Thesis (Ph.D.)--McMaster University, 2004. / Advisor: David Venus. Includes bibliographical references (leaves 138-144). Also available via World Wide Web.

Thesis (Ph.D) - University of Queensland, 2006. / Includes bibliography.

Thesis (Ph. D.)--Ohio State University, 2007. / Title from first page of PDF file. Includes bibliographical references (p. 125-129).

Thesis (Ph. D.)--University of Oregon, 2006. / Typescript. Includes vita and abstract. Includes bibliographical references (leaves 126-128). Also available for download via the World Wide Web; free to University of Oregon users.

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Orientador: Diógenes Galetti / Banca: Marcus Aloizio Martinez de Aguiar / Banca: Marcelo de Oliveira Terra Cunha / Resumo: Quando temos sistemas quânticos sem análogo clássico a descrição de Weyl- Wigner, para o espaço de fase quântico, não pode ser utilizada, pois a mesma não representa graus de liberdade associados a grandezas discretas. Um exemplo desses sistemas são os estados emaranhados bipartites de spin 1/2. Para tal, se faz necessária a descrição de um espaço de fase quântico discreto e de dimensão finita. Nessa descrição é possível se obter a caracterização do emaranhamento, bem como quantificar o grau dessas correlações entre os sub sistemas; além do que, há a possibilidade de calcular a evolução temporal nessa descrição, tanto para o sistema como um todo quanto para o emaranhamento / Abstract: For quantum systems without classical analog the Weyl-Wigner description associated to quantum phase space can not be used, since it does not represent degrees of freedom associated with discrete quantities. An example of these systems are spin 1/2 bipartite entangled states. For them, it is needed a discrete quantum phase space description which have nite dimension. In this description, it is possible to obtain entanglement characterization, and to quantify the correlation degree between the subsystems; there is also the possibility of calculating the time evolution, in this description, both for the system as a whole as well as for the entanglement / Mestre

La compréhension du mécanisme de la formation du verre est l'un des importants problèmes ouverts en recherche sur la matière condensée. De nombreuses questions restent sans réponse, en raison d'une énorme augmentation des temps de relaxation pendant le processus de refroidissement qui ne permet pas l'exploration des propriétés d'équilibre des liquides surfondus à très basses températures. Les simulations numériques des liquides surfondus sont actuellement en mesure d'atteindre l'équilibre à des températures comparables à la température du crossover de la théorie de couplages de modes, qui est bien supérieure à la température de transition vitreuse expérimentale. En conséquence, les simulations plus lentes que les expériences pour équilibrer un liquide surfondu par un facteur d'environ huit ordres de grandeur. Les progrès réalisés pour combler cet écart ont été lents et résultent essentiellement d'améliorations de l'architecture des ordinateurs. Dans cette thèse, nous résolvons en partie le problème de la thermalisation à basse température de liquides surfondus dans des simulations numériques. Nous combinons l'utilisation d'un algorithme Monte Carlo, connu sous le nom d'algorithme de swap, avec la conception de nouveaux modèles de formateurs de verre. Nous examinons systématiquement des nombreux systèmes, à la fois des mélanges discrets de particules, ainsi que des systèmes a polydispersité continue. Nous discutons le rôle que la polydispersité et la forme du potentiel entre particules jouent pour éviter la cristallisation et parvenir efficacement à des régimes de température inexplorés. De plus, nous étudions les processus dynamiques à l’œuvre pendant une simulation de swap Monte Carlo. Nous démontrons que, dans certains cas, notre technique permet de produire des configurations équilibrées à des températures inaccessibles même dans des expériences. Dans ce régime de température complètement nouveau, nous examinons plusieurs questions ouvertes concernant la physique de la transition vitreuse. Nous montrons qu'un fluide de sphères dures peut être équilibré jusqu'à la densité critique du jamming, et même au-delà. Nous mesurons l'entropie configurationelle dans un liquide refroidi à très basse température. Nous mettons en évidence une forte dépendance dimensionnelle, qui suggère l'existence d'une transition vitreuse idéale à une température finie en trois dimensions et à son absence en deux dimensions. Nous détectons l'augmentation de l'ordre amorphe quantifié par une longueur statique point-to-set pendant la formation du verre. Nous mesurons les exposants critiques introduits dans la théorie de champ moyen des verres beaucoup plus proche de la température critique prédite dans la théorie. Enfin, nous révélons l'absence de transition géométrique caractérisant le paysage d’énergie potentiel au travers de la température du crossover de la théorie de couplages de modes.Les modèles et les algorithmes développés dans cette thèse déplacent les études des liquides surfoundus vers un territoire entièrement nouveau, en réduisant l'écart entre la théorie et les expériences, ce qui nous amène plus proche de la solution du problème de la transition vitreuse. / Understanding the mechanisms that lead to glass formation is one of the open problems for the condensed matter research. Numerous questions remain unanswered, because the tremendous increase of relaxation times during the cooling process prevents the exploration of equilibrium properties of supercooled liquids at very low temperature. Computer simulations of glass-forming liquids are nowadays able to reach equilibrium at temperatures comparable to the Mode-Coupling crossover temperature, which is well above the experimental glass transition temperature. As a consequence, simulations lag eight orders of magnitude behind experiments in terms of equilibration times. Progress to close this gap has been slow, and stems mostly from hardware improvements.In this thesis we make an important step to close this gap. We combine the use of a Monte Carlo algorithm, known as the swap algorithm, with the design of novel glass-forming models. We systematically test numerous models using both discrete mixtures and polydisperse systems. We discuss the role that polydispersity and particle softness play in avoiding crystallization and in efficiently reaching previously unexplored regimes. We study the dynamical processes taking place during swap Monte Carlo simulations. We demonstrate that in some cases our technique is able to produce thermalized configurations at temperatures inaccessible even by experiments.In this newly accessible regime, we investigate some open questions concerning the glass transition. We show that a hard sphere fluid can be equilibrated at, and even beyond, the jamming packing fraction. We measure the configurational entropy in extremely supercooled liquid, finding a strong dimensional dependence that supports, on the one hand, the existence of an ideal glass transition at a finite temperature in three dimensions and, on the other hand, its absence in two dimensions. We detect the increase of amorphous order quantified through a static point-to-set length throughout the glass formation. We measure the critical exponents introduced in the mean-field theory of glasses much closer to the supposed ideal glass transition. Finally, we reveal the absence of a sharp geometric transition in the potential energy landscape across the Mode-Coupling crossover.The models and the algorithms developed in this thesis shift the computational studies of glass-forming liquids to an entirely new territory, which should help to close the gap between theory and experiments, and get us closer to solve the long-standing problem of the glass transition.

The study of supercooled liquids and glasses remains one of the most divisive and divided fields in modern physics. Despite a vast amount of effort and research time invested in this topic, the answers to many central questions remain disputed and incomplete. However, the link between the behaviour of supercooled liquids and their energy landscapes is well established and widely accepted. Understanding this link would be a key step towards resolving many of the mysteries and controversies surrounding the glass transition. Therefore the study of glassy energy landscapes is an important area of research. In this thesis, I report some of the most detailed computational studies of glassy potential energy landscapes ever performed. Using geometry optimisation techniques, I have sampled the local minima and saddle points of the landscapes for several supercooled liquids to analyse their dynamics and thermodynamics. Some of my analysis follows previous work on the binary Lennard-Jones fluid (BLJ), a model atomic liquid. BLJ is a fragile glass former, meaning that its transport coefficients have super-Arrhenius temperature dependence, rather than the more usual Arrhenius behaviour exhibited by strong liquids. The difference in behaviour between these two classes of liquid has previously been attributed to differing degrees of structure in the relevant energy landscapes. I have studied models for both fragile and strong glass formers: the molecular liquid ortho-terphenyl (OTP) and viscous silica (SiO$_{2}$) respectively. My results for OTP agree closely with trends observed for BLJ, suggesting that the same diffusion mechanism is applicable to fragile molecular liquids as well as to atomic. However, the dynamics and energy landscape of OTP are made complicated by the molecular orientational degrees of freedom, making the analysis more challenging for this system. Dynamics of BLJ, OTP and silica are all dominated by cage-breaking events: structural rearrangements in which atoms change their nearest neighbours. I propose a robust and general method to identify cage breaks for small rigid molecules, and compare some properties of cage breaks between strong and fragile systems. The energy landscapes of BLJ and OTP both display hierarchical ordering of potential energy minima into metabasins. These metabasins can be detected by the cage-breaking method. It has previously been suggested that metabasins are responsible for super-Arrhenius behaviour, and are absent from the landscapes of strong liquids such as SiO2. My results indicate that metabasins are present on the silica landscape, but that they each contain fewer minima than metabasins in BLJ or OTP. Metabasins are associated with anticorrelated particle motion, mediated by reversed transitions between minima of the potential energy landscape. I show that accounting for time-correlation of particle displacement vectors is essential to describe super-Arrhenius behaviour in BLJ and OTP, but also required to reproduce strong behaviour in silica. I hypothesise that the difference between strong and fragile liquids arises from a longer correlation timescale in the latter case, and I suggest a number of ways in which this proposition could be tested. I have investigated the effect on the landscape of freezing the positions of some particles in a BLJ fluid. This “pinning” procedure induces a dynamical crossover that has been described as an equilibrium “pinning transition”, related to the hypothetical ideal glass transition. I show that the pinning transition is related to (and probably caused by) a dramatic change in the potential energy landscape. Pinning a large fraction of the particles in a supercooled liquid causes its energy landscape to acquire global structure and hence structure-seeking behaviour, very different from the landscape of a typical supercooled liquid. I provide a detailed description of this change in structure, and investigate the mechanism underlying it. I introduce a new algorithm for identifying hierarchical organisation of a landsape, which uses concepts related to the pinning transition but is applicable to unpinned liquids as well. This definition is complementary to metabasins, but the two methods often identify the same higher-order structures. The new “packings” algorithm offers a route to test thermodynamic theories of the glass transition in the context of the potential energy landscape. Over the course of this thesis, I discuss several different terms and methods to identify higher-order structures in the landscapes of model glass formers, and investigate how this organisation varies between different systems. Although little variation is immediately apparent between most glassy landscapes, deeper analysis reveals a surprising diversity, which has important implications for dynamical behaviour in the vicinity of the glass transition.

The recent development of a framework called non-affine lattice dynamics made it possible to calculate the elastic moduli of disordered systems directly from their microscopic structure and potential energy landscape at zero temperature. In this thesis different types of disordered systems were studied using this framework. By comparing the shear modulus and vibrational properties of nearest neighbour spring networks based on depleted lattices we were able to show that the dominating quantity of the system’s non-affine reorganisation during shear deformation is the affine force field. Furthermore we found that different implementation of disorder lead to the same behaviour at the isostatic point. Later we studied the effect of long range interaction in such depleted lattices with regard to spatial correlation local elasticity. We found that the implementation of long springs with decaying spring constant reproduced the spatial correlation observed in simulations of Lennard-Jones glasses. Finally we looked at simple freely rotating polymer model chains by extending the framework to angular forces and studied the dependence of the shear modulus and the vibrational density of states (VDOS) and length and bending stiffness of the chains. We found that the effect of chain length on the shear modulus and the vibrational density of states diminishes as it depends on the number of backbone bonds in the system. This number increases fast for short chains as many new backbone bonds are introduced but slows down significantly when the chain length reaches 50 monomers per chain. For the dependence on the bending stiffness we found a rich phenomenology that can be understood by looking at specific motions of the monomers relative the the chain geometry. We were able to trace back the different regimes of the VDOS to the simple model of the triatomic molecule. We also explored the limits of non-affine lattice dynamics when describing systems at temperatures T > 0 and gave an approximate solution for the shear modulus in this case.

No description available.