This research studied the Anderson localization of electrons in two-channel wires with correlated disorder and in DNA molecules. It involved an analytical calculation part where the formula for the inverse localization length for electron states in a two-channel wire is derived. It also involved a computational part where the localization length is calculated for some DNA molecules. Electron localization in two-channel wires with correlated disorder was studied using a single-electron tight-binding model. Calculations were within second-order Born-approximation to second-order in disorder parameters. An analytical expression for localization length as a functional of correlations in potentials was found. Anderson localization in DNA molecules were studied in single-channel wire and two-channel models for electron transport in DNA. In both of the models, some DNA sequences exhibited delocalized electron states in their energy spectrum. Studies with two-channel wire model for DNA yielded important link between electron localization properties and genetic information.

Dans cette thèse, nous étudions la diffusion cohérente de la lumière se propageant dans un milieu désordonné. Nous nous intéressons à des phénomènes tels que la super- et sousradiance et la localisation d’Anderson qui sont liées aux interférences et au désordre spatial. Cependant, la différence fondamentale entre la sousradiance et la localisation d'Anderson doit encore être clarifiée. Cette thèse donne de nouvelles idées pour la compréhension de ces phénomènes et nous présentons une nouvelle méthode pour observer la localisation d'Anderson. On développe un modèle à champ moyen qui ne contient pas de désordre, et nous montrons que super- et sousradiance ne nécessitent pas de désordre contrairement à la localisation d’Anderson. Dans ce travail théorique, le couplage entre la lumière et les atomes est réduit à une matrice de couplage entre les atomes en calculant la trace sur les degrés de liberté de la lumière, ce qui nous amène à un problème linéaire pour les dipôles atomiques. L'étude des valeurs propres et des modes propres de cette matrice permet de déterminer des modes super- et sousradiant, et de sonder la transition de phase de localisation avec une scaling analysis. De plus, le lien avec l'expérience est fait en montrant que les fluctuations de l’intensité augmentent à travers la transition de localisation. Le système est étudié en régime stationnaire, quand le milieu est continûment chargé par un laser et que celui-ci atteint l’équilibre, et en dynamique, quand le laser est éteint et que le milieu se décharge de l’énergie stockée. Enfin, nous présentons un travail préliminaire qui montre que le désordre diagonal peut être une bonne stratégie pour atteindre la localisation d’Anderson. / In this thesis, we investigate the coherent scattering of light propagating in a random medium. We are interested in phenomena like the super- and subradiance and Anderson localization that are related to waves interferences and spatial disorder. However, the fundamental difference between subradiance and Anderson localization still needs to be clarified. This thesis gives new elements for the understanding of these phenomena and we present a new method to observe Anderson localization. A mean-field model that does not contain disorder is developed, and we show that super- and subradiance do not require disorder whereas Anderson localization does. In this theoretical work, the coupling between the light and many atoms is reduced to a coupling matrix between the atoms by tracing over the degrees of freedom of the light, which results in a linear problem for the atomic dipoles. The study of the eigenvalues and eigenmodes of this matrix then allows to determine the super- and subradiant modes, and to probe the Anderson localization phase transition with a scaling analysis. Furthermore, the link to the experiment is realized by showing that the intensity fluctuations present an increase at the localization transition. The system is studied in the steady-state regime when the medium is continuously charged by a laser until reaches a stationary regime, and the decay dynamics, when the laser is switched off, so the cloud releases the energy stored. Finally, we present a preliminary work that shows that the diagonal disorder might be a good strategy to reach Anderson localization.

Motivated by previous relevant research on phononics including both active and passive phononics, the interest of faster turnability and more functions of the active phononics of further study led to this proposing research topic: magnetic field tunable active functional phononics. The first design of magnetic field tunable reciprocal--non-reciprocal transmission acoustic device was established, material was characterized, and numerical simulation has been performed. The simulation results show clear T-symmetric breaking non-reciprocity due to energy level splitting effect with Doppler effect – an acoustic Zeeman effect. Inspired by this preliminary work, further experiments were planned to demonstrate this effective Zeeman effect in phononics and effectively charged phonons in water based ferro-fluid. The objectives of this work as the next series of tasks were to illustrate acoustic Zeeman effect and acoustic Landau levels in various strength of magnetic field to investigate a design non-reciprocal sound device with magnetic field switching, which could be controlled on the amount of non-reciprocity with the strength of magnetic field. Once this new field first discovered by the proposed study tasks, more active tunable magnetic field phononics devices could be designed and exemplified in terms of both simulations and experiments. Faster and more controllable active phononic devices could be designed and made based on this study. The experimental maximum non-reciprocity was measured as 22 dB difference and the amount of the non-reciprocity can be further controlled by adjusting the strength of the external magnetic field. The remote pumping system in the device worked as expected and did not introduce any impact of the cavity properties.

Ultrasonic wave transport in strongly scattering, disordered media is investigated via analysis of the multiply-scattered transmitted field. Measurements of transverse confinement, statistics, and correlations of the intensity were performed on an aluminum mesoglass, where aluminum beads were brazed together to form a porous slab sample. Comparison of the transverse confinement measurements with the self-consistent theory of localization was used to identify and locate a mobility edge in the sample at f = 1.1011 MHz, enabling a measurement of the critical exponent nu characterizing the Anderson transition, nu ~ 1.6–2. Infinite-range C0 correlations were observed, and observed to grow dramatically near the mobility edge, along with the C2 and C3 correlations. Measurements of the multifractal exponent Delta_2 were able to confirm the link between C0 correlations and Anderson localization. Experiments using the aluminum mesoglass with ethanol-filled pores showed evidence of two nearly-independent propagating modes, one of which appears to be characterized by a strongly renormalized diffusion coefficient. The density of states and level spacing statistics were investigated using a different mesoglass, constructed by sintering glass beads percolated on a random lattice. Direct measurements of these quantities were obtained by cutting small samples of this mesoglass, allowing individual vibrational modes to be resolved. The density of states showed a plateau extending well into the expected Debye regime, and evidence of a Boson peak was observed at low frequencies. The level spacing statistics indicated that transport in the frequency ranges measured was on the diffusive side of the mobility edge, showing agreement with the predictions of the GOE from random matrix theory. The dynamics of a suspension of bubbles were investigated using phase-based Diffusing Acoustic Wave Spectroscopy, where phase correlations were found to give additional information beyond traditional field- and intensity-based correlation measurements. / October 2015

We develop methods how to calculate charge transport in disordered systems applicable in all disorder regimes. They allow to calculate vertex corrections to the electrical conductivity and the diffusion coefficient in models of elastically scattered electrons in the presence of random scatterers. These methods are based on an asymptotic limit to high spatial dimensions. The resulting formulas lead to reliable results free of unphysical behavior, as illustrated on a gallery of numerical examples.

Dans cette thèse, nous étudions théoriquement plusieurs effets liés à la localisation d'Anderson, dans le contexte des atomes froids. Dans les systèmes d'atomes froids, le désordre est généralement créé à l'aide d'une figure de tavelure optique. Dans la première partie de la thèse, nous discutons des spécificités de ces potentiels optiques, et nous nous intéressons en particulier aux propriétés spectrales. Les expériences usant de l'interaction lumière-matière offrent d'intéressantes possibilités. Dans ce cadre, nous considérons dans une deuxième partie de la thèse l'étalement d'un paquet d'ondes atomique, initialement lancé avec une vitesse non nulle dans un potentiel désordonné. Nous trouvons qu'après un mouvement balistique, le centre de masse du paquet subit une rétro-réflection et retourne lentement à sa position initialle, se comportant comme un boomerang. Nous introduisons ensuite les interactions inter-atomiques dans une troisième partie. Nous considèrons des gaz dilués de bosons condensés, et traitons les interactions au niveau champ moyen. Plusieurs situations sont étudiées numériquement, en particulier le boomerang quantique, et l'étalement dynamique -- à la fois en impulsion et en énergie -- d'ondes de matière préparées en ondes planes. Dans la dernière partie de la thèse, nous montrons que des modèles chaotiques offrent des perspectives intéressantes pour l'étude de la localisation d'Anderson. D'une part, nous présentons des éléments probants en faveur d'un kick rotor sans spin dans l'ensemble symplectique. D'autre part, le réexamen de modèles communément étudiés de kick rotors quasi-périodiques révèle des résultats intrigants. / This thesis theoretically investigates several effects related to Anderson localization, focusing on the context of disordered and chaotic cold-atomic systems. In cold-atomic systems, optical speckle patterns are often used to create the disorder. The resulting potentials felt by the atoms differ from Gaussian random potentials, commonly assumed in the description of condensed-matter systems. In the first part of the thesis, we discuss their specificities, with an emphasis on the spectral properties. Atom-optics experiments offer interesting possibilities, such as the possibility to directly probe the atoms inside the disordered potential. In view of these possibilities, we consider in the second part of the thesis the spreading of matter wave packets initially launched with a non-zero velocity. We find that after an initial ballistic motion, the packet center-of-mass experiences a retroreflection and slowly returns to its initial position, mimicking a boomerang. Atom-atom interactions are then introduced in a third part. We consider dilute condensed bosonic gases, and treat the interactions at the mean-field (Gross-Pitaevskii) level. Various situations are studied numerically, in particular the quantum boomerang scenario, and the dynamical spreading both in momentum and energy of matter waves prepared as plane waves. In the last part, we show that chaotic models offer interesting prospects for the study of Anderson localization. On the one hand, we present strong evidences in favor of a spinless kicked rotor in the sympletic ensemble. On the other hand, a second look at a commonly studied quasi-periodically modulated kicked rotor reveals intriguing results.

Cette thèse vise à étudier la stabilité des phases métalliques et isolantes en compétition dans les systèmes 2D 1T-VS2 et composés dérivés, Cu⅔V⅓V2S4 et Sr3V5S11. Pour atteindre cet objectif, nous avons développé et optimisé des voies ad hoc de synthèse à hautes pressions pour stabiliser les nouvelles phases sous forme de monocristal de haute qualité, qui nous permettrait d’étudier les propriétés électroniques et de transport. Un important résultat de notre étude est le contrôle de la concentration, x, des atomes interstitiels V situés entre les plans adjacents VS2 dans le système V1+xS2, qui est obtenu en variant la pression de synthèse. Cela nous a permis d’explorer le diagramme de phase T-x du système. Le résultat principal de cette étude est que la phase CDW observée dans la phase stoichiométrique (x = 0) disparait rapidement avec x, alors que les propriétés métalliques sont augmentées. Dans Cu⅔V⅓V2S4, la substitution partielle du V par Cu dans le site interstitiel change complètement le système en un fermion semi-lourd aux caractéristiques prononcées du liquide de Fermi jusqu’à ~ 20 K, où la transition de Kondo apparait. Ce phénomène inattendu dans les sulfures suggère que la force des corrélations électroniques dans ces composés peut être pilotée en variant simplement la nature chimique et la concentration de l’atome intercalé. La force modérée des corrélations dans Cu⅔V⅓V2S4 ouvre le chemin vers une description théorique fiable de la disparition du régime de liquide de Fermi. Les corrélations électroniques apparaissent importantes aussi pour piloter une phase isolante dans Sr3V5S11, qui devrait être un métal d’après la théorie conventionnelle de bande. Dans ce cas, les corrélations peuvent être augmentées par la dimensionnalité réduite créée par un large écartement des couches VS2 et par une modulation structurale 1D des couches. Des études supplémentaires pourront clarifier s’il s’agit d’un mécanisme d’Anderson de faible localisation qui contribue à la stabilisation d’un état isolant dans les plans pristine métalliques VS2. / This thesis work aims at studying the stability of the metallic and insulating phases that compete in the two-dimensional 1T-VS2 system and related compounds, Cu⅔V⅓V2S4, and Sr3V5S11. We have developed and optimized ad hoc high-pressure synthesis routes in order to stabilize the above novel phases in the form of high-quality single crystals, which enabled us to reliably investigate their electronic and transport properties. An important achievement of our study is the control of the concentration, x, of interstitial V atoms located between adjacent VS2 planes in the V1+xS2 system, which is obtained by varying synthesis pressure. This has enabled us to explore the T-x phase diagram of the system. The main result of this study is that the CDW phase observed in the stoichiometric (x=0) phase quickly disappears with x, whilst the metallic properties are enhanced. In Cu⅔V⅓V2S4, the partial substitution of V for Cu in the interstitial site is found to completely change the system into a semi-heavy fermion with pronounced Fermi-liquid characteristics down to ~20 K, where a Kondo transition occurs. These unexpected phenomena in sulfides suggest that the strength of the electronic correlations in these compounds can be tuned by simply varying the chemical nature and concentration of the intercalant atom. The moderate strength of the correlations in Cu⅔V⅓V2S4 opens the way towards a reliable theoretical description of the breakdown of the Fermi liquid regime. Electronic correlations appear to be important also to drive an insulating phase in Sr3V5S11, which should be a metal within a conventional band picture. In this case, the correlations may be enhanced by the reduced dimensionality caused by a large spacing between VS2 layers and by a 1D structural modulation of the layers. Further studies may clarify whether the Anderson’s mechanism of weak localization contributes to the stabilization of an insulating state in the pristine metallic VS2 planes.

La problématique de cette thèse est l'étude de la localisation d'un condensat de Bose-Einstein confiné harmoniquement et quasi-1D à travers lequel différents potentiels désordonnés sont transportés. Cette problématique qui se veut pleinement pertinente pour les expérimentalistes est à priori difficile à traiter. Cela est dû au caractère non-linéaire, inhomogène et hors-équilibre du système. De ce fait, la plage des vitesses du désordre est limitée d'une part par la vitesse critique de superfluidité et d'autre part par la configuration inhomogène du système. Des notions habituelles de localisation telles que transmission ou exposant de Lyapunov ne sont plus applicables. Donc, il a fallu apporter une nouvelle mesure de localisation pour notre problématique: le ratio du déplacement du centre de masse du condensat au déplacement du désordre qu'on a identifié à la fraction d'atomes localisés. De plus, nous avons des corrélations dans le désordre qui introduisent l'effet d'un comportement non-monotone de l'efficacité de la localisation du potentiel désordonné en fonction de l'énergie. Ainsi, les corrélations peuvent être un moyen pour mettre en évidence la nature quantique de la localisation. Chose que nous avont fait dans un premier temps avec du désordre de type Modèle d'Edwards et dans une seconde partie avec du désordre de type speckle, qu'on nomme le Random Dimer speckle. Pour ce deuxième cas, nous avons proposé une procédure pour contrôler les corrélations et introduire un pic de localisation dans une certaine région énergétique. Cette configuration pourrait être vérifié dans les expériences à l'aide d'un modulateur spatial de lumière. / The topic of this thesis is the study of localization of a quasi-one-dimensional and harmonically trapped Bose-Einstein condensate through which various disordered potentials are transported. This problem, which wants itself to be fully relevant to experimenters, is a priori difficult to deal with. This is due to the non-linear, inhomhogeneous and out-of-equilibrium nature of the system. Because of this, the range of speeds of disorder is limited on one side by the critical speed of superfluidity and on the other side by the inhomogeneous setting of the system. Usual notions of localization like transmission and Lyapunov exponent are no longer applicable. Thus, we had to introduce a novel measure of localization for our problem: the ratio of the distance moved by the condensate center of mass to the distance moved by the disordered potential that we identify as the fraction of localized atoms. Furthermore, we have correlations in the disorder that introduce the effect of non-monotonic behavior of the localization efficiency of the disordered potential as a function of energy. A a result, correlations can be used as a tool to point the quantum nature of the localization. We did this in a first part with Edwards Model type disorders and in a second part with speckle type disorders, a new one that we call the Random Dimer speckle. For this second part, we propose a scheme to control the correlations and introduce a localization peak in a certain energy region. This device can be verified in experiments with the help of a Spatial Light Modulator.

The interplay between quenched disorder and interaction effects opens the possibility in a closed quantum many-body system of a phase transition at finite energy density between an ergodic phase, which is governed by the laws of statistical physics, and a localized one, in which the degrees of freedom are frozen and ergodicity breaks down. The possible existence of a quantum phase transition at finite energy density is strongly questioning our understanding of the fundamental laws of nature and has generated an active field of research called many-body localization. This thesis consists of three parts and is dedicated to the understanding and characterization of the phenomenon of many-body localization, approaching it from complementary facets. In particular, borrowing methods and tools from different fields, we analyze timely problems. The first part of the thesis is devoted to detecting the many-body localization transition and to characterize both the ergodic and the localized phase it separates. Here we provide a characterization from two different perspectives: the first one is based on the study of local entanglement properties. In the second one, using tools from quantum-chaos theory, we attempt to answer the question of understanding time-irreversibility, and thus probing the breaking of ergodicity. We analyze experimentally viable observables. Moreover, we propose two different quantities to distinguish an Anderson insulating phase from a many-body localized one, which is one of the issues in experiments. The second part focuses on understanding the existence of a putative subdiffusive multifractal phase. Analyzing the quantum dynamics of the system in this region of the phase diagram, we point out the importance of finite-size effects, questioning the existence of this multifractal phase. We speculate with a possible scenario in which the diffusivity and thus ergodicity could be restored in the thermodynamic limit. Furthermore, we find that the propagation is highly non-Gaussian, which could have an important effect on understanding the critical point of the according transition. We tackle this problem also from a different angle. A possible toy-model to understand many-body localization entails the Anderson model on a random-regular graph. Also in the latter model the possible existence of an intermediate multifractal phase has been conjectured. There, studying the survival return probability of a particle with time, we give a new characterization of multifractal phases and give indication of the possible existence of this phase. Nevertheless, we also outline possible caveats. In the last part of this thesis we study the interplay between symmetry and correlated disorder in a non-interacting fermionic system. We show another possible mechanism for breaking localization. In particular, we focus on studying information and particle transport, emphasizing how the two types of propagation can be different.

Cette thèse présente une étude du transport quantique et de la localisation d’Anderson d’ondes de matière sans interaction dans des désordres anisotropes. À l’aide d’approches microscopiques, nous étudions l’effet des corrélations du désordre dont nous démontrons qu’elles peuvent considérablement modifier les propriétés du transport quantique à 1D, 2D et 3D. Nous développons des outils généraux et les appliquons à des modèles de désordre continu pertinents pour les expériences d’atomes ultrafroids : les potentiels de tavelures optiques (« speckle »). Dans un premier temps, à une dimension, nous raffinons les précédents modèles du processus de localisation d’un nuage d’atomes ultrafroids en expansion dans un potentiel de speckle usuel, et nous montrons que la prise en compte de nouveaux éléments devrait permettre d’expliquer les écarts entre les résultats expérimentaux et théoriques observés précédemment. Nous étudions ensuite le transport quantique et la localisation d’Anderson en dimensions supérieures, plus particulièrement dans des désordres aux corrélations anisotropes, ce qui est naturellement le cas dans la plupart des potentiels de speckle. Nous calculons les propriétés de transport quantique et proposons une nouvelle méthode pour estimer la position du seuil de localisation à 3D (seuil de mobilité). Nos prédictions théoriques sont ensuite comparées aux résultats obtenus par deux expériences récentes ayant observé la localisation tri-dimensionnelle d’ondes de matière. Enfin, nous approfondissons notre étude des effets des corrélations du désordre. Nous démontrons qu’elles peuvent induire l’inversion des anisotropies de localisation et une amplification de la localisation d’Anderson avec l’énergie de la particule, lorsqu’elles sont judicieusement adaptées. / In this thesis we investigate quantum transport and Anderson localization of non- interacting matterwaves in anisotropic disorder. Using microscopic approaches, we study the effect of disorder correlations, which are shown to significantly modify quantum transport properties in 1D, 2D and 3D. We develop general theoretical tools and apply them to particular models of continuous disorder, which are relevant to ultracold atom experiments : speckle potentials. First, in the one-dimensional case we extend previous models for the localization process of ultracold atoms expanding in a standard speckle potential and show that taking into account new ingredients could permit to understand deviations between experiments and theory observed previously. We then study quantum transport and Anderson localization in dimensions higher than one, with special emphasis on anisotropic correlations, which are naturally present in most speckle potentials. We compute quantum transport properties and propose a new method to estimate the 3D localization threshold (mobility edge). Our theoretical findings are compared with the results of two recent experiments which report evidence of 3D localization of matterwaves. Eventually, we further study effects of disorder correlations, which can induce inversion of localization anisotropies and enhancement of Anderson localization with the particle energy, when appropriately tailored.