Despite of enormous progress in experimental nanophysics theoretical studies of low-dimensional electron systems still remains a challenging task. Indeed, most of the structures are strongly correlated, so that an effective perturbative treatment is impossible due to the lack of a small parameter. The problem can be partly solved within the dynamical mean-field theory (DMFT) paradigm, nevertheless the correlations in physically relevant high-temperature superconductors are of purely non-local nature. The recently developed dual fermion approximation, combining field-theoretical diagram technique and numerical methods, allows for explicit account of spatial correlations. The approximation was shown to be of fastest convergence compared with standard DMFT extensions, and along with renormalization group is used here to study Fermi condensation on a triangular lattice near van Hove singularities. The still debated phenomenon of Fermi condensation is believed to be a precursor to strongly correlated low-temperature instability and is found in this thesis to be robust even at high temperature, making its experimental verification feasible. Unlike homogeneous ferromagnetic ordering a variety of non-collinear ground state configurations emerge as a result of competition among exchange, anisotropy, and dipole-dipole interaction. These particle-like states, e.g. magnetic soliton, skyrmion, domain wall, form a spatially localized clot of magnetic energy. Consistent study of spin, which essentially is a quantum mechanical entity, led to the emergence of spintronics (spin-based electronics) and magnonics (photonics with spin waves), in the meanwhile topologically protected magnetic solitons and skyrmions might potentially be applied for data processing and information storage in next generation of electronic technology (rapidly advancing solitonics and skyrmionics). An ability to easily create, address, and manipulate such structures is among the prerequisite forming a basis of "-onics" technology. It is shown here that spins on a kagome lattice, interacting via Heisenberg exchange and Dzyaloshinskii-Moriya coupling, allow the formation of topologically protected edge states through which a skyrmion can propagate. Not only can chemical methods be used to design novel functionality, but also geometric structuring. It is demonstrated that for graphene sandwiched between two insulating media external circularly-polarized light serves as an effective magnetic field. The direct practical implication permits to control light polarization and induce spin-waves propagating on the surface of e.g. a topological insulator. The newly discovered Dirac materials, graphene and three-dimensional topological insulators, are not easy to handle. In fact, the quasiparticle band function is gapless preventing them from being used in integrated circuits, nevertheless the problem is shown here to be partially relaxed by placing a vacancy on top of it.

We present an effective field theory for interacting electrons in clean semimetals (both three dimensional Dirac semimetals and graphene) in terms of their soft or massless bosonic degrees of freedom. We show, by means of a Ward identity, that the intrinsic semimetal ground state breaks the Sp(4M) symmetry of the theory. In Fermi liquids this enables one to identify the massive, non-Goldstone modes of the theory and integrate them out. Due to the vanishing density of states in semimetals, unlike in Fermi liquids, both Goldstone and non-Goldstone modes are equally soft, and so all two-particle correlations need to be kept. The resulting theory is not perturbative with respect to the electron-electron interaction; rather, it is controlled by means of a systematic loop expansion and allows one to determine the exact asymptotic form of observables in the limits of small frequencies and/or wave vectors. Equivalently, it provides a mechanism of determining the long time-tail and long wavelength behavior of observables and excitations. As a representative application, we use the theory to compute the zero-bias anomaly for the density of states for both short and long-range interactions in two and three dimensions. We find that the leading nonanalyticity in semimetals with a long-ranged interaction appears at the same order in frequency as the one in Fermi liquids, since the effects of the vanishing density of states at the Fermi level are offset by the breakdown of screening. Consequently, we are able to provide a logical scheme to determine the leading non-analytical behavior of observables in semimetals using knowledge of the corresponding non-analyticities in a Fermi liquid. / 2020-01-11

In this thesis we investigate numerically SU(2) theories with Dirac—or Majorana—fermions in the adjoint representation. Majorana fermions have historically proven difficult to treat numerically; here, a change of basis is introduced that allows two Majorana fermions to be expressed in terms of one Dirac fermion. This also provides greater insight into the analysis of the properties of theories with Dirac fermions. Attention is focused on the SU(2) theory with a single Dirac flavour (or equivalently two Majorana flavours). Its lattice phase diagram, spectrum, and the anomalous dimension of the chiral condensate are investigated. We observe a long region of constant mass ratios and an anomalous dimension 0.9 ≲ γ∗ ≲ 0.95. The behaviour of the pion mass and the presence of a light scalar in particular point to behaviour that is not traditionally confining; instead the theory appears to lie in or near the conformal window. The topological susceptibility and instanton size distribution are also investigated, for the one-Dirac-flavour theory and additionally the pure-gauge and two-Dirac-flavour (Minimal Walking Technicolor) theories. The properties are found to not depend on number of flavours, indicating a quenching of the fermions in the topology, also consistent with (near-)conformal behaviour (as has previously been reported in studies of other observables for Minimal Walking Technicolor). The code used is described, and a high-performance computing benchmark developed from it is detailed. While the benchmark was originally developed to investigate the performance of different supercomputer architectures for the class of problems we are interested in. Due to the nature of the code on which it is based, it has an unusual flexibility in the demands it may place on machine’s performance characteristics, which may allow it to be applicable to problems outside of lattice physics. The benchmark is used to characterise a number of machines’ relative performance.

The interfacial adsorption and bulk properties of a collagenous polypeptide derived from chicken eggshell membranes, the 40 KDa polypeptide, and its mixtures with common low molecular weight (LMW) surfactants, SDS, DTAB and C10E8, have been studied for the first time using surface tension, ζ-potential, foam observations and neutron scattering techniques. The biopolymer has been shown to act as an effective biosurfactant by lowering the surface tension of water below the values commonly achieved with conventional LMW surfactants, i.e. γ = 32 ± 1 mN/m. This capability is maximized at its isoelectric point, pH ~5, and addition of NaCl does not have a major impact upon adsorption. On its own, the 40 KDa polypeptide lacks the ability to foam. When mixed with cationic and anionic surfactants, a positive synergy is observed at low concentrations of both materials that exceeds the expectations from the individual components due to the formation of polypeptide/surfactant complexes with high surface activity and high ability to foam and foam stability. At these concentrations, maximum interfacial adsorption is achieved. The synergy is observed in spite of the type of charges present in the surfactant polar head. However, under the conditions studied, there is a difference in behaviour in regards to colloidal stability and surface film formation between the mixed solutions with the anionic SDS and the cationic DTAB. The non-existence of the synergy in the surface adsorption profile of the mixtures of the polypeptide with the non-ionic surfactant C10E8, as obtained via the plate method, suggests that electrostatic interactions are necessary for this strong synergy to act. ζ-potential has been used to prove the electrostatic nature of the synergy. Specular neutron reflection and SANS measurements offered an insight into the complex size and structure. The 40 KDa polypeptide thus offers a promising alternative to the use of high amounts of LMW surfactants in a range of products in which low surface tension and/or high and stable volumes of foams are needed, by combining small amounts of polypeptide and an ionic surfactant. This could be exploited by industries which have an interest in nanoparticle formation such as personal care or pharmaceutical companies. However, further work is needed to fully characterize these interactions.

No description available.

Cette thèse est consacrée à l’étude des propriétés dynamiques des solutions de type soliton d'équations aux dérivées partielles (EDP) dispersives non linéaires. `A travers des exemples-type de telles équations, l'équation de Schrödinger non-linéaire (NLS), l'équation de Korteweg-de Vries généralisée (gKdV) et le système de Schrödinger, on traite du comportement des solutions convergeant en temps grand vers des sommes de solitons (multi-solitons). Dans un premier temps, nous montrons que dans une configuration symétrique, avec des interactions fortes, le comportement de séparation des solitons logarithmique en temps est universel à la fois dans le cas sous-critique et sur-critique pour (NLS). Ensuite, en adaptant les techniques précédentes à l'équation (gKdV), nous prouvons un résultat similaire de l'existence de multi-solitons avec distance relative logarithmique; pour (gKdV), les solitons sont répulsifs dans le cas sous-critique et attractifs dans le cas sur-critique. Finalement, nous identifions un nouveau régime de distance logarithmique où les solitons sont non-symétriques pour le système de Schrödinger non-intégrable; une telle solution n'existe pas dans le cas intégrable pour le système et pour (NLS). / This thesis deals with long time dynamics of soliton solutions for nonlinear dispersive partial differential equation (PDE). Through typical examples of such equations, the nonlinear Schrödinger equation (NLS), the generalized Korteweg-de Vries equation (gKdV) and the coupled system of Schrödinger, we study the behavior of solutions, when time goes to infinity, towards sums of solitons (multi-solitons). First, we show that in the symmetric setting, with strong interactions, the behavior of logarithmic separation in time between solitons is universal in both subcritical and supercritical case. Next, adapting previous techniques to (gKdV) equation, we prove a similar result of existence of multi-solitons with logarithmic relative distance; for (gKdV), the solitons are repulsive in the subcritical case and attractive in the supercritical case. Finally, we identify a new logarithmic regime where the solitons are non-symmetric for the non-integrable coupled system of Schrödinger; such solution does not exist in the integrable case for the system and for (NLS).

La compréhension des effets des interactions dans un ensemble de particules quantiques représente un enjeu majeur de la physique moderne. Les atomes ultra-froids sont rapidement devenus un outil incomparable pour étudier ces systèmes quantiques fortement corrélés. Dans cette thèse, nous présentons plusieurs travaux portant sur les propriétés d’un mélange de superfluides de Bose et de Fermi créé à l’aide de vapeurs ultra-froides de ⁷Li et de ⁶Li. Nous étudions tout d'abord les propriétés hydrodynamiques du mélange en créant un contre-courant entre les superfluides. L'écoulement est dissipatif uniquement au dessus d'une vitesse critique que nous mesurons dans le crossover BEC-BCS. Une simulation numérique d’un contre-courant de deux condensats permet de mieux comprendre les mécanismes sous-jacents mis en jeu dans la dynamique. En particulier, l'étude numérique fournit des preuves supplémentaires que l'origine de la dissipation dans nos expériences est liée à l'émission d'excitation élémentaires dans chaque superfluide. Finalement, nous nous intéressons aux pertes inélastiques par recombinaison à trois corps qui peuvent limiter la stabilité de nos nuages. Ces pertes sont intimement liées aux corrélations à courte distance présentes dans le système et sont ainsi connectées aux propriétés universelles du gaz quantique. Cela se manifeste notamment par l’apparition de dépendances en densité ou en température inusuelles du taux de perte lorsque le système devient fortement corrélé. Nous démontrons cet effet dans deux exemples où les interactions sont résonantes, le cas du gaz de Bose unitaire et celui de notre mélange de superfluides Bose-Fermi. Plus généralement, nos travaux montrent que ces pertes inélastiques peuvent être utilisées pour sonder les corrélations quantiques dans un système en fortes interactions. / Understanding the effect of interactions in quantum many-body systems presents some of the most compelling challenges in modern physics. Ultracold atoms have emerged as a versatile platform to engineer and investigate these strongly correlated systems. In this thesis, we study the properties of a mixture of Bose and Fermi superfluids with tunable interactions produced using ultracold vapors of ⁷Li and ⁶Li. We first study the hydrodynamic properties of the mixture by creating a counterflow between the superfluids. The relative motion only exhibit dissipation above a critical velocity that we measure in the BEC-BCS crossover. A numerical simulation of counterflowing condensates allows for a better understanding of the underlying mechanisms at play in the dynamics. In particular, this numerical study provides additional evidence that the onset of friction in our experiment is due to the simultaneous generation of elementary excitations in both superfluids. Finally, we consider the inelastic losses that occur via three-body recombination in our cold gases. This few-body process is intimately related to short-distance correlations and is thereby connected to the universal properties of the many-body system. This manifests as the apparition of an unusual dependence on density or temperature in the loss rate when increasing the interactions. We demonstrate this effect in two examples where interactions are resonant: the case of a dilute unitary Bose gas and the one of impurities weakly coupled to a unitary Fermi gas. More generally, our work shows that inelastic losses can be used to probe quantum correlations in a many-body system.