1 and Hc2). In this phase, the low temperature divergence of the NMR
relaxation demonstrates its Luttinger liquid nature as well as the novel
quantum critical regime at higher temperature. The general behaviour close
these quantum critical points can be tied to known models of quantum magnetism.Comment: few corrections made, 15 pages, to be published in European Journal
of Physics
SUBCOOLED-BLOWDOWN FORCES ON REACTOR-SYSTEM COMPONENTS: CALCULATIONAL METHOD AND EXPERIMENTAL CONFIRMATION.
Geometry of Discrete Quantum Computing
Conventional quantum computing entails a geometry based on the description of
an n-qubit state using 2^{n} infinite precision complex numbers denoting a
vector in a Hilbert space. Such numbers are in general uncomputable using any
real-world resources, and, if we have the idea of physical law as some kind of
computational algorithm of the universe, we would be compelled to alter our
descriptions of physics to be consistent with computable numbers. Our purpose
here is to examine the geometric implications of using finite fields Fp and
finite complexified fields Fp^2 (based on primes p congruent to 3 mod{4}) as
the basis for computations in a theory of discrete quantum computing, which
would therefore become a computable theory. Because the states of a discrete
n-qubit system are in principle enumerable, we are able to determine the
proportions of entangled and unentangled states. In particular, we extend the
Hopf fibration that defines the irreducible state space of conventional
continuous n-qubit theories (which is the complex projective space CP{2^{n}-1})
to an analogous discrete geometry in which the Hopf circle for any n is found
to be a discrete set of p+1 points. The tally of unit-length n-qubit states is
given, and reduced via the generalized Hopf fibration to DCP{2^{n}-1}, the
discrete analog of the complex projective space, which has p^{2^{n}-1}
(p-1)\prod_{k=1}^{n-1} (p^{2^{k}}+1) irreducible states. Using a measure of
entanglement, the purity, we explore the entanglement features of discrete
quantum states and find that the n-qubit states based on the complexified field
Fp^2 have p^{n} (p-1)^{n} unentangled states (the product of the tally for a
single qubit) with purity 1, and they have p^{n+1}(p-1)(p+1)^{n-1} maximally
entangled states with purity zero.Comment: 24 page
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