1,077 research outputs found
Metastates in mean-field models with random external fields generated by Markov chains
We extend the construction by Kuelske and Iacobelli of metastates in
finite-state mean-field models in independent disorder to situations where the
local disorder terms are are a sample of an external ergodic Markov chain in
equilibrium. We show that for non-degenerate Markov chains, the structure of
the theorems is analogous to the case of i.i.d. variables when the limiting
weights in the metastate are expressed with the aid of a CLT for the occupation
time measure of the chain. As a new phenomenon we also show in a Potts example
that, for a degenerate non-reversible chain this CLT approximation is not
enough and the metastate can have less symmetry than the symmetry of the
interaction and a Gaussian approximation of disorder fluctuations would
suggest.Comment: 20 pages, 2 figure
An ultrametric state space with a dense discrete overlap distribution: Paperfolding sequences
We compute the Parisi overlap distribution for paperfolding sequences. It
turns out to be discrete, and to live on the dyadic rationals. Hence it is a
pure point measure whose support is the full interval [-1; +1]. The space of
paperfolding sequences has an ultrametric structure. Our example provides an
illustration of some properties which were suggested to occur for pure states
in spin glass models
Unified N=2 Maxwell-Einstein and Yang-Mills-Einstein Supergravity Theories in Four Dimensions
We study unified N=2 Maxwell-Einstein supergravity theories (MESGTs) and
unified Yang-Mills Einstein supergravity theories (YMESGTs) in four dimensions.
As their defining property, these theories admit the action of a global or
local symmetry group that is (i) simple, and (ii) acts irreducibly on all the
vector fields of the theory, including the ``graviphoton''. Restricting
ourselves to the theories that originate from five dimensions via dimensional
reduction, we find that the generic Jordan family of MESGTs with the scalar
manifolds [SU(1,1)/U(1)] X [SO(2,n)/SO(2)X SO(n)] are all unified in four
dimensions with the unifying global symmetry group SO(2,n). Of these theories
only one can be gauged so as to obtain a unified YMESGT with the gauge group
SO(2,1). Three of the four magical supergravity theories defined by simple
Euclidean Jordan algebras of degree 3 are unified MESGTs in four dimensions.
Two of these can furthermore be gauged so as to obtain 4D unified YMESGTs with
gauge groups SO(3,2) and SO(6,2), respectively. The generic non-Jordan family
and the theories whose scalar manifolds are homogeneous but not symmetric do
not lead to unified MESGTs in four dimensions. The three infinite families of
unified five-dimensional MESGTs defined by simple Lorentzian Jordan algebras,
whose scalar manifolds are non-homogeneous, do not lead directly to unified
MESGTs in four dimensions under dimensional reduction. However, since their
manifolds are non-homogeneous we are not able to completely rule out the
existence of symplectic sections in which these theories become unified in four
dimensions.Comment: 47 pages; latex fil
The Photon Sector in the Quantum Myers-Pospelov Model: An improved description
The quantization of the electromagnetic sector of the Myers-Pospelov model
coupled to standard fermions is studied. Our main objective is to construct an
effective quantum theory that results in a genuine perturbation of QED, such
that setting zero the Lorentz invariance violation (LIV) parameters will
reproduce it. This is achieved by introducing an additional low energy scale
, together with a physically motivated prescription to take the QED limit.
The prescription is successfully tested in the calculation of the electron
self-energy in the one loop approximation. The LIV radiative corrections turn
out to be properly scaled by very small factors for any reasonable values of
the parameters, no fine-tuning problems are found at this stage and the choice
for to be of the order of the electroweak symmetry breaking scale is
consistent with the stringent bounds for the LIV parameters, in particular with
those arising from induced dimension three operators.Comment: 11 pages, no figures, shortened version, new interpretation of the
scale M, additional references added, accepted for publication in Phys. Lett.
The General Solution of Bianchi Type Vacuum Cosmology
The theory of symmetries of systems of coupled, ordinary differential
equations (ODE) is used to develop a concise algorithm in order to obtain the
entire space of solutions to vacuum Bianchi Einstein Field Equations (EFEs).
The symmetries used are the well known automorphisms of the Lie algebra for the
corresponding isometry group of each Bianchi Type, as well as the scaling and
the time re-parametrization symmetry. The application of the method to Type
VII_h results in (a) obtaining the general solution of Type VII_0 with the aid
of the third Painlev\'{e} transcendental (b) obtaining the general solution of
Type with the aid of the sixth Painlev\'{e} transcendental (c) the
recovery of all known solutions (six in total) without a prior assumption of
any extra symmetry (d) The discovery of a new solution (the line element given
in closed form) with a G_3 isometry group acting on T_3, i.e. on time-like
hyper-surfaces, along with the emergence of the line element describing the
flat vacuum Type VII_0 Bianchi Cosmology.Comment: latex2e source file, 27 pages, 2 tables, no fiure
Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields
In this article we study the phase transition phenomenon for the Ising model
under the action of a non-uniform external magnetic field. We show that the
Ising model on the hypercubic lattice with a summable magnetic field has a
first-order phase transition and, for any positive (resp. negative) and bounded
magnetic field, the model does not present the phase transition phenomenon
whenever , where is the external
magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201
Resummation of Nonalternating Divergent Perturbative Expansions
A method for the resummation of nonalternating divergent perturbation series
is described. The procedure constitutes a generalization of the Borel-Pad\'{e}
method. Of crucial importance is a special integration contour in the complex
plane. Nonperturbative imaginary contributions can be inferred from the purely
real perturbative coefficients. A connection is drawn from the quantum field
theoretic problem of resummation to divergent perturbative expansions in other
areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman
criterion added; version to appear in Phys. Rev.
Electroweak Supersymmetry around the Electroweak Scale
Inspired by the phenomenological constraints, LHC supersymmetry and Higgs
searches, dark matter search as well as string model building, we propose the
electroweak supersymmetry around the electroweak scale: the squarks and/or
gluinos are around a few TeV while the sleptons, sneutrinos, bino and winos are
within one TeV. The Higgsinos can be either heavy or light. We consider bino as
the dominant component of dark matter candidate, and the observed dark matter
relic density is achieved via the neutralino-stau coannihilations. Considering
the Generalized Minimal Supergravity (GmSUGRA), we show explicitly that the
electroweak supersymmetry can be realized, and the gauge coupling unification
can be preserved. With two Scenarios, we study the viable parameter spaces that
satisfy all the current phenomenological constraints, and we present the
concrete benchmark points. Furthermore, we comment on the fine-tuning problem
and LHC searches.Comment: RevTex4, 28 pages, 8 figures, 8 tables, version to appear in EPJ
Impact of disease, cognitive and behavioural factors on caregiver outcome in amyotrophic lateral sclerosis
Up to 50% of patients with amyotrophic lateral sclerosis (ALS) show mild to moderate cognitive-behavioural change alongside their progressive functional impairment. This study examines the relative impact of patients' disease symptoms, behavioural change and current executive function and social cognition abilities on psychosocial outcomes in spouse caregivers of people with ALS. Thirty-five spouse caregivers rated their own levels of depression and anxiety, subjective burden and marital satisfaction. Caregivers also rated their partner's everyday behaviour. The patients were assessed for disease severity and cognitive function, with composite scores derived for executive function and social cognition. Regression analyses revealed that caregiver burden was predicted by the severity of patients' limb involvement and behavioural problems. Depression was predicted by patients' limb involvement, while behavioural problems and patient age predicted caregiver anxiety. Current marital satisfaction was predicted by patient behavioural problems beyond the level of pre-illness marital satisfaction. In conclusion, the study highlights the potential impact of ALS patients' functional impairment and behavioural change on ALS caregivers' psychosocial functioning. Clinical communication with ALS families should emphasise both physical and psychological challenges presented by the disease
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