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This thesis explores the effects singularities have on stationary and dynamical properties of many-body quantum systems. In papers I and II we find that the ground state suffers a Z2 symmetry breaking phase transition (PT) when a single impurity is added to a Bose-Einstein condensate (BEC) in a double well (bosonic Josephson junction). The PT occurs for a certain value of the BEC-impurity interaction energy, Λc . A result of the PT is the mean-field dynamics undergo chaotic motion in phase space once the symmetry is broken. We determine the critical scaling exponents that characterize the divergence of the correlation length and fidelity susceptibility at the PT, finding that the BEC-impurity system belongs to the same universality class as the Dicke and Lipkin-Meshkov-Glick models (which also describe symmetry breaking PTs in systems of bosons). In paper III we study the dynamics of a generic two-mode quantum field following a quench where one of the terms in the Hamiltonian is flashed on and off. This model is relevant to BECs in double wells as well as other simple many-particle systems found in quantum optics and optomechanics. We find that when plotted in Fock-space plus time, the semiclassical wave function develops prominent cusp-shaped structures after the quench. These structures are singular in the classical limit and we identify them as catastrophes (as described by the Thom-Arnold catastrophe theory) and show that they arise from the coalescence of classical (mean-field) trajectories in a path integral description. Furthermore, close to the cusp the wave function obeys a remarkable set of scaling relations signifying these structures as examples of universality in quantum dynamics. Within the cusp we find a network of vortex-antivortex pairs which are phase singularities caused by interference. When the mean-field Hamiltonian displays a Z2 symmetry breaking PT modelled by the Landau theory of PTs we calculate scaling exponents describing how the separation distance between the members of each pair diverges as the PT is approached. We also find that the cusp becomes infinitely stretched out at the PT due to critical slowing down. In paper IV we investigate in greater detail the morphology of the vortex network found within cusp catastrophes in many-body wave functions following a quench. In contrast to the cusp catastrophes studied so far in the literature, these structures live in Fock space which is fundamentally granular. As such, these cusps represent a new iii type of catastrophe, which we term a ‘quantum catastrophe’. The granularity of Fock space introduces a new length scale, the quantum length lq = N −1 which effectively removes the vortex cores. Nevertheless, a subset of the vortices persist as phase singularities as can be shown by integrating the phase of the wave function around circuits in Fock-space plus time. Whether or not the vortices survive in a quantum catastrophe is governed by the separation of the vortex-antivortex pairs lv ∝ N −3/4 in comparison to lq , i.e. they survive if lv lq . When particle numbers are reached such that lq ≈ lv the vortices annihilate in pairs. / Thesis / Doctor of Philosophy (PhD)

We study the phase diagram of an interacting lattice gas of two species of particles and holes, driven out of equilibrium by a local hopping bias (denoted by `E'). Particles interact by excluded volume and nearest-neighbor attractions. We present a detailed Monte Carlo investigation of the phase diagram. Three phases are found, with a homogenous phase at high temperatures and two distinct ordered phases at lower temperatures. Which ordered phase is observed depends on the parameter f, which controls the ratio of the two types of particles. At small f, there is nearly a single species, and a transition is observed into a KLS-type ordered phase. At larger f, the minority species are sufficiently dense to form a transverse blockage, and a sequence of two transitions are observed as the temperature is lowered. First, a continuous boundary is crossed into an SHZ-type ordered phase, then at a lower temperature a first-order boundary is crossed into the KLS-type ordered phase. At some critical value of f is a bicritical point, where the first-order line branches from the two continuous boundaries. We also consider correlations in the homogenous phase, by constructing a continuum description and comparing to the results of simulations. Long range correlations are present in both the theoretical results and the simulations, though certain details of the theory do not fit the observations very well. Finally, we examine the beahvior of three-point correlations in the single-species (KLS) limit. Nontrivial three-point correlations are directly related to the nonzero bias E. We therefore consider the behavior of the three-point correlations as a function of E. We find that the three-point signal saturates very rapidly with E. There are some difficulties interpreting the data at small E. / Ph. D.

Phospholipid bilayers constitute the primary structural element of biological membranes, and as such, they play a central role in biochemical and biophysical processes at the cellular level, including cell protection, intercellular interactions, trans-membrane transport, cell morphology, and protein function, to name a few. The properties of phospholipid bilayers are thus of great interest from both experimental and theoretical standpoints. Although experiments have provided much of the macroscopic functions and properties of biological membranes, insight into specific mechanisms at the molecular level are seldom accessible by conventional methods. To obtain a better understanding of biochemical and biophysical processes at the molecular level involving phospholipid bilayers, we apply molecular simulation methods to investigate the complexity of the membrane matrix using atomistic models. Here, we discuss three specific biological processes that are associated with biological membranes: 1) membrane stabilization, 2) membrane phase behavior, and 3) fatty acid-induced toxicity in cell membranes. For membrane stabilization, molecular dynamics studies were performed for mixed phospholipid bilayers containing two of the most prevalent phospholipids (phosphatidylcholine and phosphatidylethanolamime) in biological membranes. We presented structural and dynamics properties of these systems, as well as the effect of stabilizing agents, such as trehalose, on their properties. Furthermore, we performed a comprehensive analysis of the phase transition of lipid bilayers and investigated the interactions of stabilizing agents (glucose or trehalose) with lipid bilayers under dehydrated conditions to understand the mechanisms for preservation of cellular systems. For membrane phase behavior, a comprehensive study of the structural properties of saturated and monounsaturated lipid bilayers near the main phase transition were investigated using molecular dynamics simulations. In this study, we demonstrated that atomistic simulations are capable of capturing the phase transformation process of lipid bilayers, providing a valuable set of molecular and structural information at and near its transition state. Lastly, the third study investigated the mechanism for fatty acid-induced toxicity by integrating in vitro and in silico experiments to reveal the biophysical interactions of saturated fatty acid (palmitate) with the cellular membranes and the role of trehalose and unsaturated fatty acids (oleate and linoleate) in preventing changes to the membrane structure. Knowledge gained from this study is essential in the prevention and treatment of obesity-associated cirrhosis diseases. / Ph. D.

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The thesis entitled “In situ crystallography and charge density analysis of phase transitions in complex inorganic sulfates” consists of six chapters. Structural changes exhibited by ferroic and conducting materials are studied as a function of temperature via in situ crystallography on the same single crystal. These unique experiments bring out the changes in the crystal system resulting in subtle changes in the complex polyhedra, distortions in bond lengths and bond angles, rotation of sulfate tetrahedral around metal atoms, phase separations and charge density features. The results provide new insights into the structural changes during the phase transition in terms of coordination changes, variable bond paths and variability in electrostatic potentials while suggesting possible reaction pathways hitherto unexplored. Chapter 1 gives a brief review of the basic features of structural phase transitions in terms of types of phase transitions, their mechanisms and related properties and outlines some of the key characterization techniques employed in structural phase transition studies like single crystal diffraction, thermal analysis, conductivity, dielectric relaxation, Raman spectroscopy and charge density studies. Chapter 2 deals with the group of compounds A3H(SO4)2, where A= Rb, NH4, K, Na which undergoes ferroelastic to paraelastic phase transitions with increase in temperature. Crystal structures of these compounds have been determined to a high degree of accuracy employing the same single crystal at room temperature at 100K and at higher temperatures. The data collection at 100K allows the examination of the ordered and disordered hydrogen atom positions. Rb3H(SO4)2 show two intermediate phases before reaching the paraelastic phase with increase in temperature. However, in case of (NH4)3H(SO4)2 and K3H(SO4)2, the paraelastic phase transition involves a single step. Chapter 3 deals with variable temperature in situ single crystal X-ray diffraction studies on fast super protonic conductors AHSO4, where A= Rb, NH4, K to characterize the structural phase transitions as well as the dehydration mechanism. The structure of KHSO4 at room temperature belongs to an orthorhombic crystal system with the space group symmetry Pbca and on heating to 463K it transforms to a C centered orthorhombic lattice, space group Cmca. The high temperature structure contain two crystallographically independent units of KHSO4 of which one KHSO4 unit is disordered at oxygen and hydrogen sites an shows a remarkable increase of sulfur oxygen bond distance – 1.753(4)Å. On heating to 475K, two units of disordered KHSO4 combine and loose one molecule of water to result in a structure K2S2O7 along with an ordered KHSO4 in a monoclinic system [space group P21/c]. On further heating to 485K two units of ordered KHSO4 combine, again to lose one water molecule to give K2S2O7 in a monoclinic crystal system [space group C2/c]. In the case of RbHSO4, both the high temperature structural phase transition and a serendipitous polymorph have been characterized by single crystal X-ray diffraction. The room temperature structure is monoclinic, P21/n, and on heating the crystal insitu On the diffractometer to 460K the structure changes to an orthorhombic system [space group Pmmn]. On keeping the crystallization temperature at 80°C polymorph crystals of RbHSO4 were grown. In case of NH4HSO4 both the room temperature and high temperature structures are structurally similar to those in RbHSO4, but the transition temperature is found to be 413K. Chapter 4 deals with the crystal structure, ionic conduction, dielectric relaxation, Raman spectroscopy phase transition pf a fast ion conductor Na2Cd(SO4)2. The structure is monoclinic, space group C2/c, and is built up with inter connecting CdO6 octahedra and SO4 tetrahedra resulting in a framework structure. The mobile Na atoms are present in the framework, resulting in a high ionic conductivity. The conductivity measurement shows two phase transitions one at around 280°C, which was confirmed later from DTA, dielectric relaxation, high temperature powder diffraction and Raman spectroscopy. Chapter 5 describes the structure and in situ phase separation in two different bimetallic sulfates Na2Mn1.167(SO4)2S0.33O1.1672H2O and K4Cd3(SO4)5.3H2O. These compounds were synthesized keeping them as mimics of mineral structures. The structure of Na2Mn1.167(SO4)2S0.33O1.1672H2O is trigonal, space group R . The stiochiometry can be viewed as a combination of Na2Mn(SO4)22H2O resembling the mineral Krohnkite with an additional (Mn0.167S0.333O1.167) motif. On heating the parent compound on the diffractometer to 500K and keeping the capillary at this temperature for one hour, a remarkable structural phase separation occurs with one phase showing a single crystal-single crystal transition and the other generating a polycrystalline phase. The resulting single crystal spots can be indexed in a monoclinic C2/c space group and the structure determination unequivocally suggests the formation of Na2Mn(SO4)2, isostructural to Na2Cd(SO4)z. The mechanism follows the symmetry directed pathway from the rhombohedral → monoclinic symmetry with the removal of symmetry subsequent to the loss of the two coordinated water molecules. In case of K4Cd3(SO4)5.3H2O the structure belongs to the space group P21/n at room temperature and on heating to 500K and holding the capillary at this temperature for 60 minutes as before, the CCD images can be indexed in a cubic P213 space group after the phase separation, generating K2Cd2(SO4)3, belonging to the well known Langbeinite family, while the other phase is expected to be the sought after K2Cd(SO4)2. The possible pathways have been discussed. Chapter 6 reports the charge density studies of phase transitions in a type II langbeinite, Rb2Mn2(SO4)3. The structure displays two different phases, cubic at 200K, orthorhombic at 100K respectively. After multiple refinements it is found that there are significant differences in the actual bond path (Rij) and the conventional bond length. In the cubic phase the distortions in sulfate tetrahedral are more than in the orthorhombic phase which could be the expected driving force for the phase transition to occur. Appendix contains reprints of the work done on the structures of the following: a) Rb2Cd3(SO4)3(OH)2.2H2O: structural stability at 500 K b) Structure of (NH4)2Cd3(SO4)4.5H2O c) Structure of Rb2Cd3(SO4)4.5H2O

Thesis (M.S.)--Miami University, Dept. of Physics, 2005. / Title from first page of PDF document. Document formatted into pages; contains [1], vii, 55 p. : ill. Includes bibliographical references (p. 53-55).

Les perovskites hybrides organique-halogénure de plomb représentent une classe de matériaux émergents, proposés en tant qu'absorbeur de lumière dans le cadre d'une nouvelle génération de cellules solaires. La formule chimique de ces composés est APbX3, où A est un cation organique, X représente un anion halogénure (normalement Cl-, Br-, ou l-, ou alors un alliage composé par ces éléments). Les perovskite hybrides combinent d'excellentes propriétés d'absorption avec une grande longueur de diffusion et de longues durées de vie des porteurs de charge, ce qui permet d'atteindre des efficacités de conversion de photons de 22%. Un autre avantage réside dans leur bas coût de fabrication. Par conséquent, avec le développement de cette classe de matériaux, le photovoltaïque basé sur les perovskites sera potentiellement capable de fortement améliorer les performances de la technologie photovoltaïque actuelle, basée sur le silicium. Dans cette thèse, nous utilisons des méthodes optiques afin d'étudier les propriétés électroniques de base et la morphologie de couches minces de plusieurs représentants des perovskites. Nous étudions notamment des composés ayant le methylammonium et le formamidinium en tant que cations organiques ainsi que les iodures et les bromures à large bande interdite et nous montrons de quelle manière la composition chimique influence les paramètres étudiés. Par magnéto-transmission, nous déterminons directement l'énergie de liaison de l'exciton et sa masse réduite. Nous avons trouvé que les énergies de liaison à T = 2K sont comprises de 14 à 25 meV, plus petites ou comparables à l'énergie thermique moyenne à la température ambiante (25meV). De plus, ces valeurs diminuent à T=160K jusqu'à 10-24meV. Suite à ces résultats, nous concluons que les porteurs photocréés dans les perovksites peuvent être considérés ionisés thermiquement à la température ambiante. Les valeurs de masse effective sont comprises entre 0.09-0.13 fois la masse de l'électron libre. Nous montrons également que l'énergie de liaison de l'exciton ainsi que la masse effective dépendent linéairement de la valeur de la bande interdite. Nos résultats permettent donc d'estimer la valeur des paramètres de ces nouveaux composés perovksites. Nous avons étudié la morphologie de couches minces de perovskite par photoluminescence résolue spatialement avec une résolution micrométrique. Cette technique nous a permis d'observer des grains cristallins uniques. Nous démontrons que la transition de la phase tétragonale à orthorhombique à basse température est incomplète dans tous les matériaux étudiés, comme montré par les résidus de phase tétragonale trouvés à T =4K. En étudiant structurellement certaines régions endommagées et photo-recuites, nous montrons que la présence de la phase tétragonale à basse température augmente, causée par une déplétion de l'halogène. / The hybrid organo-lead halide perovskites are an emerging class of materials, proposed for use as light absorbers in a new generation of photovoltaic solar cells. The chemical formula for these materials is APbX3, where A is an organic cation and X represents halide anions (most commonly Br-, Cl- or I-, or alloyed combination of these). The hybrid perovskies combine excellent absorption properties with large diffusion lengths and long lifetime of the carriers, resulting in photon conversion efficiencies as high as 22%. Another advantage is the inexpensiveness of the fabrication process. Therefore, with the rapid development of this class of materials, the perovskite photovoltaics has perspectives to outperform the well-established silicon technology. Here, we use optical methods to investigate the basic electronic properties and morphology in the thin films of several representatives of the hybrid perovskites. We study the compounds based on Methylammonium and Formamidinium organic cations; the iodides and wide band-gap bromides, showing how the chemical composition influences the investigated parameters. Using magneto-transmission, we directly determine the values of exciton binding energy and reduced mass. We find that the exciton binding energies at T = 2 K, varying from 14 to 25 meV, are smaller or comparable to the average thermal energy at room temperature (˜25 meV). Moreover, these values fall further at T = 160 K, to 10-24 meV. Based on that we conclude that the carriers photocreated in a perovskite material can be considered to be thermally ionized at room temperature. The measured reduced masses are in the range of 0.09-0.13 of the electron rest mass. We also show that both exciton binding energy and reduced mass depend linearly on the band gap energy. Therefore, the values of these parameters can be easily estimated for the synthesis of new perovskite compounds. With the spatially resolved photoluminescence, we probe the morphology of perovskite films with micrometer resolution, which enables us to observe single crystalline grains. The resulting maps show that all investigated thin films are composed from the dark and bright crystalline grains. We demonstrate that the low temperature phase transition from tetragonal to orthorhombic phase is incomplete in all studied materials, as the remains of the tetragonal phase are found even at T = 4 K. By investigating structurally damaged and photo annealed regions, where the occurrence of the tetragonal phase at low temperatures is enhanced, we attribute its presence to the depleted halide content.

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