Non-power positional number representation systems, bijective numeration, and the Mesoamerican discovery of zero

Pre-Columbian Mesoamerica was a fertile crescent for the development of number systems. A form of vigesimal system seems to have been present from the first Olmec civilization on wards, to which succeeding peoples made contributions. We discuss the Maya use of the representational redundancy present in their Long Count calendar, a non-power positional number representation system with multipliers 1, 20, 18 x 20, ..., 18 x 20(n). We demonstrate that the Mesoamericans did not need to invent positional notation and discover zero at the same time because they were not afraid of using a number system in which the same number can be written indifferent ways. A Long Count number system with digits from 0 to 20 is seen later to pass to one using digits 0 to 19, which leads us to propose that even earlier there may have been an initial zeroless bijective numeration system whose digits ran from 1 to 20. Mesoamerica was able to make this conceptual leap to the concept of a cardinal zero to perform arithmetic owing to a familiarity with multiple and redundant number representation systems

Four new planets around giant stars and the mass-metallicity correlation of planet-hosting stars

CONTEXT. Exoplanet searches have demonstrated that giant planets are preferentially found around metal-rich stars and that their fraction increases with the stellar mass. AIMS. During the past six years, we have conducted a radial velocity follow-up program of 166 giant stars, to detect substellar companions, and characterizing their orbital properties. Using this information, we aim to study the role of the stellar evolution in the orbital parameters of the companions, and to unveil possible correlations between the stellar properties and the occurrence rate of giant planets. METHODS. Using FEROS and CHIRON spectra, we have computed precision radial velocities and we have derived atmospheric and physical parameters for all of our targets. Additionally, velocities computed from UCLES spectra are presented here. By studying the periodic radial velocity signals, we have detected the presence of several substellar companions. RESULTS. We present four new planetary systems around the giant stars HIP8541, HIP74890, HIP84056 and HIP95124. Additionally, we find that giant planets are more frequent around metal-rich stars, reaching a peak in the detection of $f$ = 16.7$^{+15.5}_{-5.9}$% around stars with [Fe/H] $\sim$ 0.35 dex. Similarly, we observe a positive correlation of the planet occurrence rate with the stellar mass, between M$_\star$ $\sim$ 1.0 -2.1 M$_\odot$, with a maximum of $f$ = 13.0$^{+10.1}_{-4.2}$%, at M$_\star$ = 2.1 M$_\odot$. CONCLUSIONS. We conclude that giant planets are preferentially formed around metal-rich stars. Also, we conclude that they are more efficiently formed around more massive stars, in the mass range of M$_\star$ $\sim$ 1.0 - 2.1 M$_\odot$. These observational results confirm previous findings for solar-type and post-MS hosting stars, and provide further support to the core-accretion formation model.Comment: Accepted for publication in A&

Frictional Drag between Two Dilute Two-Dimensional Hole Layers

We report drag measurements on dilute double layer two-dimensional hole systems in the regime of r_s=19~39. We observed a strong enhancement of the drag over the simple Boltzmann calculations of Coulomb interaction, and deviations from the T^2 dependence which cannot be explained by phonon-mediated, plasmon-enhanced, or disorder-related processes. We suggest that this deviation results from interaction effects in the dilute regime.Comment: 4 pages, 3 figures, accepted in Phys. Rev. Lett. Added single layer transport dat

Absence of gap for infinite half--integer spin ladders with an odd number of legs

A proof is presented for the absence of gap for spin $1/2$ ladders with an odd number of legs, in the infinite leg length limit. This result is relevant to the current discussion of coupled one--dimensional spin systems, a physical realization of which are vanadyl pyrophosphate, (VO)$_2$P$_2$O$_7$, and stoichiometric Sr$_{n-1}$ Cu$_{n+1}$ O$_{2n}$ (with $n=3,5,7,9,\dots$).Comment: REVTeX, 8 page

Freezing transition of the vortex liquid in anisotropic superconductors

We study the solid-liquid transition of a model of pancake vortices in laminar superconductors using a density functional theory of freezing. The physical properties of the system along the melting line are discussed in detail. We show that there is a very good agreement with experimental data in the shape and position of the first order transition in the phase diagram and in the magnitude and temperature dependence of the magnetic induction jump at the transition. We analyze the validity of the Lindemann melting criterion and the Hansen-Verlet freezing criterion. Both criteria are shown to be good to predict the phase diagram in the region where a first order phase transition is experimentally observed.Comment: 9 pages, 10 figure

Many-body solitons in a one-dimensional condensate of hard core bosons

A mapping theorem leading to exact many-body dynamics of impenetrable bosons in one dimension reveals dark and gray soliton-like structures in a toroidal trap which is phase-imprinted. On long time scales revivals appear that are beyond the usual mean-field theory

Hole dynamics in generalized spin backgrounds in infinite dimensions

We calculate the dynamical behaviour of a hole in various spin backgrounds in infinite dimensions, where it can be determined exactly. We consider hypercubic lattices with two different types of spin backgrounds. On one hand we study an ensemble of spin configurations with an arbitrary spin probability on each sublattice. This model corresponds to a thermal average over all spin configurations in the presence of staggered or uniform magnetic fields. On the other hand we consider a definite spin state characterized by the angle between the spins on different sublattices, i.e a classical spin system in an external magnetic field. When spin fluctuations are considered, this model describes the physics of unpaired particles in strong coupling superconductors.Comment: Accepted in Phys. Rev. B. 18 pages of text (1 fig. included) in Latex + 2 figures in uuencoded form containing the 2 postscripts (mailed separately

Spin-Hall effect and spin-Coulomb drag in doped semiconductors

In this review, we describe in detail two important spin-transport phenomena: the extrinsic spin-Hall effect (coming from spin-orbit interactions between electrons and impurities) and the spin-Coulomb drag. The interplay of these two phenomena is analyzed. In particular, we discuss the influence of scattering between electrons with opposite spins on the spin current and the spin accumulation produced by the spin-Hall effect. Future challenges and open questions are briefly discussed.Comment: Topical revie