Conservation laws in Skyrme-type models

The zero curvature representation of Zakharov and Shabat has been generalized recently to higher dimensions and has been used to construct non-linear field theories which either are integrable or contain integrable submodels. The Skyrme model, for instance, contains an integrable subsector with infinitely many conserved currents, and the simplest Skyrmion with baryon number one belongs to this subsector. Here we use a related method, based on the geometry of target space, to construct a whole class of theories which are either integrable or contain integrable subsectors (where integrability means the existence of infinitely many conservation laws). These models have three-dimensional target space, like the Skyrme model, and their infinitely many conserved currents turn out to be Noether currents of the volume-preserving diffeomorphisms on target space. Specifically for the Skyrme model, we find both a weak and a strong integrability condition, where the conserved currents form a subset of the algebra of volume-preserving diffeomorphisms in both cases, but this subset is a subalgebra only for the weak integrable submodel.Comment: Latex file, 22 pages. Two (insignificant) errors in Eqs. 104-106 correcte

Quantum Stochastic Processes: A Case Study

We present a detailed study of a simple quantum stochastic process, the quantum phase space Brownian motion, which we obtain as the Markovian limit of a simple model of open quantum system. We show that this physical description of the process allows us to specify and to construct the dilation of the quantum dynamical maps, including conditional quantum expectations. The quantum phase space Brownian motion possesses many properties similar to that of the classical Brownian motion, notably its increments are independent and identically distributed. Possible applications to dissipative phenomena in the quantum Hall effect are suggested.Comment: 35 pages, 1 figure

Discrete approximation of the free Fock space

International audienceWe prove that the free Fock space {\F}(\R^+;\C), which is very commonly used in Free Probability Theory, is the continuous free product of copies of the space \C^2. We describe an explicit embeding and approximation of this continuous free product structure by means of a discrete-time approximation: the free toy Fock space, a countable free product of copies of \C^2. We show that the basic creation, annihilation and gauge operators of the free Fock space are also limit of elementary operators on the free toy Fock space. When applying these constructions and results to the probabilistic interpretations of these spaces, we recover some discrete approximations of the semi-circular Brownian motion and of the free Poisson process. All these results are also extended to the higher multiplicity case, that is, {\F}(\R^+;\C^N) is the continuous free product of copies of the space \C^{N+1}

Caractérisation physico-chimique de tourbe utilisée en épuration d'eau usée urbaine

International audiencePeat beds are currently used for urban water treatment procedures, although reactions occuring within such beds are still unknown : filtration, ion exchange, adsorption or biodégradation by immobilized biomass. This work intends to characterize by physico-chemical parameters the evolution of peat used in water treatment. It is based upon comparison of 5 physical and 4 physico-chemical parameters on peat sampled either on 2 french treatment plants located in Queveauvillers (Somme department) and in Levis Saint Nom (Yvelynes department) or from 2 commercially available eutrophic and oligotrophic sources. Heurteauville and Floratorf, respectively.Among physical parameter tested, namely humidity and (M.O.T.) organic matter content, (R.A.) air and (R.F..) water retention values and (M.V.A.) apparent density, most significant changes were observed with organic matter content, i.e. its weight loss between 105 and 500 "C.Several physico-chemical parameter determinations have been tested, including equilibrium pH in peat suspensions, (C.E.P.) proton, (C.F.C.) alcaline and (C.E.M.) metallic cation exchange capacities. The first and most easily measured parameters, i.e. equilibrium pH within 40 g/1 peat suspensions, showed most significant variations when peat was used in treatment plants. Thus we recomend to compare organic matter content and/or equilibrium pH of peat sampled either on water treatment beds or on a reference source, i.e. « unused » peat, before deciding the renewal of such beds. Both parameters evolution may be related to inorganic deposition on beds, biodégradation of peat organic matter and/or partial dissolution of humic and fulvie acids in neutral or slightly basic pH waste waters, which all may play a prominent role in this treatment procedure.Des lits de tourbe sont couramment utilisés en assainissement urbain bien que la nature des phénomènes d'épuration soient encore inconnus : filtration, échange d'ions, adsorption ou biodégradation par biomasse immobilisée. Ce travail tente de caractériser l'évolution de la tourbe au cours de son utilisation en station à l'aide de paramètres physico-chimiques. Il repose sur la comparaison des valeurs de 5 paramètres physiques et 4 paramètres physico-chimiques d'échantillons de tourbe provenant soit de 2 stations françaises situées à Queveauvillers (Somme) et Levis Saint-Nom (Yvelynes), soit de 2 sources disponibles commercialement, à savoir une tourbe brune eutrophe d'Heurteauville et une tourbe blonde oligotrophe Floratorf. Parmi les paramètres physiques que nous avons testés, le taux d'humidité ou de matière organique (M.O.T.), de rétention d'air (R.A.) ou d'eau (R.E.) et la masse volumique apparente (M.V.A.), les variations les plus significatives ont été observées avec les taux de matière organique des échantillons de tourbe, c'est-à-dire leur perte de poids entre 105 et 500 "C. Nous avons mesuré plusieurs paramètres physico-chimiques, en particulier le pH d'équilibre, les capacités d'échange protonique (C.E.P.), canonique (C.E.C.) et métallique (C.E.M.) : la détermination du pH d'équilibre de suspensions de tourbe à 40 g/1 semble la méthode la plus simple à mettre en oeuvre et celle qui a permis de mettre en évidence les variations les plus significatives lors de l'utilisation de la tourbe en station. Nous suggérons par conséquent de comparer le taux de matière organique et/ou le pH d'équilibre d'échantillons de tourbe prélevés dans les lits et dans des lots de référence, c'est-à-dire non utilisés en station, avant de décider de renouveler ces lits. Les variations de ces deux paramètres lors de l'utilisation de la tourbe sont la conséquence de dépôts de matière minérale sur les lits, de biodégradation de la matière organique de la tourbe et/ou de la dissolution partielle des acides humiques et fulviques dans des eaux usées de pH neutre ou légèrement alcalin, phénomènes qui peuvent tous avoir un effet important sur ce procédé de traitement

A partition-free approach to transient and steady-state charge currents

We construct a non-equilibrium steady state and calculate the corresponding current for a mesoscopic Fermi system in the partition-free setting. To this end we study a small sample coupled to a finite number of semi-infinite leads. Initially, the whole system of quasi-free fermions is in a grand canonical equilibrium state. At t = 0 we turn on a potential bias on the leads and let the system evolve. We study how the charge current behaves in time and how it stabilizes itself around a steady state value, which is given by a Landauer-type formula.Comment: 14 pages, submitte

Non-equilibrium states of a photon cavity pumped by an atomic beam

We consider a beam of two-level randomly excited atoms that pass one-by-one through a one-mode cavity. We show that in the case of an ideal cavity, i.e. no leaking of photons from the cavity, the pumping by the beam leads to an unlimited increase in the photon number in the cavity. We derive an expression for the mean photon number for all times. Taking into account leaking of the cavity, we prove that the mean photon number in the cavity stabilizes in time. The limiting state of the cavity in this case exists and it is independent of the initial state. We calculate the characteristic functional of this non-quasi-free non-equilibrium state. We also calculate the energy flux in both the ideal and open cavity and the entropy production for the ideal cavity.Comment: Corrected energy production calculations and made some changes to ease the readin

Non Markovian Quantum Repeated Interactions and Measurements

A non-Markovian model of quantum repeated interactions between a small quantum system and an infinite chain of quantum systems is presented. By adapting and applying usual pro jection operator techniques in this context, discrete versions of the integro-differential and time-convolutioness Master equations for the reduced system are derived. Next, an intuitive and rigorous description of the indirect quantum measurement principle is developed and a discrete non Markovian stochastic Master equation for the open system is obtained. Finally, the question of unravelling in a particular model of non-Markovian quantum interactions is discussed.Comment: 22 page

Fluctuations of Quantum Currents and Unravelings of Master Equations

The very notion of a current fluctuation is problematic in the quantum context. We study that problem in the context of nonequilibrium statistical mechanics, both in a microscopic setup and in a Markovian model. Our answer is based on a rigorous result that relates the weak coupling limit of fluctuations of reservoir observables under a global unitary evolution with the statistics of the so-called quantum trajectories. These quantum trajectories are frequently considered in the context of quantum optics, but they remain useful for more general nonequilibrium systems. In contrast with the approaches found in the literature, we do not assume that the system is continuously monitored. Instead, our starting point is a relatively realistic unitary dynamics of the full system.Comment: 18 pages, v1-->v2, Replaced the former Appendix B by a (thematically) different one. Mainly changes in the introductory Section 2+ added reference

Impact of recycling and lateral sediment input on grain size fining trends – implications for reconstructing tectonic and climate forcings in ancient sedimentary systems

Grain size trends in basin stratigraphy are thought to preserve a rich record of the climatic and tectonic controls on landscape evolution. Stratigraphic models assume that over geological timescales, the downstream profile of sediment deposition is in dynamic equilibrium with the spatial distribution of tectonic subsidence in the basin, sea level and the flux and calibre of sediment supplied from mountain catchments. Here, we demonstrate that this approach in modelling stratigraphic responses to environmental change is missing a key ingredient: the dynamic geomorphology of the sediment routing system. For three large alluvial fans in the Iglesia basin, Argentine Andes we measured the grain size of modern river sediment from fan apex to toe and characterise the spatial distribution of differential subsidence for each fan by constructing a 3D model of basin stratigraphy from seismic data. We find, using a self-similar grain size fining model, that the profile of grain size fining on all three fans cannot be reproduced given the subsidence profile measured and for any sediment supply scenario. However, by adapting the self-similar model, we demonstrate that the grain size trends on each fan can be effectively reproduced when sediment is not only sourced from a single catchment at the apex of the system, but also laterally, from tributary catchments and through fan surface recycling. Without constraint on the dynamic geomorphology of these large alluvial systems, signals of tectonic and climate forcing in grain size data are masked and would be indecipherable in the geological record. This has significant implications for our ability to make sensitive, quantitative reconstructions of external boundary conditions from the sedimentary record