55 research outputs found
Infinite loop superalgebras of the Dirac theory on the Euclidean Taub-NUT space
The Dirac theory in the Euclidean Taub-NUT space gives rise to a large
collection of conserved operators associated to genuine or hidden symmetries.
They are involved in interesting algebraic structures as dynamical algebras or
even infinite-dimensional algebras or superalgebras. One presents here the
infinite-dimensional superalgebra specific to the Dirac theory in manifolds
carrying the Gross-Perry-Sorkin monopole. It is shown that there exists an
infinite-dimensional superalgebra that can be seen as a twisted loop
superalgebra.Comment: 16 pages, LaTeX, references adde
Contraction of broken symmetries via Kac-Moody formalism
I investigate contractions via Kac-Moody formalism. In particular, I show how
the symmetry algebra of the standard 2-D Kepler system, which was identified by
Daboul and Slodowy as an infinite-dimensional Kac-Moody loop algebra, and was
denoted by , gets reduced by the symmetry breaking term,
defined by the Hamiltonian For this I
define two symmetry loop algebras , by
choosing the `basic generators' differently. These
can be mapped isomorphically onto subalgebras of , of
codimension 2 or 3, revealing the reduction of symmetry. Both factor algebras
, relative to the corresponding
energy-dependent ideals , are isomorphic to
and for , respectively, just as for the
pure Kepler case. However, they yield two different non-standard contractions
as , namely to the Heisenberg-Weyl algebra or to an abelian Lie algebra, instead of the Euclidean algebra
for the pure Kepler case. The above example suggests a
general procedure for defining generalized contractions, and also illustrates
the {\em `deformation contraction hysteresis'}, where contraction which involve
two contraction parameters can yield different contracted algebras, if the
limits are carried out in different order.Comment: 21 pages, 1 figur
Exact, E=0, Solutions for General Power-Law Potentials. I. Classical Orbits
For zero energy, , we derive exact, classical solutions for {\em all}
power-law potentials, , with and . When the angular momentum is non-zero, these solutions lead to
the orbits , for all . When , the orbits are bound and go through the origin.
This leads to discrete discontinuities in the functional dependence of
and , as functions of , as the orbits pass through the origin. We
describe a procedure to connect different analytic solutions for successive
orbits at the origin. We calculate the periods and precessions of these bound
orbits, and graph a number of specific examples. Also, we explain why they all
must violate the virial theorem. The unbound orbits are also discussed in
detail. This includes the unusual orbits which have finite travel times to
infinity and also the special case.Comment: LaTeX, 27 pages with 12 figures available from the authors or can be
generated from Mathematica instructions at end of the fil
Test of Universality in the Ising Spin Glass Using High Temperature Graph Expansion
We calculate high-temperature graph expansions for the Ising spin glass model
with 4 symmetric random distribution functions for its nearest neighbor
interaction constants J_{ij}. Series for the Edwards-Anderson susceptibility
\chi_EA are obtained to order 13 in the expansion variable (J/(k_B T))^2 for
the general d-dimensional hyper-cubic lattice, where the parameter J determines
the width of the distributions. We explain in detail how the expansions are
calculated. The analysis, using the Dlog-Pad\'e approximation and the
techniques known as M1 and M2, leads to estimates for the critical threshold
(J/(k_B T_c))^2 and for the critical exponent \gamma in dimensions 4, 5, 7 and
8 for all the distribution functions. In each dimension the values for \gamma
agree, within their uncertainty margins, with a common value for the different
distributions, thus confirming universality.Comment: 13 figure
Hidden symmetries and Killing tensors on curved spaces
Higher order symmetries corresponding to Killing tensors are investigated.
The intimate relation between Killing-Yano tensors and non-standard
supersymmetries is pointed out. In the Dirac theory on curved spaces,
Killing-Yano tensors generate Dirac type operators involved in interesting
algebraic structures as dynamical algebras or even infinite dimensional
algebras or superalgebras. The general results are applied to space-times which
appear in modern studies. One presents the infinite dimensional superalgebra of
Dirac type operators on the 4-dimensional Euclidean Taub-NUT space that can be
seen as a twisted loop algebra. The existence of the conformal Killing-Yano
tensors is investigated for some spaces with mixed Sasakian structures.Comment: 12 pages; talk presented at Group 27 Colloquium, Yerevan, Armenia,
August 200
Quantum gates on hybrid qudits
We introduce quantum hybrid gates that act on qudits of different dimensions.
In particular, we develop two representative two-qudit hybrid gates (SUM and
SWAP) and many-qudit hybrid Toffoli and Fredkin gates. We apply the hybrid SUM
gate to generating entanglement, and find that operator entanglement of the SUM
gate is equal to the entanglement generated by it for certain initial states.
We also show that the hybrid SUM gate acts as an automorphism on the Pauli
group for two qudits of different dimension under certain conditions. Finally,
we describe a physical realization of these hybrid gates for spin systems.Comment: 8 pages and 1 figur
L2 series solutions of the Dirac equation for power-law potentials at rest mass energy
We obtain solutions of the three dimensional Dirac equation for radial
power-law potentials at rest mass energy as an infinite series of square
integrable functions. These are written in terms of the confluent
hypergeometric function and chosen such that the matrix representation of the
Dirac operator is tridiagonal. The "wave equation" results in a three-term
recursion relation for the expansion coefficients of the spinor wavefunction
which is solved in terms of orthogonal polynomials. These are modified versions
of the Meixner-Pollaczek polynomials and of the continuous dual Hahn
polynomials. The choice depends on the values of the angular momentum and the
power of the potential.Comment: 13 pages, 1 Tabl
Perturbation theory for quantum-mechanical observables
The quantum-mechanical state vector is not directly observable even though it
is the fundamental variable that appears in Schrodinger's equation. In
conventional time-dependent perturbation theory, the state vector must be
calculated before the experimentally-observable expectation values of relevant
operators can be computed. We discuss an alternative form of time-dependent
perturbation theory in which the observable expectation values are calculated
directly and expressed in the form of nested commutators. This result is
consistent with the fact that the commutation relations determine the
properties of a quantum system, while the commutators often have a form that
simplifies the calculation and avoids canceling terms. The usefulness of this
method is illustrated using several problems of interest in quantum optics and
quantum information processing.Comment: Submitted to Phys. Rev. A. 17 pages, 4 figures. Minor change
Extent of liver inflammation in predicting response to interferon α & Ribavirin in chronic hepatitis C patients: a cohort study
Effect of SGLT2 inhibitors on stroke and atrial fibrillation in diabetic kidney disease: Results from the CREDENCE trial and meta-analysis
BACKGROUND AND PURPOSE: Chronic kidney disease with reduced estimated glomerular filtration rate or elevated albuminuria increases risk for ischemic and hemorrhagic stroke. This study assessed the effects of sodium glucose cotransporter 2 inhibitors (SGLT2i) on stroke and atrial fibrillation/flutter (AF/AFL) from CREDENCE (Canagliflozin and Renal Events in Diabetes With Established Nephropathy Clinical Evaluation) and a meta-Analysis of large cardiovascular outcome trials (CVOTs) of SGLT2i in type 2 diabetes mellitus. METHODS: CREDENCE randomized 4401 participants with type 2 diabetes mellitus and chronic kidney disease to canagliflozin or placebo. Post hoc, we estimated effects on fatal or nonfatal stroke, stroke subtypes, and intermediate markers of stroke risk including AF/AFL. Stroke and AF/AFL data from 3 other completed large CVOTs and CREDENCE were pooled using random-effects meta-Analysis. RESULTS: In CREDENCE, 142 participants experienced a stroke during follow-up (10.9/1000 patient-years with canagliflozin, 14.2/1000 patient-years with placebo; hazard ratio [HR], 0.77 [95% CI, 0.55-1.08]). Effects by stroke subtypes were: ischemic (HR, 0.88 [95% CI, 0.61-1.28]; n=111), hemorrhagic (HR, 0.50 [95% CI, 0.19-1.32]; n=18), and undetermined (HR, 0.54 [95% CI, 0.20-1.46]; n=17). There was no clear effect on AF/AFL (HR, 0.76 [95% CI, 0.53-1.10]; n=115). The overall effects in the 4 CVOTs combined were: Total stroke (HRpooled, 0.96 [95% CI, 0.82-1.12]), ischemic stroke (HRpooled, 1.01 [95% CI, 0.89-1.14]), hemorrhagic stroke (HRpooled, 0.50 [95% CI, 0.30-0.83]), undetermined stroke (HRpooled, 0.86 [95% CI, 0.49-1.51]), and AF/AFL (HRpooled, 0.81 [95% CI, 0.71-0.93]). There was evidence that SGLT2i effects on total stroke varied by baseline estimated glomerular filtration rate (P=0.01), with protection in the lowest estimated glomerular filtration rate (45 mL/min/1.73 m2]) subgroup (HRpooled, 0.50 [95% CI, 0.31-0.79]). CONCLUSIONS: Although we found no clear effect of SGLT2i on total stroke in CREDENCE or across trials combined, there was some evidence of benefit in preventing hemorrhagic stroke and AF/AFL, as well as total stroke for those with lowest estimated glomerular filtration rate. Future research should focus on confirming these data and exploring potential mechanisms
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