Out-of-equilibrium Correlated Systems : Bipartite Entanglement as a Probe of Thermalization

Thermalization play a central role in out-of-equilibrium physics of ultracold atoms or electronic transport phenomena. On the other hand, entanglement concepts have proven to be extremely useful to investigate quantum phases of matter. Here, it is argued that **bipartite** entanglement measures provide key information on out-of-equilibrium states and might therefore offer stringent thermalization criteria. This is illustrated by considering a global quench in an (extended) XXZ spin-1/2 chain across its (zero-temperature) quantum critical point. A non-local **bipartition** of the chain **preserving translation symmetry** is proposed. The time-evolution after the quench of the **reduced** density matrix of the half-system is computed and its associated (time-dependent) entanglement spectrum is analyzed. Generically, the corresponding entanglement entropy quickly reaches a "plateau" after a short transient regime. However, in the case of the integrable XXZ chain, the low-energy entanglement spectrum still reveals strong time-fluctuations. In addition, its infinite-time average shows strong deviations from the spectrum of a Boltzmann thermal density matrix. In contrast, when the integrability of the model is broken (by small next-nearest neighbor couplings), the entanglement spectra of the time-average and thermal density matrices become remarkably similar.Comment: extended version: 15 pages, 9 figure

Confidence regions for the multinomial parameter with small sample size

Consider the observation of n iid realizations of an experiment with d>1 possible outcomes, which corresponds to a single observation of a multinomial distribution M(n,p) where p is an unknown discrete distribution on {1,...,d}. In many applications, the construction of a confidence region for p when n is small is crucial. This concrete challenging problem has a long history. It is well known that the confidence regions built from asymptotic statistics do not have good coverage when n is small. On the other hand, most available methods providing non-asymptotic regions with controlled coverage are limited to the binomial case d=2. In the present work, we propose a new method valid for any d>1. This method provides confidence regions with controlled coverage and small volume, and consists of the inversion of the "covering collection"' associated with level-sets of the likelihood. The behavior when d/n tends to infinity remains an interesting open problem beyond the scope of this work.Comment: Accepted for publication in Journal of the American Statistical Association (JASA

Experimental evolution induces loss of female-fertility in vitro in the fungal pathogen of rice, Magnaporthe oryzae

Sexual reproduction is widespread in eukaryotic organisms. Inmany fungal species previously known to reproduce asexually, some populations have been shown to encounter episodes of sexual reproduction. It has been suggested that mostfungi that are pathogenic on plants may reproduce sexually near their center of origin but have lost this ability during their dispersion. If a population reproduces exclusively clonally forseveral generations, individuals may accumulate deleterious mutations in loci controlling sexual reproduction. This may result in a complete loss of sexual reproduction ability. We tested this hypothesis on /Magnaporthe oryzae/, which is responsible for the most important fungal disease on cultivated rice worldwide: blast. In this species, only asexual spores are observed in the field. However, some strains coming from the putative center of origin of the fungus (in South East Asia, near the Himalayan Foothills) are able to produce viable sexual spores /in vitro/, and indirect evidence that sexual reproduction do occur /in natura/ in this region have been recently provided (see the abstract by E. Fournier).//In this heterothallic fungus,//sexual reproduction can occur only between two different strains of opposite mating type. Moreover, at least one of them, independently from the mating type, must be female-fertile, that is to be able to produce the sexual organs (perithecia) where meiosis takes place. We performed /in vitro /experimental evolution of four female-fertile strains for 10-20 "clonal generations". These strains came from a recombinant population of the center of origin. Each of the four strains became female-sterile in about 100 days in at least one of the two replicates we performed. This loss of female-fertility was accompanied by a reduction of asexual sporulation /in vitro /and /in planta/.//As epigenetical effects could explain the frequent loss of female-fertility observed, we tested if stress could restore it. Four different stresses were tested: extremely low temperature (-80°C), mycelium fragmentation by sonication, monosporic isolation, growth on plant. None of these stresses achieved to restore female-fertility, so the loss of female-fertility might be explained by genetical rather than epigenetical mechanisms. Crosses were performed between mutant strains that had lost female-fertility and wild type strains. In the offspring, the female-fertility phenotype segregated in 1:3 proportions. Backcrosses between F1 female-sterile strains and wild type strains gave the same result, supporting the hypothesis of a genetic control. Here we showed for the first time that female-fertility could be rapidly lost in theabsence of sexual reproduction in /M. oryzae/ strains from rice. We showed that it might be due to mutation accumulation, probably at several loci. From these results we hypothesize that sexual reproduction ability may have been lost rapidly during the dispersion of the disease from Asia to the rest of the world. More generally, this study provides a case study to test hypotheses on the enigma of sex. (Texte intégral

Calculation of Delta (k,omega) for a 2D t-J cluster

Using numerical techniques, the diagonal and off-diagonal superconducting one-electron Green's functions are calculated for a two-dimensional (2D) t-J model on a periodic 32-site cluster at low doping. From these Green's functions, the momentum and frequency dependence of the pairing gap $\Delta ({\bf k}, \omega)$ are extracted. It has $d_{x^2-y^2}$ symmetry and exhibits $\omega$-dependent structure which depend upon J/t. We find that the pairing gap persists down to small J/t values. The frequency- and momentum-dependent renormalized energy and renormalization factor are also calculated.Comment: 4 pages, 4 figures, 1 table, submitted to PR

Electronic Transport in Graphene: Quantum Effects and Role of Local Defects

In this paper we present generic properties of quantum transport in mono-layer graphene. In the scheme of the Kubo-Geenwood formula, we compute the square spreading of wave packets of a given energy with is directly related to conductivity. As a first result, we compute analytically the time dependent diffusion for pure graphene. In addition to the semi-classical term a second term exists that is due to matrix elements of the velocity operator between electron and hole bands. This term is related to velocity fluctuations i.e. Zitterbewegung effect. Secondly, we study numerically the quantum diffusion in graphene with simple vacancies and pair of neighboring vacancies (divacancies), that simulate schematically oxidation, hydrogenation and other functionalisations of graphene. We analyze in particular the time dependence of the diffusion and its dependence on energy in relation with the electronic structure. We compute also the mean free path and the semi-classical value of the conductivity as a function of energy in the limit of small concentration of defects.Comment: 10 pages, 5 figure

The Gap Function Phi(k,w) for a Two-leg t-J Ladder and the Pairing Interaction

The gap function phi(k,omega), determined from a Lanczos calculation for a doped 2-leg t-J ladder, is used to provide insight into the spatial and temporal structure of the pairing interaction. It implies that this interaction is a local near-neighbor coupling which is retarded. The onset frequency of the interaction is set by the energy of an S=1 magnon-hole-pair and it is spread out over a frequency region of order the bandwith

La production laitière des dromadaires Dankali (Ethiopie)

Un suivi sur trois ans et demi de 5 femelles de race Dankali entretenues sur pâturages naturels a permis d'observer 6 lactations complètes, 6 intervall es entre mises bas, 11 naissances et la croissance de 5 chamelons; 99 contrôles laitiers ont été pratiqués. La production moyenne de lait est de 1 123 litres sur 12,25 mois. Le coefficient de persistance est élevé : de 97,1 p.100 et de 74,1 p. 100 pour des périodes de 100 jours. Le pic de lactation est atteint à 56,5 jours avec un volume de 4,4 litres. Les intervalles entre mises bas sont très variables : de 13 à 32 mois. L'intervall e mise bas-saillie fécondante peut être bref et la lactation peut se poursuivr e jusqu'à un stade avancé de la gestation. Les productions observées sont comparées à des relevés ponctuels de lactation rapportés dans la même région, sur le même type d'animaux mais dans des conditions d'entretien différente

Software-defined networking: guidelines for experimentation and validation in large-scale real world scenarios

Part 1: IIVC WorkshopInternational audienceThis article thoroughly details large-scale real world experiments using Software-Defined Networking in the testbed setup. More precisely, it provides a description of the foundation technology behind these experiments, which in turn is focused around OpenFlow and on the OFELIA testbed. In this testbed preliminary experiments were performed in order to tune up settings and procedures, analysing the encountered problems and their respective solutions. A methodology consisting of five large-scale experiments is proposed in order to properly validate and improve the evaluation techniques used in OpenFlow scenarios

Entanglement spectrum and boundary theories with projected entangled-pair states

In many physical scenarios, close relations between the bulk properties of quantum systems and theories associated to their boundaries have been observed. In this work, we provide an exact duality mapping between the bulk of a quantum spin system and its boundary using Projected Entangled Pair States (PEPS). This duality associates to every region a Hamiltonian on its boundary, in such a way that the entanglement spectrum of the bulk corresponds to the excitation spectrum of the boundary Hamiltonian. We study various specific models, like a deformed AKLT [1], an Ising-type [2], and Kitaev's toric code [3], both in finite ladders and infinite square lattices. In the latter case, some of those models display quantum phase transitions. We find that a gapped bulk phase with local order corresponds to a boundary Hamiltonian with local interactions, whereas critical behavior in the bulk is reflected on a diverging interaction length of the boundary Hamiltonian. Furthermore, topologically ordered states yield non-local Hamiltonians. As our duality also associates a boundary operator to any operator in the bulk, it in fact provides a full holographic framework for the study of quantum many-body systems via their boundary.Comment: 13 pages, 14 figure