1,161 research outputs found
Cliffordons
At higher energies the present complex quantum theory with its unitary group
might expand into a real quantum theory with an orthogonal group, broken by an
approximate operator at lower energies. Implementing this possibility
requires a real quantum double-valued statistics. A Clifford statistics,
representing a swap (12) by a difference of Clifford units,
is uniquely appropriate. Unlike the Maxwell-Boltzmann, Fermi-Dirac,
Bose-Einstein, and para- statistics, which are tensorial and single-valued, and
unlike anyons, which are confined to two dimensions, Clifford statistics are
multivalued and work for any dimensionality. Nayak and Wilczek proposed a
Clifford statistics for the fractional quantum Hall effect. We apply them to
toy quanta here. A complex-Clifford example has the energy spectrum of a system
of spin-1/2 particles in an external magnetic field. This supports the proposal
that the double-valued rotations --- spin --- seen at current energies might
arise from double-valued permutations --- swap --- to be seen at higher
energies. Another toy with real Clifford statistics illustrates how an
effective imaginary unit can arise naturally within a real quantum theory.Comment: 15 pages, no figures; original title ("Clifford statistics") changed;
to appear in J. Math. Phys., 42, 2001. Key words: Clifford statistics,
cliffordons, double-valued representations of permutation groups, spin, swap,
imaginary unit , applications to quantum space-time and the Standard
Model. Some of these results were presented at the American Physical Society
Centennial Meeting, Atlanta, March 25, 199
The relationship between parental education and children's schooling in a time of economic turmoil: The case of East Zimbabwe, 2001 to 2011.
Using data collected from 1998 to 2011 in a general population cohort study in eastern Zimbabwe, we describe education trends and the relationship between parental education and children's schooling during the Zimbabwean economic collapse of the 2000s. During this period, the previously-rising trend in education stalled, with girls suffering disproportionately; however, female enrolment increased as the economy began to recover. Throughout the period, children with more educated parents continued to have better outcomes such that, at the population level, an underlying increase in the proportion of children with more educated parents may have helped to maintain the upwards education trend
Decomposition of fractional quantum Hall states: New symmetries and approximations
We provide a detailed description of a new symmetry structure of the monomial
(Slater) expansion coefficients of bosonic (fermionic) fractional quantum Hall
states first obtained in Ref. 1, which we now extend to spin-singlet states. We
show that the Haldane-Rezayi spin-singlet state can be obtained without exact
diagonalization through a differential equation method that we conjecture to be
generic to other FQH model states. The symmetry rules in Ref. 1 as well as the
ones we obtain for the spin singlet states allow us to build approximations of
FQH states that exhibit increasing overlap with the exact state (as a function
of system size). We show that these overlaps reach unity in the thermodynamic
limit even though our approximation omits more than half of the Hilbert space.
We show that the product rule is valid for any FQH state which can be written
as an expectation value of parafermionic operators.Comment: 22 pages, 8 figure
A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schr\"odinger Model
We study certain non-symmetric wavefunctions associated to the quantum
nonlinear Schr\"odinger model, introduced by Komori and Hikami using Gutkin's
propagation operator, which involves representations of the degenerate affine
Hecke algebra. We highlight how these functions can be generated using a
vertex-type operator formalism similar to the recursion defining the symmetric
(Bethe) wavefunction in the quantum inverse scattering method. Furthermore,
some of the commutation relations encoded in the Yang-Baxter equation for the
relevant monodromy matrix are generalized to the non-symmetric case.Comment: 31 pages; added some references; minor corrections throughou
Synchronization of chaotic networks with time-delayed couplings: An analytic study
Networks of nonlinear units with time-delayed couplings can synchronize to a
common chaotic trajectory. Although the delay time may be very large, the units
can synchronize completely without time shift. For networks of coupled
Bernoulli maps, analytic results are derived for the stability of the chaotic
synchronization manifold. For a single delay time, chaos synchronization is
related to the spectral gap of the coupling matrix. For networks with multiple
delay times, analytic results are obtained from the theory of polynomials.
Finally, the analytic results are compared with networks of iterated tent maps
and Lang-Kobayashi equations which imitate the behaviour of networks of
semiconductor lasers
Zassenhaus conjecture for central extensions of S5
We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in
integral group rings for a covering group of the symmetric group S5 and for the general linear
group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy
question for units of prime-power order in the integral group ring of a finite Frobenius group
Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis
We combine a limited number of accurately measured transition frequencies in
hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and,
as an essential additional ingredient, a generalized least-squares analysis, to
obtain precise and optimal predictions for hydrogen and deuterium transition
frequencies. Some of the predicted transition frequencies have relative
uncertainties more than an order of magnitude smaller than that of the g-factor
of the electron, which was previously the most accurate prediction of QED.Comment: 4 pages, RevTe
Characterizing Operations Preserving Separability Measures via Linear Preserver Problems
We use classical results from the theory of linear preserver problems to
characterize operators that send the set of pure states with Schmidt rank no
greater than k back into itself, extending known results characterizing
operators that send separable pure states to separable pure states. We also
provide a new proof of an analogous statement in the multipartite setting. We
use these results to develop a bipartite version of a classical result about
the structure of maps that preserve rank-1 operators and then characterize the
isometries for two families of norms that have recently been studied in quantum
information theory. We see in particular that for k at least 2 the operator
norms induced by states with Schmidt rank k are invariant only under local
unitaries, the swap operator and the transpose map. However, in the k = 1 case
there is an additional isometry: the partial transpose map.Comment: 16 pages, typos corrected, references added, proof of Theorem 4.3
simplified and clarifie
Spatial patterns of HIV prevalence and Service Use in East Zimbabwe: implications for future targeting of interventions
Introduction: Focusing resources for HIV control on geographic areas of greatest need in countries with generalised epidemics has been recommended to increase cost-effectiveness. However, socio-economic inequalities between areas of high and low prevalence could raise equity concerns and have been largely overlooked. We describe spatial patterns in HIV prevalence in east Zimbabwe and test for inequalities in accessibility and uptake of HIV services prior to the introduction of spatially-targeted programmes. Methods: 8092 participants in an open-cohort study were geo-located to 110 locations. HIV prevalence and HIV testing and counselling (HTC) uptake were mapped with ordinary kriging. Clusters of high or low HIV prevalence were detected with Kulldorff statistics, and the socio-economic characteristics and sexual risk behaviours of their populations, and levels of local HIV service availability (measured in travel distance) and uptake were compared. Kulldorff statistics were also determined for HTC, antiretroviral therapy (ART), and voluntary medical male circumcision (VMMC) uptake. Results: One large and one small high HIV prevalence cluster (relative risk [RR]=1.78, 95% confidence interval [CI]=1.53–2.07; RR=2.50, 95% CI=2.08–3.01) and one low-prevalence cluster (RR=0.70, 95% CI=0.60–0.82) were detected. The larger high-prevalence cluster was urban with a wealthier population and more high-risk sexual behaviour than outside the cluster. Despite better access to HIV services, there was lower HTC uptake in the high-prevalence cluster (odds ratio [OR] of HTC in past 3 years: OR=0.80, 95% CI=0.66–0.97). The low-prevalence cluster was predominantly rural with a poorer population and longer travel distances to HIV services; however, uptake of HIV services was not reduced. Conclusions: High-prevalence clusters can be identified to which HIV control resources could be targeted. To date, poorer access to HIV services in the poorer low-prevalence areas has not resulted in lower service uptake, while there is significantly lower uptake of HTC in the high-prevalence cluster where health service access is better. Given the high levels of risky sexual behaviour and lower uptake of HTC services, targeting high-prevalence clusters may be cost-effective in this setting. If spatial targeting is introduced, inequalities in HIV service uptake may be avoided through mobile service provision for lower prevalence areas
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