112 research outputs found
Classical frustration and quantum disorder in spin-orbital models
The most elementary of all physical spin-orbital models is the Kugel-Khomskii
model describing a S=1/2, degenerate Mott-insulator. Recent theoretical
work is reviewed revealing that the classical limit is characterized by a point
of perfect dynamical frustration. It is suggested that this might give rise to
a quantum disordered ground state.Comment: 7 pages Revtex, 3 ps figures, proceedings 1998 NEC symposium, Nasu,
Japa
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
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
Interlayer Magnetic Frustration in Quasi-stoichiometric Li1-xNi1+xO2
Susceptibility, high-field magnetization and submillimeter wave electron spin
resonance measurements of layered quasi-stoichiometric Li1-xNi1+xO2 are
reported and compared to isomorphic NaNiO2. A new mechanism of magnetic
frustration induced by the excess Ni ions always present in the Li layers is
proposed. We finally comment on the possible realization of an orbital liquid
state in this controversial compound.Comment: 4 pages, 5 figures, submitted to Phys.Rev.B, Rapid Com
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
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Effect of rehabilitation worker input on visual function outcomes in individuals with low vision: study protocol for a randomised controlled trial
BACKGROUND: Visual Rehabilitation Officers help people with a visual impairment maintain their independence. This intervention adopts a flexible, goal-centred approach, which may include training in mobility, use of optical and non-optical aids, and performance of activities of daily living. Although Visual Rehabilitation Officers are an integral part of the low vision service in the United Kingdom, evidence that they are effective is lacking. The purpose of this exploratory trial is to estimate the impact of a Visual Rehabilitation Officer on self-reported visual function, psychosocial and quality-of-life outcomes in individuals with low vision.
METHODS/DESIGN: In this exploratory, assessor-masked, parallel group, randomised controlled trial, participants will be allocated either to receive home visits from a Visual Rehabilitation Officer (nâ=â30) or to a waiting list control group (nâ=â30) in a 1:1 ratio. Adult volunteers with a visual impairment, who have been identified as needing rehabilitation officer input by a social worker, will take part. Those with an urgent need for a Visual Rehabilitation Officer or who have a cognitive impairment will be excluded. The primary outcome measure will be self-reported visual function (48-item Veterans Affairs Low Vision Visual Functioning Questionnaire). Secondary outcome measures will include psychological and quality-of-life metrics: the Patient Health Questionnaire (PHQ-9), the Warwick-Edinburgh Mental Well-being Scale (WEMWBS), the Adjustment to Age-related Visual Loss Scale (AVL-12), the Standardised Health-related Quality of Life Questionnaire (EQ-5D) and the UCLA Loneliness Scale. The interviewer collecting the outcomes will be masked to the group allocations. The analysis will be undertaken on a complete case and intention-to-treat basis. Analysis of covariance (ANCOVA) will be applied to follow-up questionnaire scores, with the baseline score as a covariate.
DISCUSSION: This trial is expected to provide robust effect size estimates of the intervention effect. The data will be used to design a large-scale randomised controlled trial to evaluate fully the Visual Rehabilitation Officer intervention. A rigorous evaluation of Rehabilitation Officer input is vital to direct a future low vision rehabilitation strategy and to help direct government resources.
TRIAL REGISTRATION: The trial was registered with ( ISRCTN44807874 ) on 9 March 2015
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
Magnetic, orbital and charge ordering in the electron-doped manganites
The three dimensional perovskite manganites in the range of hole-doping are studied in detail using a double exchange model with degenerate
orbitals including intra- and inter-orbital correlations and near-neighbour
Coulomb repulsion. We show that such a model captures the observed phase
diagram and orbital-ordering in the intermediate to large band-width regime. It
is argued that the Jahn-Teller effect, considered to be crucial for the region
, does not play a major role in this region, particularly for systems
with moderate to large band-width. The anisotropic hopping across the
degenerate orbitals are crucial in understanding the ground state phases
of this region, an observation emphasized earlier by Brink and Khomskii. Based
on calculations using a realistic limit of finite Hund's coupling, we show that
the inclusion of interactions stabilizes th e C-phase, the antiferromagnetic
metallic A-phase moves closer to while th e ferromagnetic phase shrinks
in agreement with recent observations. The charge ordering close to and
the effect of reduction of band-width are also outlined. The effect of disorder
and the possibility of inhomogeneous mixture of competing states have been
discussed.Comment: 42 pages, 16 figure
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