189 research outputs found
Semirelativistic Hamiltonians and the auxiliary field method
Approximate analytical closed energy formulas for semirelativistic
Hamiltonians of the form are obtained within
the framework of the auxiliary field method. This method, which is equivalent
to the envelope theory, has been recently proposed as a powerful tool to get
approximate analytical solutions of the Schr\"odinger equation. Various shapes
for the potential are investigated: power-law, funnel, square root, and
Yukawa. A comparison with the exact results is discussed in detail
Extensions of the auxiliary field method to solve Schr\"{o}dinger equations
It has recently been shown that the auxiliary field method is an interesting
tool to compute approximate analytical solutions of the Schr\"{o}dinger
equation. This technique can generate the spectrum associated with an arbitrary
potential starting from the analytically known spectrum of a particular
potential . In the present work, general important properties of the
auxiliary field method are proved, such as scaling laws and independence of the
results on the choice of . The method is extended in order to find
accurate analytical energy formulae for radial potentials of the form , and several explicit examples are studied. Connections existing
between the perturbation theory and the auxiliary field method are also
discussed
Short-range potentials from QCD at order
We systematically compute the effective short-range potentials arising from
second order QCD-diagrams related to bound states of quarks, antiquarks, and
gluons. Our formalism relies on the assumption that the exchanged gluons are
massless, while the constituent gluons as well as the lightest quarks acquire a
nonvanishing constituent mass because of confinement. The potentials we obtain
include the first relativistic corrections, thus spin-spin terms, spin-orbit
terms, etc. Such effective potentials are expected to be relevant for the
building of accurate potential models describing usual hadrons as well as
exotic ones like glueballs and hybrids. In particular, we compute
for the first time an effective quark-gluon potential, and show the existence
of a quadrupolar interaction term in this case. We also discuss the influence
of a possible nonzero mass for the exchanged gluons.Comment: 33 pages, 4 tables and 12 figures ; typos correcte
Auxiliary field method and analytical solutions of the Schr\"{o}dinger equation with exponential potentials
The auxiliary field method is a new and efficient way to compute approximate
analytical eigenenergies and eigenvectors of the Schr\"{o}dinger equation. This
method has already been successfully applied to the case of central potentials
of power-law and logarithmic forms. In the present work, we show that the
Schr\"{o}dinger equation with exponential potentials of the form can also be analytically solved by using the
auxiliary field method. Formulae giving the critical heights and the energy
levels of these potentials are presented. Special attention is drawn on the
Yukawa potential and the pure exponential one
Auxiliary fields as a tool for computing analytical solutions of the Schr\"{o}dinger equation
We propose a new method to obtain approximate solutions for the
Schr\"{o}dinger equation with an arbitrary potential that possesses bound
states. This method, relying on the auxiliary field technique, allows in many
cases to find analytical solutions. It offers a convenient way to study the
qualitative features of the energy spectrum of bound states in any potential.
In particular, we illustrate our method by solving the case of central
potentials with power-law form and with logarithmic form. For these types of
potentials, we propose very accurate analytical energy formulae which improve a
lot the corresponding formulae that can be found in literature.Comment: 2 figure
Glueballs, gluon condensate, and pure glue QCD below T_c
A quasiparticle description of pure glue QCD thermodynamics at T<T_c is
proposed and compared to recent lattice data. Given that a gas of glueballs
with constant mass cannot quantitatively reproduce the early stages of the
deconfinement phase transition, the problem is to identify a relevant mechanism
leading to the observed sudden increase of the pressure, trace anomaly, etc. It
is shown that the strong decrease of the gluon condensate near T_c combined
with the increasing thermal width of the lightest glueballs might be the
trigger of the phase transition.Comment: 5 pages, 5 figures; analysis refined in v2, explanations added; v3 to
appear in EPJ
What makes SMEs more likely to collaborate? Analysing the role of regional policy
The last twenty years have witnessed the diffusion of regional innovation policies supporting networks of innovators. The underlying aim of these policies is to encourage firms, particularly SMEs, to undertake collaborations with organisations possessing complementary knowledge. Focusing on a set of SMEs that have participated, over time, in several innovation networks funded by the same regional government, the paper investigates how their relationships have evolved with respect to the following aspects: (i) reiteration of pre-existing relationships as opposed to experimentation of new relationships; (ii) collaboration with organisations possessing complementary rather than similar knowledge and competencies; (iii) creation of local relationships rather than experimentation of extra-local collaborations; (iv) reliance upon intermediaries to connect with other organisations. Our findings reveal that the involvement in these policy-supported networks changed the firms’ relational patterns, leading them to collaborate with a wider variety of agents than those with whom they were linked before the policies. Sectoral heterogeneity had a negative effect on the probability to collaborate, while co-localisation increased the likelihood to collaborate. Mutual involvement with intermediaries also had a positive effect. However, in the case of firm-to-university relationships only specialized intermediaries were likely to perform a positive role and, therefore, encourage networking
Standard care informed by the result of a placental growth factor blood test versus standard care alone in women with reduced fetal movement at or after 36+0 weeks’ gestation: a pilot randomised controlled trial
BackgroundBiomarkers of placental function can potentially aid the diagnosis and prediction of pregnancy complications. This randomised controlled pilot trial assessed whether for women with reduced fetal movement (RFM), intervention directed by the measurement of a placental biomarker in addition to standard care was feasible and improved pregnancy outcome compared with standard care alone.MethodsWomen aged 16–50 years presenting at eight UK maternity units with RFM between 36+0 and 41+0 weeks’ gestation with a viable singleton pregnancy and no indication for immediate delivery were eligible. Participants were randomised 1:1 in an unblinded manner to standard care and a biomarker blood test result revealed and acted on (intervention arm) or standard care where the biomarker result was not available (control arm). The objectives were to determine the feasibility of a main trial by recruiting 175–225 participants over 9 months and to provide proof of concept that informing care by measurement of placental biomarkers may improve outcome. Feasibility was assessed via the number of potentially eligible women, number recruited, reasons for non-recruitment and compliance. Proof of concept outcomes included the rates of the induction of labour and caesarean birth, and a composite adverse pregnancy outcome.ResultsOverall, 2917 women presented with RFM ≥ 36 weeks, 352 were approached to participate and 216 (61%) were randomised (intervention n = 109, control n = 107). The main reason for not approaching women was resource/staff issues (n = 1510). Ninety-seven women declined the trial, mainly due to not liking blood tests (n = 24) or not wanting to be in a trial (n = 21). Compliance with the trial interventions was 100% in both arms. Labour was induced in 97 (45%) participants (intervention n = 49, control n = 48), while 17 (9%) had planned caesarean sections (intervention n = 9, control n = 8). Overall, 9 (8%) babies in the intervention arm had the composite adverse pregnancy outcome versus 4 (4%) in the control arm.ConclusionsA main trial using a placental biomarker in combination with delivery, as indicated by the biomarker, in women with RFM is feasible. The frequency of adverse outcomes in this population is low, hence, a large sample size would be required along with consideration of the most appropriate outcome measures
A minimal quasiparticle approach for the QGP and its large- limits
We propose a quasiparticle approach allowing to compute the equation of state
of a generic gauge theory with gauge group SU() and quarks in an arbitrary
representation. Our formalism relies on the thermal quasiparticle masses
(quarks and gluons) computed from Hard-Thermal-Loop techniques, in which the
standard two-loop running coupling constant is used. Our model is minimal in
the sense that we do not allow any extra ansatz concerning the
temperature-dependence of the running coupling. We first show that it is able
to reproduce the most recent equations of state computed on the lattice for
temperatures higher than 2 . In this range of temperatures, an ideal gas
framework is indeed expected to be relevant. Then we study the accuracy of
various inequivalent large- limits concerning the description of the QCD
results, as well as the equivalence between the QCD limit and the SUSY Yang-Mills theory. Finally, we estimate the dissociation temperature
of the -meson and comment on the estimations' stability regarding the
different considered large- limits.Comment: 19 pages, 6 figure
Coordinated optimization of visual cortical maps (II) Numerical studies
It is an attractive hypothesis that the spatial structure of visual cortical
architecture can be explained by the coordinated optimization of multiple
visual cortical maps representing orientation preference (OP), ocular dominance
(OD), spatial frequency, or direction preference. In part (I) of this study we
defined a class of analytically tractable coordinated optimization models and
solved representative examples in which a spatially complex organization of the
orientation preference map is induced by inter-map interactions. We found that
attractor solutions near symmetry breaking threshold predict a highly ordered
map layout and require a substantial OD bias for OP pinwheel stabilization.
Here we examine in numerical simulations whether such models exhibit
biologically more realistic spatially irregular solutions at a finite distance
from threshold and when transients towards attractor states are considered. We
also examine whether model behavior qualitatively changes when the spatial
periodicities of the two maps are detuned and when considering more than 2
feature dimensions. Our numerical results support the view that neither minimal
energy states nor intermediate transient states of our coordinated optimization
models successfully explain the spatially irregular architecture of the visual
cortex. We discuss several alternative scenarios and additional factors that
may improve the agreement between model solutions and biological observations.Comment: 55 pages, 11 figures. arXiv admin note: substantial text overlap with
arXiv:1102.335
- …