Cold-atom systems and the scaling limit

With perspective to applications of cold-atom systems, some aspects of few-body physics at very low energies will be reviewed. By exploring the possibilities of varying the two-body interaction via the Feshbach resonance mechanism, some recent results are reported for condensed systems in optical lattices.

Universality and Scaling Limit of Weakly-Bound Tetramers

The occurrence of a new limit cycle in few-body physics, expressing a universal scaling function relating the binding energies of two successive tetramer states, is revealed by considering a renormalized zero-range two-body interaction in bound state of four identical bosons. The tetramer energy spectrum is obtained by adding a boson to an Efimov bound state with energy B-3 in the unitary limit (for zero two-body binding energy or infinite two-body scattering length). Each excited N-th tetramer energy B-4((N)) is shown to slide along a scaling function as a short-range four-body scale is changed, emerging from the 3+1 threshold for a universal ratio B-4((N))/B-3 = 4.6, which does not depend on N. The new scale can also be revealed by a resonance in the atom-trimer recombination process.

Combined Tevatron upper limit on gg -> H -> W+W- and constraints on the Higgs boson mass in fourth-generation fermion models

We combine results from searches by the CDF and D0 collaborations for a standard model Higgs boson (H) in the process gg -> H -> W+W- in p (p) over bar collisions at the Fermilab Tevatron Collider at root s = 1.96 TeV. With 4.8 fb(-1) of integrated luminosity analyzed at CDF and 5.4 fb(-1) at D0, the 95% confidence level upper limit on sigma(gg -> H) x B(H -> W+W-) is 1.75 pb at m(H) = 120 GeV, 0.38 pb at m(H) = 165 GeV, and 0.83 pb at m(H) = 200 GeV. Assuming the presence of a fourth sequential generation of fermions with large masses, we exclude at the 95% confidence level a standard-model-like Higgs boson with a mass between 131 and 204 GeV.

Binding and structure of tetramers in the scaling limit

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermal phase transitions for Dicke-type models in the ultrastrong-coupling limit

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Thermal behavior of Cu-Al alloys near the alpha-Cu-Al solubility limit

The thermal behavior of Cu-Al alloys with 17, 19 and 21 at.%Al was examined by differential thermal analysis (DTA), differential scanning calorimetry (DSC), X-ray diffractometry (XRD), optical microscopy (OM) and scanning electron microscopy (SEM). The presence of the gamma phase (Al4Cu9) was clearly detected for the Cu-19 at.%Al alloy and caused the alpha (2) phase disordering process in two stages. The tendency to increase the alpha (2) dissolution precipitates with the increase in the Al content seems to be reverted for compositions at about 21 at.%Al and the heating/cooling ratio seems to influence the thermal response of this process. The presence of the endothermic peak corresponding to the beta (1)--> beta transformation depends on an incomplete beta decomposition reaction. The variation of the heating rate showed that the beta (1)-->(alpha+gamma (1)) decomposition is the dominant reaction for alloys containing 19 and 21 at.%Al.

Limit between stages I and II of a seed imbibition curve

O conhecimento das fases de absorção de água das diferentes espécies é importante em pesquisas objetivando melhorar a qualidade das sementes, utilizando tratamentos como condicionamento osmótico, pré-hidratação e uso de bioreguladores. O objetivo do presente trabalho foi estabelecer uma metodologia para determinar o limite entre a primeira e a segunda fase do processo, considerando o modelo W = f(t) - (a - w0)exp(-kt), utilizando testes estatísticos. O limite entre as duas primeiras fases do processo de absorção de água pelas sementes, foi determinado utilizando-se a distribuição assintótica de uma função de estimadores. O ponto a partir do qual esta diferença (W*) deixa de ser significativa foi determinado utilizando-se o teste estatístico T de Student. Para os dados utilizados como exemplo, tem-se o modelo ou =(0,434 + 0,00162 t) - (0,434 - w o)exp(-0,121 t), com r² = 0,98 e W* = (0,434 - w o) exp(-0,121 t). O valor de t encontrado (27,2 horas) é menor do que o valor determinado, considerando-se como critério para mudança de fase a diferença de 1% entre a assíntota e o valor estimado pelo modelo ajustado. Essa diferença de duas horas corresponde a 0,28% de água absorvida.

New higher-derivative R-4 theorems for graviton scattering

The nonminimal pure spinor formalism for the superstring is used to prove two new multiloop theorems which are related to recent higher-derivative R-4 conjectures of Green, Russo, and Vanhove. The first theorem states that when 0 < n < 12, partial derivative R-n(4) terms in the Type II effective action do not receive perturbative contributions above n/2 loops. The second theorem states that when n <= 8, perturbative contributions to partial derivative R-n(4) terms in the IIA and IIB effective actions coincide. As shown by Green, Russo, and Vanhove, these results suggest that d=4 N=8 supergravity is ultraviolet finite up to eight loops.

Limit weierstrass points on nodal reducible curves

In the 1980s D. Eisenbud and J. Harris posed the following question: What are the limits of Weierstrass points in families of curves degenerating to stable curves not of compact type? In the present article, we give a partial answer to this question. We consider the case where the limit curve has components intersecting at points in general position and where the degeneration occurs along a general direction. For this case we compute the limits of Weierstrass points of any order. However, for the usual Weierstrass points, of order one, we need to suppose that all of the components of the limit curve intersect each other.

Structure, mobility and clustering of interstitial O in La2CuO4+delta in the limit of small delta

Anelastic spectra (elastic energy absorption as a function of temperature) are reported which provide evidence that excess O in La2CuO4+delta starts forming two different types of defects already at very low concentrations, where no phase separation or changes in the type of O intercalation are believed to occur. The absorption peak with the lowest activation enthalpy, H/k(B) = 5600 K, is visible at lowest values of delta and is attributed to the hopping of single interstitial O2- ions. The second process, with a slightly slower dynamics, appears at higher values of delta and soon becomes preponderant over the former process. The latter process is proposed to be due to stable pairs of O atoms and is put in connection with the formation of partially covalent bonds between interstitial and apical oxygen; such bonds would reduce the doping efficiency of excess O at increasing delta. The geometry of the interstitial O defect is discussed. O 1998 Published by Elsevier B.V. B.V. All rights reserved.

LIMIT ON A HEAVY DIRAC NEUTRINO THROUGH OBLIQUE RADIATIVE-CORRECTIONS

We compute the one-loop oblique corrections in a typical model with neutrino masses due to the seesaw mechanism. We verify that a Dirac neutrino mass up to 178 GeV is still allowed by the experimental data.

Conjectures and theorems in the theory of entire functions

Motivated by the recent solution of Karlin's conjecture, properties of functions in the Laguerre-Polya class are investigated. The main result of this paper establishes new moment inequalities fur a class of entire functions represented by Fourier transforms. The paper concludes with several conjectures and open problems involving the Laguerre-Polya class and the Riemann xi -function.

On the limit cycles of a class of piecewise linear differential systems in R-4 with two zones

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Bifurcation of limit cycles from a centre in R-4 in resonance 1:N

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)