146 research outputs found
Order parameters in the Verwey phase transition
The Verwey phase transition in magnetite is analyzed on the basis of the
Landau theory. The free energy functional is expanded in a series of components
belonging to the primary and secondary order parameters. A low-temperature
phase with the monoclinic P2/c symmetry is a result of condensation of two
order parameters X_3 and \Delta_5 . The temperature dependence of the shear
elastic constant C_44 is derived and the mechanism of its softening is
discussed.Comment: 4 pages, 1 figur
How strongly are electrons correlated in the high-tc superconducting materials
Wetensch. publicatieFaculteit der Wiskunde en Natuurwetenschappe
Lamp-pumped laser performance of Nd3+:Sr-5(PO4)(3)F operating both separately and simultaneously at 1.059 and 1.328 mu m
Lamp-pumped laser performance of Nd3+-doped strontium fluorapatite, Sr-5(PO4)(3)F or S-FAP, has been characterized and compared with that of Nd3+-doped yttrium aluminum garnet (YAG) at both 1.06 and 1.3 mu m. Nd3+:S-FAP was found to exhibit lower thresholds and lower slope efficiencies than Nd3+:YAG. The former is attributed to the higher emission cross section, and the latter to lower Nd3+ concentration in S-FAP. The 1.3 mu m lasing of Nd3+:S-FAP is of particular interest because of its high emission cross section (2.4X10(-19) cm(2)). Q-switched and dual-wavelength lasing operation were also demonstrated in Nd3+:S-FAP
Random tree growth by vertex splitting
We study a model of growing planar tree graphs where in each time step we
separate the tree into two components by splitting a vertex and then connect
the two pieces by inserting a new link between the daughter vertices. This
model generalises the preferential attachment model and Ford's -model
for phylogenetic trees. We develop a mean field theory for the vertex degree
distribution, prove that the mean field theory is exact in some special cases
and check that it agrees with numerical simulations in general. We calculate
various correlation functions and show that the intrinsic Hausdorff dimension
can vary from one to infinity, depending on the parameters of the model.Comment: 47 page
Regularly alternating spin-1/2 anisotropic XY chains: The ground-state and thermodynamic properties
Using the Jordan-Wigner transformation and continued fractions we calculate
rigorously the thermodynamic quantities for the spin-1/2 transverse Ising chain
with periodically varying intersite interactions and/or on-site fields. We
consider in detail the properties of the chains having a period of the
transverse field modulation equal to 3. The regularly alternating transverse
Ising chain exhibits several quantum phase transition points, where the number
of transition points for a given period of alternation strongly depends on the
specific set of the Hamiltonian parameters. The critical behavior in most cases
is the same as for the uniform chain. However, for certain sets of the
Hamiltonian parameters the critical behavior may be changed and weak
singularities in the ground-state quantities appear. Due to the regular
alternation of the Hamiltonian parameters the transverse Ising chain may
exhibit plateau-like steps in the zero-temperature dependence of the transverse
magnetization vs. transverse field and many-peak temperature profiles of the
specific heat. We compare the ground-state properties of regularly alternating
transverse Ising and transverse XX chains and of regularly alternating quantum
and classical chains.
Making use of the corresponding unitary transformations we extend the
elaborated approach to the study of thermodynamics of regularly alternating
spin-1/2 anisotropic XY chains without field. We use the exact expression for
the ground-state energy of such a chain of period 2 to discuss how the exchange
interaction anisotropy destroys the spin-Peierls dimerized phase
The Sheaf-Theoretic Structure Of Non-Locality and Contextuality
We use the mathematical language of sheaf theory to give a unified treatment
of non-locality and contextuality, in a setting which generalizes the familiar
probability tables used in non-locality theory to arbitrary measurement covers;
this includes Kochen-Specker configurations and more. We show that
contextuality, and non-locality as a special case, correspond exactly to
obstructions to the existence of global sections. We describe a linear
algebraic approach to computing these obstructions, which allows a systematic
treatment of arguments for non-locality and contextuality. We distinguish a
proper hierarchy of strengths of no-go theorems, and show that three leading
examples --- due to Bell, Hardy, and Greenberger, Horne and Zeilinger,
respectively --- occupy successively higher levels of this hierarchy. A general
correspondence is shown between the existence of local hidden-variable
realizations using negative probabilities, and no-signalling; this is based on
a result showing that the linear subspaces generated by the non-contextual and
no-signalling models, over an arbitrary measurement cover, coincide. Maximal
non-locality is generalized to maximal contextuality, and characterized in
purely qualitative terms, as the non-existence of global sections in the
support. A general setting is developed for Kochen-Specker type results, as
generic, model-independent proofs of maximal contextuality, and a new
combinatorial condition is given, which generalizes the `parity proofs'
commonly found in the literature. We also show how our abstract setting can be
represented in quantum mechanics. This leads to a strengthening of the usual
no-signalling theorem, which shows that quantum mechanics obeys no-signalling
for arbitrary families of commuting observables, not just those represented on
different factors of a tensor product.Comment: 33 pages. Extensively revised, new results included. Published in New
Journal of Physic
Semantics for probabilistic programming: higher-order functions, continuous distributions, and soft constraints
We study the semantic foundation of expressive probabilistic programming languages, that support higher-order functions, continuous distributions, and soft constraints (such as Anglican, Church, and Venture). We define a metalanguage (an idealised version of Anglican) for probabilistic computation with the above features, develop both operational and denotational semantics, and prove soundness, adequacy, and termination. They involve measure theory, stochastic labelled transition systems, and functor categories, but admit intuitive computational readings, one of which views sampled random variables as dynamically allocated read-only variables. We apply our semantics to validate nontrivial equations underlying the correctness of certain compiler optimisations and inference algorithms such as sequential Monte Carlo simulation. The language enables defining probability distributions on higher-order functions, and we study their properties
Equivalence and noninferiority trials – are they viable alternatives for registration of new drugs? (III)
The scientific community's reliance on active-controlled trials is steadily increasing, as widespread agreement emerges concerning the role of these trials as viable alternatives to placebo trials. These trials present substantial challenges with regard to design and interpretation as their complexity increases, and the potential need for larger sample sizes impacts the cost and time variables of the drug development process. The potential efficacy and safety benefits derived from these trials may never be demonstrated by other methods. Active-controlled trials can develop valuable data to inform both prescribers and patients about the dose- and time-dependent actions of any new drug and can contribute to the management and communication of risks associated with the relevant therapeutic products
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