Expansion potentials for exact far-from-equilibrium spreading of particles and energy

The rates at which energy and particle densities move to equalize arbitrarily large temperature and chemical potential differences in an isolated quantum system have an emergent thermodynamical description whenever energy or particle current commutes with the Hamiltonian. Concrete examples include the energy current in the 1D spinless fermion model with nearest-neighbor interactions (XXZ spin chain), energy current in Lorentz-invariant theories or particle current in interacting Bose gases in arbitrary dimension. Even far from equilibrium, these rates are controlled by state functions, which we call ``expansion potentials'', expressed as integrals of equilibrium Drude weights. This relation between nonequilibrium quantities and linear response implies non-equilibrium Maxwell relations for the Drude weights. We verify our results via DMRG calculations for the XXZ chain.Comment: v2: to appear in PR

Universal nonequilibrium signatures of Majorana zero modes in quench dynamics

The quantum evolution after a metallic lead is suddenly connected to an electron system contains information about the excitation spectrum of the combined system. We exploit this type of "quantum quench" to probe the presence of Majorana fermions at the ends of a topological superconducting wire. We obtain an algebraically decaying overlap (Loschmidt echo) ${\cal L}(t)=| < \psi(0) | \psi(t) > |^2\sim t^{-\alpha}$ for large times after the quench, with a universal critical exponent $\alpha$=1/4 that is found to be remarkably robust against details of the setup, such as interactions in the normal lead, the existence of additional lead channels or the presence of bound levels between the lead and the superconductor. As in recent quantum dot experiments, this exponent could be measured by optical absorption, offering a new signature of Majorana zero modes that is distinct from interferometry and tunneling spectroscopy.Comment: 9 pages + appendices, 4 figures. v3: published versio

Solvable Hydrodynamics of Quantum Integrable Systems

The conventional theory of hydrodynamics describes the evolution in time of chaotic many-particle systems from local to global equilibrium. In a quantum integrable system, local equilibrium is characterized by a local generalized Gibbs ensemble or equivalently a local distribution of pseudo-momenta. We study time evolution from local equilibria in such models by solving a certain kinetic equation, the "Bethe-Boltzmann" equation satisfied by the local pseudo-momentum density. Explicit comparison with density matrix renormalization group time evolution of a thermal expansion in the XXZ model shows that hydrodynamical predictions from smooth initial conditions can be remarkably accurate, even for small system sizes. Solutions are also obtained in the Lieb-Liniger model for free expansion into vacuum and collisions between clouds of particles, which model experiments on ultracold one-dimensional Bose gases.Comment: 6+5 pages, published versio

Essais de génotoxicité in vitro et in vivo applicables à l'environnement hydrique

Cet article est une revue des essais in vitro et in vivo utilisés pour évaluer le caractère génotoxique des micropolluants des milieux environnementaux relatifs aux eaux continentales et marines, rejets liquides d'origine domestique, industrielle ou agricole, sédiments de rivières et boues de stations de traitement d'épuration.Les essais in vitro réalisés sur cellules eucaryotes ou procaryotes sont fondés sur la détection des mutations géniques et chromosomiques, ou la mesure des adduits à l'ADN. Ils constituent des systèmes d'épreuve miniaturisés qui requièrent des volumes d'échantillons faibles; ils se prêtent ainsi au dépistage à grande échelle de la génotoxicité et à l'étude des concentrats et des extraits préparés à partir des milieux contaminés. Ils sont cependant moins bien adaptés à la prédiction de l'impact des micropolluants sur l'environnement.La recherche de conditions d'essai plus proches de la réalité environnementale a conduit au développement des essais in vivo réalisés sur organismes supérieurs, mollusques, poissons ou amphibiens, qui évaluent un potentiel génotoxique à partir d'études cytogénétiques ou d'études du caryotype des organismes exposés.Les critères de génotoxicité étudiés in vitro peuvent être utilisés dans le cadre d'études écoépidémiologiques, sur le terrain, afin d'évaluer l'impact réel des micropolluants présents dans les milieux environnementaux sujets à des contaminations d'origines diverses.This review deals with in vitro and in vivo genotoxicity bioassays carried out to evaluate the genotoxic potential of polluted environmental samples : continental and marine waters, domestic and industrial wastewaters, aquatic sediments and sludges of urban or industrial wastewater treatment plants.The end-points of the in vitro and in vivo assays are : genetic alterations, i.e. reverse and forward mutations, DNA adducts or chramosomic damages, i.e. chromosomic aberrations (AC), micronuclei (MN) and sister chromatid exchanges (SCE).The in vitro assays generally detect adverse effects on DNA only alter concentration or extraction of micropollutants. They constitute miniaturized tools, rapid and easy to use, thus well-suited for large screening studies. In vitro genotoxicity bioassays requiring only small volumes of samples are therefore systems of choice for testing concentrates or extracts from environmental contaminated samples. Among the in vitro assays reviewed, the Salmonella typhimurium gene mutation test is the most often used to assess the genotoxic potential of contaminated samples. However, genotoxicity tests performed on eukaryotic cell cultures are more relevant than those using bacteria for evaluating environmental pollution. The use of fish cell fines appears superior to the use of mammalian cells for assessing an aquatic impact.In vitro bioassays, whether performed on prokaryotic or eukaryotic cells, are limited for predicting the possible impact of genotoxic pollutants on the environment. It is clear that it is difficult to extrapolate in vitro bioassay results to higher organisms in which the response obtained integrates effects of complex metabolizing systems, hormonal regulation and immunological defenses.Therefore, genotoxicity studies performed with aquatic organisms such as molluscs (Mytilus sp.), fish (Umbra pygmaea, Notobranchius rachowi) or amphibians (Pleurodeles waltl) appear more representative of environmental conditions. The genotoxicity end-points of in vivo assays are mainly cytogenetic damage such as the SCE, AC or MN but also take into account DNA adducts. Direct testing of environmental samples without preconcentration is possible with in vivo assays. This means that factors such as bioavailability and metabolism will be integrated direcrly in the response of these assays. Hence, these in vivo assays are more sensitive titan in vitro genotoxicity tests. However, in vivo tests require important volumes of sample and it will be difficult or almost impossible to apply them for testing concentrates or sample extracts, generally only available in small quantities. An interesting area of application of in vivo assays is field studies and ecoepidemioiogy. In this respect, they would constitue an a posteriori control system of pollution effects, assuming that suitable control areas are available to eliminate the influence of confounding factors.As a general conclusion, if is important to emphasize the interest of using both in vitro and in vivo bioassays for evaluating the genotoxicity of contaminated environmental samples. This rationale is based on the fact that in vitro bioassays are well adapted for genotoxicity screening or concentrates and extracts testing, white in vivo tests are interesting because of their better representativity in terms of environmental conditions of exposure to pollutants

Weak in Space, Log in Time Improvement of the Lady{\v{z}}enskaja-Prodi-Serrin Criteria

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time variable.Comment: 14 pages, to appea

Gapless Symmetry-Protected Topological Order

We introduce exactly solvable gapless quantum systems in d dimensions that support symmetry-protected topological (SPT) edge modes. Our construction leads to long-range entangled, critical points or phases that can be interpreted as critical condensates of domain walls “decorated” with dimension (d−1) SPT systems. Using a combination of field theory and exact lattice results, we argue that such gapless SPT systems have symmetry-protected topological edge modes that can be either gapless or symmetry broken, leading to unusual surface critical properties. Despite the absence of a bulk gap, these edge modes are robust against arbitrary symmetry-preserving local perturbations near the edges. In two dimensions, we construct wave functions that can also be interpreted as unusual quantum critical points with diffusive scaling in the bulk but ballistic edge dynamics