Numerical Simulations

This book will interest researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modeling and computer simulation. Although it represents only a small sample of the research activity on numerical simulations, the book will certainly serve as a valuable tool for researchers interested in getting involved in this multidisciplinary field. It will be useful to encourage further experimental and theoretical researches in the above mentioned areas of numerical simulation

Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference

We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today, there is no longer an established or dominant interpretation of quantum theory, so it is important to re-evaluate the historical sources and keep the interpretation debate open. In this spirit, we provide a complete English translation of the original proceedings (lectures and discussions), and give background essays on the three main interpretations presented: de Broglie's pilot-wave theory, Born and Heisenberg's quantum mechanics, and Schroedinger's wave mechanics. We provide an extensive analysis of the lectures and discussions that took place, in the light of current debates about the meaning of quantum theory. The proceedings contain much unexpected material, including extensive discussions of de Broglie's pilot-wave theory (which de Broglie presented for a many-body system), and a "quantum mechanics" apparently lacking in wave function collapse or fundamental time evolution. We hope that the book will contribute to the ongoing revival of research in quantum foundations, as well as stimulate a reconsideration of the historical development of quantum physics. A more detailed description of the book may be found in the Preface. (Copyright by Cambridge University Press (ISBN: 9780521814218).)Comment: 553 pages, 33 figures. Draft of a book (as of Sept. 2006, same as v1). Published in Oct. 2009, with corrections and an appendix, by Cambridge University Press (available at http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521814218

Sterile Neutrino Dark Matter in Non-Standard Scenarios

Sterile neutrino with a mass of O(keV) is a well-motivated candidate to play the roleof dark matter (DM), one of the most abundant constituents of our Universe whosenature remains still unknown. It arises as a natural and straightforward extension ofthe particle content of the standard model (SM), it is neutral under all SM charges, itcan be stable over cosmological time scales, and it can be produced in adequate amountin the early Universe to account for today’s DM abundance. In this thesis, we studysterile neutrinos as DM candidates produced in the early Universe through oscillationand collisions induced by their mixing with one of the active neutrino species, i.e. in theframework of the Dodelson-Widrow and the Shi-Fuller mechanisms. In particular, weinvestigate the parameter space of sterile neutrinos in two non-standard scenarios. Thefirst scenario studied is a non-standard cosmological scenario in which the productionof sterile neutrinos is delayed and starts at a critical temperature associated with alow reheating temperature of the Universe or with a dynamical change in the sterileneutrino mass. Here, we show that the discovery potential in terrestrial experiments isconsiderably enhanced. In the second scenario, the production through the Dodelson-Widrow mechanism is modified by non-standard interactions among active neutrinos.An effective formalism to include such neutrino non-standard self-interactions in theDM production is developed, and the sensitivity of the HUNTER experiment to thisspecific model is highlighted. At the same time, we demonstrate that the stringentlimit on sterile neutrino DM coming from observations in the X-ray band should beconsidered model-dependent and can be relaxed in different ways, thereby letting opena window in the parameter space of utmost interest for experimental searches

Étude de la dépendance en température de la structure électronique à l'aide de la théorie de la fonctionnelle de la densité : effets non adiabatiques, dilatation du point zéro, couplage spin-orbite et application aux transitions de phase topologiques

Les signatures de l’existence des phonons sont omniprésentes dans les propriétés des matériaux. En première approximation, on peut scinder l'effet des phonons sur la structure électronique en deux contributions. D’une part, l'interaction électron-phonon capture la réponse électronique aux vibrations des noyaux du cristal, et d’autre, l'énergie libre de la population de phonons modifie le volume cristallin à l’équilibre. En plus d'être responsables de la dépendance en température de la structure électronique, ces deux mécanismes affectent les niveaux d'énergie à température nulle, à travers le mouvement du point zéro et l'énergie du point zéro. Cette thèse analyse l’apport de ces deux mécanismes à la renormalisation du point zéro (ZPR) de l'énergie de la bande interdite des semi-conducteurs. Une généralisation du modèle de Fröhlich prenant en compte l'anisotropie et les dégénérescences présentes dans les matériaux réels révèle que l'interaction non adiabatique entre les électrons et les noyaux domine le ZPR dans les matériaux polaires. La prise en compte de ce mécanisme dans l'évaluation de l'interaction électron-phonon est déterminante pour reproduire adéquatement les données expérimentales. L'approche développée par Grüneisen, qui néglige communément les effets du point zéro, reproduit la dilatation du point zéro du réseau (ZPLE) et sa contribution au ZPR obtenues avec la méthode standard basée sur la minimisation de l'énergie libre à moindre coût numérique, y compris pour les matériaux anisotropes. La contribution du ZPLE au ZPR total, qui a reçu peu d'attention dans la littérature, peut atteindre de 20% à plus de 80% de la contribution de l'interaction électron-phonon, y compris dans des matériaux constitués de noyaux légers. Elle domine même le ZPR du GaAs dans le contexte de la DFT semi-locale. Il est donc essentiel de traiter les deux contributions sur le même pied d'égalité pour modéliser le ZPR avec précision. L'inclusion du couplage spin-orbite (SOC) diminue le ZPR d'un ensemble substantiel de matériaux cubiques de structure zinc-blende, diamant et rock-salt. L'essentiel de cette variation tire son origine de l'effet du SOC sur les énergies électroniques statiques, qui provient en grande partie de la variation des masses effectives des bandes de valence au point $\Gamma$. La réduction du ZPR peut être estimée à partir d'un modèle de Fröhlich généralisé auquel on a introduit le SOC. Les subtilités numériques liées au traitement de la séparation de Dresselhaus dans les matériaux non centrosymétriques sont discutées. On démontre enfin comment l'effet combiné de l'interaction électron-phonon et de la dilatation thermique affecte le diagramme de phase topologique du BiTeI. L'augmentation de la température repousse l'apparition de la phase d'isolant topologique $\mathbb{Z}_2$ vers des pressions plus élevées et élargit la plage de pressions correspondant à la phase intermédiaire de type semi-métal de Weyl. Le caractère orbital dominant des extrema de bande influence significativement leur sensibilité à la pression et au changement de topologie. Pour guider la recherche expérimentale de phases topologiquement non triviales dans les matériaux de façon adéquate, les études numériques doivent donc considérer l'effet de la température.Phonon signatures are ubiquitous in material properties. At first order, the effect of phonons on the electronic structure can be split into two contributions. On the one hand, the electron-phonon interaction captures the electronic response to the vibrations of the nuclei. On the other hand, the free energy of the phonon population modifies the crystalline volume at equilibrium. In addition to driving the temperature dependence of the electronic structure, these two mechanisms affect the energy levels at zero temperature through zero-point motion and zero-point energy. This thesis investigates the contribution of these two mechanisms to the zero point renormalization (ZPR) of the band gap energy of semiconductors. A generalized Fröhlich model taking into account the anisotropy and degeneracies occurring in real materials reveals that the non-adiabatic interaction between electrons and nuclei dominates the ZPR in polar materials. Taking this mechanism into account when evaluating the electron-phonon interaction is crucial to reproduce experimental data adequately. The Grüneisen formalism, which commonly neglects zero-point effects, reproduces the zero-point lattice expansion (ZPLE) and its contribution to the ZPR obtained from the standard method based on free energy minimization at lower numerical cost, including for anisotropic materials. The ZPLE contribution to the total ZPR, which has received little attention in the literature, can reach from 20% to more than 80% of the contribution of the electron-phonon interaction, including in materials containing light atoms. It even dominates the ZPR of GaAs within semilocal DFT. Therefore, both contributions should be treated on an equal footing to model the ZPR accurately. The inclusion of spin-orbit coupling (SOC) decreases the ZPR of a substantial set of cubic materials of zincblende, diamond and rocksalt structure. This variation originates mostly from the effect of SOC on the static electronic eigenvalues, which comes largely from the variation of the effective masses of the valence bands at the $\Gamma$ point. The reduction of the ZPR can be estimated from a generalized Fröhlich model in which SOC has been introduced. Numerical subtleties related to the treatment of Dresselhaus separation in non-centrosymmetric materials are discussed. We finally show how the combination of electron-phonon interaction and thermal expansion affects the topological phase diagram of BiTeI. An increase in temperature pushes the $\mathbb{Z}_2$ topological insulator phase towards higher pressures and widens the pressure range corresponding to the Weyl semi-metal intermediate phase. The leading orbital character of the band extrema significantly influences their sensitivity to variations in pressure and topology. To adequately guide the experimental search for topologically non-trivial phases in materials, numerical studies must therefore consider the effect of temperature

Theoretical investigation of scanning probe lithography in field-emission mode

Die Miniaturisierung der kleinsten Bauelemente, d. h. der Transistoren, in integrierten Schaltungen auf Siliziumbasis nähert sich langsam den physikalischen Grenzen und alternative Strukturierungs- und Strukturübertragungsmethoden werden benötigt um zu noch kleineren Strukturen zu gelangen. Eine dieser alternativen Strukturierungsverfahren ist die feldemissionsbasierte Rastersondenlithographie. Diese Technologie beruht auf der Belichtung einer Resistschicht mittels Elektronen, welche aus der Rastersondenspitze aufgrund des angelegten elektrischen Feldes emittiert werden. Das Verfahren wurde schon erfolgreich zur Herstellung neuartiger Einzelquantenpunkttransistoren verwendet, welche bei Raumtemperatur arbeiten und kann Strukturgrößen von unter 10 nm erzeugen. Nichtsdestotrotz mangelt es an einer theoretischen Beschreibung, welche insbesondere den Einfluss der Resistschicht auf das Emissionsverhalten der Elektronen aus der Spitze wie auch die Wechselwirkung der Elektronen mit den Molekülen der Resistschicht umfasst. Optimale Parameter zum Erreichen der besten Auflösung mit einer bestimmten Emissionsspitze müssen zurzeit in einem empirischen Versuch bestimmt werden. Das ist sowohl zeitaufwendig, nutzt die Spitze ab und birgt das Risiko einer Berührung der Spitze mit der Probe. Dadurch entsteht wiederum die Gefahr, dass die empirische Optimierung wiederholt werden muss. Um dies zu vermeiden, wäre ein theoretisches Modell wünschenswert, welches die optimalen Parameter vorhersagen kann. In dieser Arbeit wird ein umfassendes numerisches Modell der Rastersondenlithographie vorgestellt, welches die Berechnung des elektrischen Feldes, der Emissionsstromdichte aus der Spitze und der Elektronentrajektorien beinhaltet sowie eine Monte Carlo Simulation zur Berechnung der elektronischen Wechselwirkungen in der Resistschicht einschließt. Dieses Modell ist für beliebige zylindersymmetrische Spitzen anwendbar (u. a. für Spitzen mit einer umschließenden Elektrode) und berücksichtigt den Einfluss der Resistschicht in der gesamten Berechnung. Zur Verbesserung des Verständnisses der physikalischen Grundlagen, zur Vorhersage optimaler Parameter und zur Resourcenminimierung der Berechnung wurde ein analytisches Modell abgeleitet, welches, bis auf die Wechselwirkungen in der Resistschicht, alle Teile des numerischen Modells für eine typische Spitzenform beinhaltet. Damit konnte der Einfluss der durch die Spitze vorgegebenen Parameter (z. B. Spitzenradius) und der extern einstellbaren Parameter (z. B. Spannung, Schreibgeschwindigkeit) untersucht werden. Das analytische Modell wurde erfolgreich zur Analyse von Feldemissionsexperimenten genutzt und es konnte damit die systemeigene Driftgeschwindigkeit beziehungsweise die Wachstumsrate der experimentell beobachteten Strukturen abgeschätzt werden. Weiterhin konnte es die experimentell beobachtete Abhängigkeit der Linienbreite von der Bestrahlungsdosis und der Spannung reproduzieren. Somit steht erstmals ein vollständiges theoretisches Modell zur Beschreibung der feldemissionsbasierten Rastersondenlithographie zur Verfügung, welches alle relevanten Parametereinflüsse (im Vakuumbetrieb) beinhaltet. Der analytische Teil des Modells kann zur Vorhersage der zu schreibenden Strukturen und zur Parameteranpassung verwendet und in die Software des Lithographiesystems eingebaut werden.The miniaturization of the smallest devices of silicon-based integrated circuits, namely transistors, using conventional optical lithography techniques reaches slowly their physical limitations and alternative patterning and pattern transfer methods are needed to further reduce the device size. One of such patterning alternatives is field-emission scanning probe lithography. This technique uses electrons to expose the resist layer. The electrons are emitted from an ultrasharp tip (r ≲ 10nm) of a scanning probe due to a strong applied electric field. This scanning probe method was already successfully applied to fabricate single quantum-dot transistors working at room temperature and is capable of high-resolution lithography with critical dimensions in the sub-10nm range. Nevertheless, a theoretical description was not available, which considers the influences of the resist layer on the electron emission from the nanotip and the interaction of the electrons within the resist. Furthermore, the optimal parameters for high-resolution patterning had to be determined experimentally, which is time-consuming, increases tip wear and the risk of tip crashes. Therefore, a theoretical model would be useful, which can predict the optimal parameters for a specific tip. Here, a comprehensive numerical model of the field-emission scanning probe lithography is presented, which consists of the calculation of the electric field, the emission current density at the tip and the trajectories of the electrons as well as a Monte Carlo simulation to compute the scattering of electrons in the resist. The model is applicable for any cylinder symmetric tip (including also e. g., volcano-gated tips) and takes the influence of the resist layer into account. For predicting optimal parameters, describing the underlying physics and minimizing the computational resources an analytical model (for a typical tip geometry) was derived. It includes all calculation steps of the numerical model except the scattering in the resist. It allows studying the various dependencies arising from tip-related constants (e. g., tip radius and material) and from externally adjustable parameters (e. g., bias voltage). The analytical model was successfully applied to explain field-emission experiments and to estimate the system inherent drift velocity and the growth rate of experimentally observed structures at the sample, respectively. Furthermore, it could describe the experimentally obtained dependence of the line width on the exposure dose. Therewith, a comprehensive theoretical model to describe field-emission scanning probe lithography was achieved, which considers all relevant parameters (under vacuum conditions). The analytical model can be used to predict the properties of patterns to be written, to adjust external parameters for optimal results and it can be also included in the software of an actual field-emission scanning probe lithography tool

The World in Eleven Dimensions

A unified theory embracing all physical phenomena is a major goal of theoretical physics. In the early 1980s, many physicists looked to eleven-dimensional supergravity in the hope that it might provide that elusive superunified theory. In 1984 supergravity was knocked off its pedestal by ten-dimensional superstrings, one-dimensional objects whose

Effets de cohérence en diffusion multiple de la lumière et intrication des états cohérents

This work is devoted on the one hand to the investigation of coherence effects in multiple scattering of light by an atomic cloud and on the other hand to the entanglement of a deformed coherent state. The interaction between light and a dilute disordered atomic cloud gives rise to collective coherent effects due to the interaction of the induced dipoles via the external field. The behavior of such coherent effects in multiple scattering regime is an important question for various physical systems. We present two theoretical models describing those coherence effects in different scattering regimes. The scattering order expansion treatment of light scattering allows us to highlight the role of the first and second scattering orders as well as the interference between the resulting scattered fields. In the multiple scattering regime we show that the radiation pressure force is not a good observable to probe cooperative effects. Furthermore, we discover a surprising phase coherence that hints that collective effects may survive in multiple scattering regime. That could be due to a synchronization between the induced atomic dipoles. In a second part, we study the effect of an algebra deformation on entangled coherent states. Such an approach allows to describe decoherence in perturbed entangled quantum systems. We construct a deformed coherent state and calculate their concurrence. We show that algebra deformation could have a non negligible impact on bipartite entangled coherent states if those later are not maximally entangled.L’interaction entre la lumière et un nuage atomique désordonné et dilué donne lieu à des effets de cohérence collectifs dus à l’interaction des dipôles induits par le biais du champ lumineux. L'influence de tels effets de cohérence en diffusion multiple suscite beaucoup d’intérêt. Nous présentons deux modèles théoriques qui décrivent ces effets de cohérence dans différents régimes de diffusion. Le traitement du processus à travers un développement en ordres successifs de diffusion nous permet de mettre en évidence la contribution du premier et second ordres ainsi que l'interférence entre les champs diffusés qui en résultent. Dans le régime de diffusion multiple, nous montrons que la force de pression de radiation n'est pas une bonne observable pour sonder les effets coopératifs. Par ailleurs, nous mettons en évidence une surprenante cohérence de phase qui suggère une persistance des effets coopératifs en diffusion multiple. Cela pourrait être le résultat d'une synchronisation entre les dipôles atomiques couplés. Dans une deuxième partie, nous étudions l'effet d'une déformation de l'algèbre de Weyl-Heisenberg sur l'intrication des états cohérents. Une telle approche permet de décrire la décohérence dans des systèmes quantiques intriqués soumis à une perturbation extérieure. Nous construisons des états cohérents déformés intriqués et nous calculons leur concurrence. Nous montrons que la déformation de l'algèbre pourrait avoir un impact non négligeable sur la qualité de l'intrication bipartie des états cohérents, si cette dernière n'est pas maximale