Bound States in n Dimensions (Especially n = 1 and n = 2)

We stress that in contradiction with what happens in space dimensions $n \geq 3$, there is no strict bound on the number of bound states with the same structure as the semi-classical estimate for large coupling constant and give, in two dimensions, examples of weak potentials with one or infinitely many bound states. We derive bounds for one and two dimensions which have the "right" coupling constant behaviour for large coupling.Comment: Talk given by A. Martin at Les Houches, October 2001, to appear in "Few-Body Problems

Noise correlations, entanglement, and Bell inequalities

The aim of this chapter is to describe two situations where positive noise correlations can be directly monitored using a transport experiment, either with a superconductor or with a correlated electron system. To be more precise, the present text reflects the presentations made by the three authors during the Delft NATO workshop. Bell inequalities and quantum mechanical non-locality with electrons injected from a superconductor will be addressed first. Next, noise correlations will be computed in a carbon nanotube where electrons are injected in the bulk from a STM tip. The first topic is the result of an ongoing collaboration with G. Lesovik and G. Blatter over the years. The unifying theme is that in both branched quantum circuits, entanglement is explicit and can be illustrated via noise correlations. Entanglement can be achieved either for pairs of electrons in the case of superconductor sources connected to Fermi liquid leads, or alternatively for pairs of quasiparticle excitations of the correlated electron fluid.Comment: 24 pages, 7 figures, Proceedings of the NATO ARW workshop on Quantum Noise, Y. Nazarov and Y. Blanter editors (Kluwer 2002

Visible-IR Colors and Lightcurve Analysis of Two Bright TNOs: 1999 TC36 and 1998 SN165

We report on observations of two bright Trans-Neptunian Objects (TNOs) - 1999 TC36 and 1998 SN165}- during two observational campaigns, as part of the Meudon Multicolor Survey of Outer Solar System Objects. V-J color was measured for 1999 TC36 (V-J=2.34+/-0.18), which combined with previous measured colors in the visible, indicate a red reflectivity spectrum at all wavelengths. Photometric V-band lightcurves were taken for both objects over a time span of around 8 hours. We have determined a possible rotational period of P=10.1+/-0.8 h for 1998 SN165, making it the seventh TNO with an estimated period. From its lightcurve variation of Dm=0.151(+0.022/-0.030), we have inferred an asymmetry ratio of a/b >=1.148(+0.024/-0.031). For 1999 TC36, we did not detect any rotational period or periodic signal variation within the uncertainties, but the analysis of its lightcurve hints to a slight systematic magnitude decrease.Comment: Accepted for publication in New Astronomy (13 pages, inc. 4 figures

Two-Page Book Embeddings of 4-Planar Graphs

Back in the Eighties, Heath showed that every 3-planar graph is subhamiltonian and asked whether this result can be extended to a class of graphs of degree greater than three. In this paper we affirmatively answer this question for the class of 4-planar graphs. Our contribution consists of two algorithms: The first one is limited to triconnected graphs, but runs in linear time and uses existing methods for computing hamiltonian cycles in planar graphs. The second one, which solves the general case of the problem, is a quadratic-time algorithm based on the book-embedding viewpoint of the problem.Comment: 21 pages, 16 Figures. A shorter version is to appear at STACS 201

Bright solitary waves of atomic Bose-Einstein condensates under rotation

We analyse the rotation of bright solitary waves formed of atomic Bose-Einstein condensates with attractive atomic interactions. By employing a variational technique and assuming an irrotational quadrupolar flow field, we map out the variational solutions in the rotating frame. In particular, we show that rotation has a considerable stabilising effect on the system, significantly raising the critical threshold for collapse of the bright solitary waves.Comment: 4 pages, 3 figure

Structural and mutagenic analysis of the RM controller protein C.Esp1396I

Bacterial restriction-modification (RM) systems are comprised of two complementary enzymatic activities that prevent the establishment of foreign DNA in a bacterial cell: DNA methylation and DNA restriction. These two activities are tightly regulated to prevent over-methylation or auto-restriction. Many Type II RM systems employ a controller (C) protein as a transcriptional regulator for the endonuclease gene (and in some cases, the methyltransferase gene also). All high-resolution structures of C-protein/DNA-protein complexes solved to date relate to C.Esp1396I, from which the interactions of specific amino acid residues with DNA bases and/or the phosphate backbone could be observed. Here we present both structural and DNA binding data for a series of mutations to the key DNA binding residues of C.Esp1396I. Our results indicate that mutations to the backbone binding residues (Y37, S52) had a lesser affect on DNA binding affinity than mutations to those residues that bind directly to the bases (T36, R46), and the contributions of each side chain to the binding energies are compared. High-resolution X-ray crystal structures of the mutant and native proteins showed that the fold of the proteins was unaffected by the mutations, but also revealed variation in the flexible loop conformations associated with DNA sequence recognition. Since the tyrosine residue Y37 contributes to DNA bending in the native complex, we have solved the structure of the Y37F mutant protein/DNA complex by X-ray crystallography to allow us to directly compare the structure of the DNA in the mutant and native complexes

Universal amplitude ratios in the 3D Ising Universality Class

We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain A_+/A_-=0.536(2) and C_+/C_-=4.713(7), where A_+- and C_+- are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts + and - indicate the high and the low temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high and low temperature series expansions, field theoretic methods and experiments.Comment: 18 pages, two figures, typos corrected, discussion on finite size corrections extende

Comparing supernova remnants around strongly magnetized and canonical pulsars

The origin of the strong magnetic fields measured in magnetars is one of the main uncertainties in the neutron star field. On the other hand, the recent discovery of a large number of such strongly magnetized neutron stars, is calling for more investigation on their formation. The first proposed model for the formation of such strong magnetic fields in magnetars was through alpha-dynamo effects on the rapidly rotating core of a massive star. Other scenarios involve highly magnetic massive progenitors that conserve their strong magnetic moment into the core after the explosion, or a common envelope phase of a massive binary system. In this work, we do a complete re-analysis of the archival X-ray emission of the Supernova Remnants (SNR) surrounding magnetars, and compare our results with all other bright X-ray emitting SNRs, which are associated with Compact Central Objects (CCOs; which are proposed to have magnetar-like B-fields buried in the crust by strong accretion soon after their formation), high-B pulsars and normal pulsars. We find that emission lines in SNRs hosting highly magnetic neutron stars do not differ significantly in elements or ionization state from those observed in other SNRs, neither averaging on the whole remnants, nor studying different parts of their total spatial extent. Furthermore, we find no significant evidence that the total X-ray luminosities of SNRs hosting magnetars, are on average larger than that of typical young X-ray SNRs. Although biased by a small number of objects, we found that for a similar age, there is the same percentage of magnetars showing a detectable SNR than for the normal pulsar population.Comment: 16 pages, 5 figures, Accepted for publication in MNRA