Multidimensional continued fractions, dynamical renormalization and KAM theory

The disadvantage of `traditional' multidimensional continued fraction algorithms is that it is not known whether they provide simultaneous rational approximations for generic vectors. Following ideas of Dani, Lagarias and Kleinbock-Margulis we describe a simple algorithm based on the dynamics of flows on the homogeneous space SL(2,Z)\SL(2,R) (the space of lattices of covolume one) that indeed yields best possible approximations to any irrational vector. The algorithm is ideally suited for a number of dynamical applications that involve small divisor problems. We explicitely construct renormalization schemes for (a) the linearization of vector fields on tori of arbitrary dimension and (b) the construction of invariant tori for Hamiltonian systems.Comment: 51 page

Interwell coupling effect in Si/SiGe quantum wells grown by ultra high vacuum chemical vapor deposition

Si/Si0.66Ge0.34coupled quantum well (CQW) structures with different barrier thickness of 40, 4 and 2 nm were grown on Si substrates using an ultra high vacuum chemical vapor deposition (UHV-CVD) system. The samples were characterized using high resolution x-ray diffraction (HRXRD), cross-sectional transmission electron microscopy (XTEM) and photoluminescence (PL) spectroscopy. Blue shift in PL peak energy due to interwell coupling was observed in the CQWs following increase in the Si barrier thickness. The Si/SiGe heterostructure growth process and theoretical band structure model was validated by comparing the energy of the no-phonon peak calculated by the 6 + 2-bandk·pmethod with experimental PL data. Close agreement between theoretical calculations and experimental data was obtained

ϒ production in p–Pb collisions at √sNN=8.16 TeV

ϒ production in p–Pb interactions is studied at the centre-of-mass energy per nucleon–nucleon collision √sNN = 8.16 TeV with the ALICE detector at the CERN LHC. The measurement is performed reconstructing bottomonium resonances via their dimuon decay channel, in the centre-of-mass rapidity intervals 2.03 < ycms < 3.53 and −4.46 < ycms < −2.96, down to zero transverse momentum. In this work, results on the ϒ(1S) production cross section as a function of rapidity and transverse momentum are presented. The corresponding nuclear modification factor shows a suppression of the ϒ(1S) yields with respect to pp collisions, both at forward and backward rapidity. This suppression is stronger in the low transverse momentum region and shows no significant dependence on the centrality of the interactions. Furthermore, the ϒ(2S) nuclear modification factor is evaluated, suggesting a suppression similar to that of the ϒ(1S). A first measurement of the ϒ(3S) has also been performed. Finally, results are compared with previous ALICE measurements in p–Pb collisions at √sNN = 5.02 TeV and with theoretical calculations.publishedVersio

(Anti-)deuteron production in pp collisions at 1as=13TeV

The study of (anti-)deuteron production in pp collisions has proven to be a powerful tool to investigate the formation mechanism of loosely bound states in high-energy hadronic collisions. In this paper the production of (anti-)deuterons is studied as a function of the charged particle multiplicity in inelastic pp collisions at s=13 TeV using the ALICE experiment. Thanks to the large number of accumulated minimum bias events, it has been possible to measure (anti-)deuteron production in pp collisions up to the same charged particle multiplicity (d Nch/ d \u3b7 3c 26) as measured in p\u2013Pb collisions at similar centre-of-mass energies. Within the uncertainties, the deuteron yield in pp collisions resembles the one in p\u2013Pb interactions, suggesting a common formation mechanism behind the production of light nuclei in hadronic interactions. In this context the measurements are compared with the expectations of coalescence and statistical hadronisation models (SHM)

Multiplicity dependence of inclusive J/psi production at midrapidity in pp collisions at root s=13 TeV

Measurements of the inclusive J/psi yield as a function of charged-particle pseudorapidity density dN(ch)/d eta in pp collisions at root s = 13 TeV with ALICE at the LHC are reported. The J/psi meson yield is measured at midrapidity (vertical bar y vertical bar <0.9) in the dielectron channel, for events selected based on the charged-particle multiplicity at midrapidity (vertical bar eta vertical bar <1) and at forward rapidity (-3.7 <eta <-1.7 and 2.8 <eta <5.1); both observables are normalized to their corresponding averages in minimum bias events. The increase of the normalized J/psi yield with normalized dN(ch)/d eta is significantly stronger than linear and dependent on the transverse momentum. The data are compared to theoretical predictions, which describe the observed trends well, albeit not always quantitatively. (C) 2020 European Organization for Nuclear Research. Published by Elsevier B.V.Peer reviewe