Diffusion in stationary flow from mesoscopic nonequilibrium thermodynamics

We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of nonequilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation that is compared with others derived from the kinetic theory and projector operator techniques. This equation exhibits violation of the fluctuation-dissipation theorem. By implementing the hydrodynamic regime described by the first moments of the nonequilibrium distribution, we find relaxation equations for the diffusion current and pressure tensor, allowing us to arrive at a complete description of the system in the inertial and diffusion regimes. The simplicity and generality of the method we propose makes it applicable to more complex situations, often encountered in problems of soft-condensed matter, in which not only one but more degrees of freedom are coupled to a nonequilibrium bath.

Kinetic equations for difussion in the presence of entropic barriers

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

Algebraic decay of velocity fluctuations near a wall

Computer simulations of the dynamics of a colloidal particle suspended in a fluid confined by an interface show that the asymptotic decay of the velocity correlation functions is algebraic. The exponents of the long-time tails depend on the direction of motion of the particle relative to the surface, as well as on the specific nature of the boundary conditions. In particular, we find that for the angular velocity correlation function, the decay in the presence of a slip surface is faster than the one corresponding to a stick one. An intuitive picture is introduced to explain the various long-time tails, and the simulations are compared with theoretical expressions where available.

Entropic transport in confined media: a challenge for computational studies in biological and soft-matter systems

Transport in small-scale biological and soft-matter systems typically occurs under confinement conditions in which particles proceed through obstacles and irregularities of the boundaries that may significantly alter their trajectories. A transport model that assimilates the confinement to the presence of entropic barriers provides an efficient approach to quantify its effect on the particle current and the diffusion coefficient. We review the main peculiarities of entropic transport and treat two cases in which confinement effects play a crucial role, with the appearance of emergent properties. The presence of entropic barriers modifies the mean first-passage time distribution and therefore plays a very important role in ion transport through micro- and nano-channels. The functionality of molecular motors, modeled as Brownian ratchets, is strongly affected when the motor proceeds in a confined medium that may constitute another source of rectification. The interplay between ratchet and entropic rectification gives rise to a wide variety of dynamical behaviors, not observed when the Brownian motor proceeds in an unbounded medium. Entropic transport offers new venues of transport control and particle manipulation and new ways to engineer more efficient devices for transport at the nanoscale.

Bose-Fermi mixtures in optical lattices

Using mean field theory, we have studied Bose-Fermi mixtures in a one-dimensional optical lattice in the case of an attractive boson-fermion interaction. We consider that the fermions are in the degenerate regime and that the laser intensities are such that quantum coherence across the condensate is ensured. We discuss the effect of the optical lattice on the critical rotational frequency for vortex line creation in the Bose-Einstein condensate, as well as how it affects the stability of the boson-fermion mixture. A reduction of the critical frequency for nucleating a vortex is observed as the strength of the applied laser is increased. The onset of instability of the mixture occurs for a sizably lower number of fermions in the presence of a deep optical lattice.

Dynamic arrest in polymer melts: competition between packing and intramolecular barriers

We present molecular dynamics simulations of a simple model for polymer melts with intramolecular barriers. We investigate structural relaxation as a function of the barrier strength. Dynamic correlators can be consistently analyzed within the framework of the mode coupling theory of the glass transition. Control parameters are tuned in order to induce a competition between general packing effects and polymer-specific intramolecular barriers as mechanisms for dynamic arrest. This competition yields unusually large values of the so-called mode coupling theory exponent parameter and rationalizes qualitatively different observations for simple bead-spring and realistic polymers. The systematic study of the effect of intramolecular barriers presented here also establishes a fundamental difference between the nature of the glass transition in polymers and in simple glass formers.

Quantum Hall Phases of two-component bosons

The recent production of synthetic magnetic fields acting on electroneutral particles, such as atoms or photons, has boosted interest in the quantum Hall physics of bosons. Adding pseudospin 1/2 to the bosons greatly enriches the scenario, as it allows them to form an interacting integer quantum Hall (IQH) phase with no fermionic counterpart. Here we show that, for a small two-component Bose gas on a disk, the complete strongly correlated regime, extending from the integer phase at filling factor ν = 2 to the Halperin phase at filling factor ν = 2 / 3, is well described by composite fermionization of the bosons. Moreover we study the edge excitations of the IQH state, which, in agreement with expectations from topological field theory, are found to consist of forward-moving charge excitations and backward-moving spin excitations. Finally, we demonstrate how pair-correlation functions allow one to experimentally distinguish the IQH state from competing states, such as non-Abelian spin singlet (NASS) states.

Persistent random walk model for transport trough thin slabs

We present a model for transport in multiply scattering media based on a three-dimensional generalization of the persistent random walk. The model assumes that photons move along directions that are parallel to the axes. Although this hypothesis is not realistic, it allows us to solve exactly the problem of multiple scattering propagation in a thin slab. Among other quantities, the transmission probability and the mean transmission time can be calculated exactly. Besides being completely solvable, the model could be used as a benchmark for approximation schemes to multiple light scattering.

Effects of the epitaxial layer thickness on the noise properties of Schottky barrier diodes

An analytical theory to describe the combined effects of the epitaxial layer thickness and the ohmic contact on the noise properties of Schottky barrier diodes is presented. The theory, which provides information on both the local and the global noise properties, takes into account the finite size of the epitaxial layer and the effects of the back ohmic contact, and applies to the whole range of applied bias. It is shown that by scaling down the epitaxial layer thickness, the current regime in which the noise temperature displays a shot-noise-like behavior increases at the cost of reducing the current range in which the thermal-noise-like behavior dominates. This improvement in noise temperature is limited by the effects of the ohmic contact, which appear for large currents. The theory is formulated on general trends, allowing its application to the noise analysis of other semiconductor devices operating under strongly inhomogeneous distributions of the electric field and charge concentrations.

Effects of the epitaxial layer thickness on the noise properties of Schottky barrier diodes

An analytical theory to describe the combined effects of the epitaxial layer thickness and the ohmic contact on the noise properties of Schottky barrier diodes is presented. The theory, which provides information on both the local and the global noise properties, takes into account the finite size of the epitaxial layer and the effects of the back ohmic contact, and applies to the whole range of applied bias. It is shown that by scaling down the epitaxial layer thickness, the current regime in which the noise temperature displays a shot-noise-like behavior increases at the cost of reducing the current range in which the thermal-noise-like behavior dominates. This improvement in noise temperature is limited by the effects of the ohmic contact, which appear for large currents. The theory is formulated on general trends, allowing its application to the noise analysis of other semiconductor devices operating under strongly inhomogeneous distributions of the electric field and charge concentrations.

Étude, par principes premiers, des effets de la corrélation entre électrons sur les propriétés électroniques et magnétiques de polymères pontés et de supraconducteurs à haute température critique

La présente thèse traite de la description de systèmes complexes, notamment des polymères et des cuprates, par la théorie de la fonctionnelle de la densité. En premier lieu, la théorie de la fonctionnelle de la densité ainsi que différentes fonctionnelles utilisées pour simuler les matériaux à l’étude sont présentées. Plus spécifiquement, les fonctionnelles LDA et GGA sont décrites et leurs limites sont exposées. De plus, le modèle de Hubbard ainsi que la fonctionnelle LDA+U qui en découle sont abordés dans ce chapitre afin de permettre la simulation des propriétés de matériaux à forte corrélation électronique. Par la suite, les résultats obtenus sur les polymères sont résumés par deux articles. Le premier traite de la variation de la bande interdite entre les polymères pontés et leurs homologues non pontés. Le second se penche sur l’étude de polymères à faible largeur de bande interdite. Dans ce dernier, il sera démontré qu’une fonctionnelle hybride, contenant de l’échange exact, est nécessaire afin de décrire les propriétés électroniques des systèmes à l’étude. Finalement, le dernier chapitre est consacré à l’étude des cuprates supraconducteurs. La LDA+U pouvant rendre compte de la forte localisation dans les orbitales 3d des atomes de cuivre, une étude de l’impact de cette fonctionnelle sur les propriétés électroniques est effectuée. Un dernier article investiguant différents ordres magnétiques dans le La2CuO4 dopé termine le dernier chapitre. On trouve aussi, en annexe, un complément d’information pour le second article et une description de la théorie de la supraconductivité de Bardeen, Cooper et Schrieffer.

Etudes ab initio des effets de la température sur le spectre optique des semi-conducteurs

Thèse réalisée en cotutelle avec l'Université Catholique de Louvain (Belgique)

Caractérisation et modélisation de l’aimant organique NIT-2Py

L'aimant organique NIT-2Py a été caractérisé expérimentalement et ses propriétés ont été simulées numériquement à partir de la théorie de la fonctionnelle de la densité. Le magnétisme dans ce matériau provient de la présence d'un électron non apparié sur chaque molécule qui a ainsi un moment magnétique non nul. Ceci a été confirmé par des simulations sur une molécule isolée. Les molécules de NIT-2Py cristallisent dans le groupe d'espace P21/c avec huit molécules par maille élémentaire pour former la structure cristalline Alpha étudiée dans ce document. Le moment effectif de la susceptibilité et l'entropie magnétique totale montre que ce matériau est un système de spins 1/2 avec un spin par molécule. Les mesures de chaleur spécifique ont mis en évidence la présence de deux phases magnétiques ordonnées à basse température qui sont séparées par un plateau en aimantation. Une première phase est observée à des champs magnétiques inférieurs à 2.2 T et a une température de transition de 1.32 K en champ nul. Les mesures de susceptibilité magnétique et d'aimantation ont permis d'établir que cette phase ordonnée est antiferromagnétique. Ceci est confirmé par les simulations numériques. La deuxième phase est induite par le champ magnétique avec une température de transition de 0.53 K à 6 T. L'information disponible sur cette phase est limitée et l'étude du système à l'extérieur des phases ordonnées en donne une meilleure compréhension. Un modèle de spins S=1/2 isolés et de dimères S=0 isolés reproduit bien les mesures d'aimantation et de chaleur spécifique au-dessus de 3 K. L'application d'un champ magnétique réduit l'écart d'énergie entre le singulet et le triplet du dimère jusqu'au croisement qui se produit à 6 T. La phase induite émerge précisément à ce croisement et on spécule l'existence d'un condensat de Bose-Einstein des états triplets.