Low-temperature excitations within the Bethe approximation

We propose the variational quantum cavity method to construct a minimal energy subspace of wave vectors that are used to obtain some upper bounds for the energy cost of the low-temperature excitations. Given a trial wave function we use the cavity method of statistical physics to estimate the Hamiltonian expectation and to find the optimal variational parameters in the subspace of wave vectors orthogonal to the lower-energy wave functions. To this end, we write the overlap between two wave functions within the Bethe approximation which allows us to replace the global orthogonality constraint with some local constraints on the variational parameters. The method is applied to the transverse Ising model and different levels of approximations are compared with the exact numerical solutions for small systems.Comment: 14 pages, 4 figure

Bethe free-energy approximations for disordered quantum systems

Given a locally consistent set of reduced density matrices, we construct approximate density matrices which are globally consistent with the local density matrices we started from when the trial density matrix has a tree structure. We employ the cavity method of statistical physics to find the optimal density matrix representation by slowly decreasing the temperature in an annealing algorithm, or by minimizing an approximate Bethe free energy depending on the reduced density matrices and some cavity messages originated from the Bethe approximation of the entropy. We obtain the classical Bethe expression for the entropy within a naive (mean-field) approximation of the cavity messages, which is expected to work well at high temperatures. In the next order of the approximation, we obtain another expression for the Bethe entropy depending only on the diagonal elements of the reduced density matrices. In principle, we can improve the entropy approximation by considering more accurate cavity messages in the Bethe approximation of the entropy. We compare the annealing algorithm and the naive approximation of the Bethe entropy with exact and approximate numerical simulations for small and large samples of the random transverse Ising model on random regular graphs.Comment: 23 pages, 4 figures, 4 appendice

A note on rattlers in amorphous packings of binary mixtures of hard spheres

It has been recently pointed out by Farr and Groot (arXiv:0912.0852) and by Kyrylyuk and Philipse (Prog. Colloid Polym. Sci., 2010, in press) that our theoretical result for the jamming density of a binary mixture of hard spheres (arXiv:0903.5099) apparently violates an upper bound that is obtained by considering the limit where the diameter ratio r = DA/DB goes to infinity. We believe that this apparent contradiction is the consequence of a misunderstanding, which we try to clarify here.Comment: 2 pages, 2 figures; final version published on J.Chem.Phy

Efficiency and irreversibility of movements in a city

We know that maximal efficiency in physical systems is attained by reversible processes. It is then interesting to see how irreversibility affects efficiency in other systems, e.g., in a city. In this study, we focus on a cyclic process of movements (home to workplace and back to home) in a city to investigate the above question. To this end, we present a minimal model of the movements, along with plausible definitions for the efficiency and irreversibility of the process; more precisely, we take the inverse of the total travel time per number of trips for efficiency and the relative entropy of the forward and backward flow distributions for the process irreversibility. We perform numerical simulations of the model for reasonable choices of the population distribution, the mobility law, and the movement strategy. The results show that the efficiency of movements is indeed negatively correlated with the above measure of irreversibility. The structure of the network and the impact of the flows on the travel times are the main factors here that affect the time intervals of arriving to destinations and returning to origins, which are usually larger than the time interval of the departures. This in turn gives rise to diverging of the backward flows from the forward ones and results to entropy (disorder or uncertainty) production in the system. The findings of this study might be helpful in characterizing more accurately the city efficiency and in better understanding of the main working principles of these complex systems

CAOS spectroscopy of Am stars Kepler targets

The {\it Kepler} space mission and its {\it K2} extension provide photometric time series data with unprecedented accuracy. These data challenge our current understanding of the metallic-lined A stars (Am stars) for what concerns the onset of pulsations in their atmospheres. It turns out that the predictions of current diffusion models do not agree with observations. To understand this discrepancy, it is of crucial importance to obtain ground-based spectroscopic observations of Am stars in the {\it Kepler} and {\it K2} fields in order to determine the best estimates of the stellar parameters. In this paper, we present a detailed analysis of high-resolution spectroscopic data for seven stars previously classified as Am stars. We determine the effective temperatures, surface gravities, projected rotational velocities, microturbulent velocities and chemical abundances of these stars using spectral synthesis. These spectra were obtained with {\it CAOS}, a new instrument recently installed at the observing station of the Catania Astrophysical Observatory on Mt. Etna. Three stars have already been observed during quarters Q0-Q17, namely: HD\,180347, HD\,181206, and HD\,185658, while HD\,43509 was already observed during {\it K2} C0 campaign. We confirm that HD\,43509 and HD\,180347 are Am stars, while HD 52403, HD\,50766, HD\,58246, HD\,181206 and HD\,185658 are marginal Am stars. By means of non-LTE analysis, we derived oxygen abundances from O{\sc I}$\lambda$7771--5{\AA} triplet and we also discussed the results obtained with both non-LTE and LTE approaches.Comment: accepted in MNRAS main journal 13 pages, 11 figures, 3 tables. arXiv admin note: text overlap with arXiv:1404.095

Entropy production of selfish drivers: implications for efficiency and predictability of movements in a city

Characterizing the efficiency of movements is important for a better management of the cities. More specifically, the connection between the efficiency and uncertainty (entropy) production of a transport process is not established yet. In this study, we consider the movements of selfish drivers from their homes (origins) to work places (destinations) to see how interactions and randomness in the movements affect a measure of efficiency and entropy production (uncertainty in the destination time intervals) in this process. We employ realistic models of population distributions and mobility laws to simulate the movement process, where interactions are modelled by dependence of the local travel times on the local flows. We observe that some level of information (the travel times) sharing enhances a measure of predictability in the process without any coordination. Moreover, the larger cities display smaller efficiencies, for the same model parameters and population density, which limits the size of an efficient city. We find that entropy production is a good order parameter to distinguish the low- and high-congestion phases. In the former phase, the entropy production grows monotonically with the probability of random moves, whereas it displays a minimum in the congested phase; that is randomness in the movements can reduce the uncertainty in the destination time intervals. The findings highlight the role of entropy production in the study of efficiency and predictability of similar processes in a complex system like the city.Pharmacolog

The ultracool dwarf DENIS-P J104814.7-395606. Chromospheres and coronae at the low-mass end of the main-sequence

We have obtained an XMM-Newton observation and a broad-band spectrum from the ultraviolet to the near infrared with X-Shooter for one of the nearest M9 dwarfs, DENIS-P J1048-3956 (4pc). We integrate these data by a compilation of activity parameters for ultracool dwarfs from the literature with the aim to advance our understanding of these objects by comparing them to early-M type dwarf stars and the Sun. Our deep XMM-Newton observation has led to the first X-ray detection of DENIS-P J1048-3956 (log Lx = 25.1) as well as the first measurement of its V band brightness (V = 17.35mag). Flux-flux relations between X-ray and chromospheric activity indicators are here for the first time extended into the regime of the ultracool dwarfs. The approximate agreement of DENIS-P J1048-3956 and other ultracool dwarfs with flux-flux relations for early-M dwarfs suggests that the same heating mechanisms work in the atmospheres of ultracool dwarfs, albeit weaker as judged from their lower fluxes. The observed Balmer decrements of DENIS-P J1048-3956 are compatible with optically thick plasma in LTE at low, nearly photospheric temperature or optically thin LTE plasma at 20000K. Describing the decrements with CaseB recombination requires different emitting regions for Halpha and the higher Balmer lines. The high observed Halpha/Hbeta flux ratio is also poorly fitted by the optically thin models. We derive a similarly high value for the Halpha/Hbeta ratio of vB10 and LHS2065 and conclude that this may be a characteristic of ultracool dwarfs. We add DENIS-P J1048-3956 to the list of ultracool dwarfs detected in both the radio and the X-ray band. The Benz-Guedel relation between radio and X-ray luminosity of late-type stars is well-known to be violated by ultracool dwarfs. We speculate on the presence of two types of ultracool dwarfs with distinct radio and X-ray behavior.Comment: accepted for publication in Astronomy & Astrophysic

The HADES RV Programme with HARPS-N@TNG IV. Time resolved analysis of the Ca ii H&K and H{\alpha} chromospheric emission of low-activity early-type M dwarfs

M dwarfs are prime targets for planet search programs, particularly of those focused on the detection and characterization of rocky planets in the habitable zone. Understanding their magnetic activity is important because it affects our ability to detect small planets, and it plays a key role in the characterization of the stellar environment. We analyze observations of the Ca II H&K and H{\alpha} lines as diagnostics of chromospheric activity for low-activity early-type M dwarfs. We analyze the time series of spectra of 71 early-type M dwarfs collected for the HADES project for planet search purposes. The HARPS-N spectra provide simultaneously the H&K doublet and the H{\alpha} line. We develop a reduction scheme able to correct the HARPS-N spectra for instrumental and atmospheric effects, and to provide flux-calibrated spectra in units of flux at the stellar surface. The H&K and H{\alpha} fluxes are compared with each other, and their variability is analyzed. We find that the H and K flux excesses are strongly correlated with each other, while the H{\alpha} flux excess is generally less correlated with the H&K doublet. We also find that H{\alpha} emission does not increase monotonically with the H&K line flux, showing some absorption before being filled in by chromospheric emission when H&K activity increases. Analyzing the time variability of the emission fluxes, we derive a tentative estimate of the rotation period (of the order of a few tens of days) for some of the program stars, and the typical lifetime of chromospheric active regions (a few stellar rotations). Our results are in good agreement with previous studies. In particular, we find evidence that the chromospheres of early-type M dwarfs could be characterized by different filaments coverage, affecting the formation mechanism of the H{\alpha} line. We also show that chromospheric structure is likely related to spectral type

The GAPS Programme with HARPS-N at TNG. X. Differential abundances in the XO-2 planet hosting binary

Binary stars hosting exoplanets are a unique laboratory where chemical tagging can be performed to measure with high accuracy the elemental abundances of both stellar components, with the aim to investigate the formation of planets and their subsequent evolution. Here, we present a high-precision differential abundance analysis of the XO-2 wide stellar binary based on high resolution HARPS-N@TNG spectra. Both components are very similar K-dwarfs and host planets. Since they formed presumably within the same molecular cloud, we expect they should possess the same initial elemental abundances. We investigate if the presence of planets can cause some chemical imprints in the stellar atmospheric abundances. We measure abundances of 25 elements for both stars with a range of condensation temperature $T_{\rm C}=40-1741$ K, achieving typical precisions of $\sim 0.07$ dex. The North component shows abundances in all elements higher by $+0.067 \pm 0.032$ dex on average, with a mean difference of +0.078 dex for elements with $T_{\rm C} > 800$ K. The significance of the XO-2N abundance difference relative to XO-2S is at the $2\sigma$ level for almost all elements. We discuss the possibility that this result could be interpreted as the signature of the ingestion of material by XO-2N or depletion in XO-2S due to locking of heavy elements by the planetary companions. We estimate a mass of several tens of $M_{\oplus}$ in heavy elements. The difference in abundances between XO-2N and XO-2S shows a positive correlation with the condensation temperatures of the elements, with a slope of $(4.7 \pm 0.9) \times 10^{-5}$ dex K$^{-1}$, which could mean that both components have not formed terrestrial planets, but that first experienced the accretion of rocky core interior to the subsequent giant planets.Comment: 10 pages, 5 figures, accepted by Astronomy & Astrophysics. Numbering of the series change