<p> Understanding the behavior of liquid hydrocarbon propellants under high pressure and temperature conditions is a crucial step towards improving the performance of modern-day combustion engines (liquid rocket engines, diesel engines, gas turbines and so on) and designing the next generation ones. Under such harsh thermodynamic conditions (high P&T) propellent droplets may experience anywhere from sub-to-trans-to-supercritical regime. The focus of this research is to explore the dynamics of the vapor-liquid two phase system formed by a liquid hydrocarbon fuel (n-heptane or n-dodecane) and ambient (nitrogen) over a wide range of P&T leading up to the mixture critical point and beyond. Molecular dynamics (MD) has been used as the primary tool in this research along with other tools like: phase stability calculations based on Gibb’s work, Peng Robinson equation of state, density gradient theory and neural networks.</p>

We studied the structural instabilities of one-dimensional (1D) and quasi-one-dimensional (Q1D) electron-phonon systems at low temperature through two models, SuSchrieffer-Heeger (SSH) and molecular crystal (CM) with and without spin. The phase diagrams are obtained using a Kadanoff-Wilson renormalization group approach (GR). For the 1D half-filled system the study of the frequency dependence of the electronic gap allowed us to connect continuously the two limits, adiabatic and non-adiabatic. The Peierls and Cooper channels interference and the quantum fluctuations reduce the gap. A regime change occurs when the frequency becomes of the order of mean field gap, marking a quantum-classical crossover that is the Kosterlitz-Thouless type. At this level, the effective coupling behaves in power law function on frequency. For the case with spin, a gapped Peierls state is maintained in the non-adiabatic limit, while for the case without spin, the system transits to ungapped disordered state, namely the Luttinger liquid stat (LL). For the SSH model without spin, the GR confirms the existence of a threshold phonon coupling beyond which the gap is restored. The study of the rigidities of the two models without spin allowed us to trace the main features of the LL state predicted by the bosonization method. The study of the Holstein-Hubbard model has allowed us not only to reproduce the phase diagrams already obtained by the Monte Carlo method, but to highlight two additional phases, namely, free fermions phase and the bond charge-density-wave phase. We have extended this study to the quarter-filled Q1D Peierls systems at finite temperature. Within the SSH model, an unconventional superconducting phase with spin singlet symmetry SS-s emerges at low temperature when the deviation to the perfect nesting of the Fermi surface is strong enough. Peierls-SS transition is characterized by the presence of a quantum critical point at low frequency and by a power law behavior of the transition temperature as a function of frequency with an exponent identical to one of 1D system. This exponent which universality has been verified contrasts with the BCS result. Coulomb interactions have been introduced through the study of the extended SSH-Hubbard model. The extension of this work to half-filled SSH and CM cases was also performed.

This thesis reports the results of light-scattering measurements and visual investigations of critical phenomena in the complex mixture 1-propanol (1P) + water (W) + potassium chloride (KCl) which has a special critical point (or a special thermodynamic state) known as the double critical point (DCP). The main theme of the thesis is the critical behavior on approaching a special critical point (i.e., the DCP) in a complex or associating mixture in contrast with that in simple, nonassociating mixtures. The asymptotic critical behavior in complex or associating fluids, such as polymer solutions and blends, ionic and nonionic micellar solutions, microemulsions, aqueous and nonaqueous electrolyte solutions, protein solutions, etc., is now commonly accepted to belong to the 3D-Ising universality class. However, the temperature range of the asymptotic regime in these fluids, with universal behavior, has a nonuniversal width and is, in general, smaller than that in simple or nonassociating fluids. In complex mixtures, which are made up of relatively large molecules or particle clusters of mesoscopic range, the coupling between the conventional correlation length of the critical fluctuations ( ξ) and an additional length scale associated with the mesoscale structures (ξD) is known to modify the approach towards the universal nonclassical critical behavior near their critical points. Nevertheless, the generality of this approach needs to be confirmed. There are also instances of a pure classical or close to classical behavior being observed in the critical domain of complex mixtures, although recent experimental results contradict the earlier observations. Therefore, further experimental evidences than that presently available are necessary before one can say how far the analogy between simple and complex fluids can be pushed. Variations in the effective dielectric constant of a mixture have been known to affect the critical behavior. Furthermore, we anticipate the presence of special critical points in complex mixtures to cause nontrivial modifications in the approach towards the universal asymptotic critical behavior. Special thermodynamic states are characterized by critical fluctuations with exceptionally large correlation length, and are displayed by multicomponent liquid mixtures, in which there are a multitude of thermodynamic paths by which a critical point can be approached, and offers rich information about the critical phenomena. These issues are being addressed in this research work. This thesis is organized into 7 Chapters. Chapter 1 begins with an account of the historical development of the field of critical point phenomena with a brief introduction to critical phenomena in simple fluids. Critical phenomena observed in various complex systems such as aqueous and nonaqueous ionic fluids, polymer solutions and blends, micellar and microemulsion systems, etc., are discussed, with particular attention to investigations into crossover from Ising to mean-field critical behavior observed in these systems, which are relevant to the present work. Theoretical attempts at modeling ionic criticality are cited and summarized. This is followed by a discussion of re-entrant phase transitions in multicomponent liquid systems. An account of the various types of special critical points, such as double critical point, critical double point, critical inflection point, quadruple critical point, etc., highlighting the critical behavior on approaching these special critical points, and some of the models of reentrant miscibility are briefly given. The Chapter ends with a statement on the goals of the present research work. Chapter 2 describes the instrumentation developed and the data acquisition procedures adopted for the study. Details of the thermostats and precision temperature controllers used for visual and light-scattering measurements are provided. The important design considerations relating to the achievement of a high degree of temperature stability (~ ±1 mK in the range 293-383 K) are elucidated clearly. The temperature sensors used in the present experiments and their calibration procedures are discussed. The light-scattering instrumentation is discussed in depth. The problems associated with the light-scattering techniques when it is used to study critical point phenomena, and the strategies adopted to overcome them are discussed. The sample cells used for visual investigations and light- scattering experiments, along with the procedure adopted for cleaning and filling of sample cells are also described. Chapter 3 essentially deals with the characterization of the system 1P + W + KCl. It begins with a brief introduction to the critical behavior in complex mixtures, and the motivation behind choosing the present system. The phase behavior in the present mixture, the generation of the coexistence curves and the line of critical points in the mixture, and the method used for preparation of the samples are described. The criticality of the samples is judged by the equal volume phase separation criterion through visual investigations. Addition of a small amount of salt (i.e., KCl) to the 1P + W solution induces phase separation in the mixture as a result of a salting-out process. Decreasing the salt concentration has the same effect as that of increasing pressure on the liquid-liquid demixing of this mixture. Therefore, KCl may be considered as an appropriate field variable analogous to pressure in this mixture. The mixture 1P + W + KCl exhibits reentrant phase transitions and has an array of lower (TL) and upper (TU) critical solution temperatures. It is found that the line of TL’s and TU’s, known as the line of critical points, merge (TU - TL = ΔT → 0) to form a special thermodynamic state known as the DCP. The DCP is approached as close as 509 mK (i.e., ΔT ~ 509 mK) in this work. An analysis of the critical line shows that it is roughly parabolic in shape, which is in consonance with the predictions of the lattice models and the Landau-Ginzburg theory of phase transition. In addition to the presence of a special critical point, various structure probing techniques like small angle X-ray scattering (SAXS), small angle neutron scattering (SANS), etc., indicate the presence of large-scale density inhomogeneities or clusters in 1P + W solution and its augmentation on adding small amount of KCl. Therefore, the present mixture provides a unique possibility to investigate the combined effects of molecular structuring as well as a special critical point on the critical behavior. Only a section of the coexistence surface of the mixture could be generated, owing to various experimental limitations and other problems inherent to the system. This limited further studies on the coexistence curves in the mixture. Chapter 4 reports the critical behavior of osmotic susceptibility in the present mixture. The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths by varying t [ =| (T - T TL)/ TL|] from the lower one-phase region. The light-scattering data analysis emphasizes the need for correction-to-scaling terms for a proper description of the data over the investigated t range. Renormalization of the critical exponents is observed as the critical line is approached along certain special paths. Experimental evidence for the doubling of the extended scaling exponent Δ1 near the DCP is shown. There is no signature of Fisher renormalization in the values of the critical exponents. The data analysis yields very large magnitudes for the correction amplitudes A1 and A2, with the first-correction amplitude A1 being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. The magnitudes of the correction amplitudes are observed to increase gradually as TL approaches the DCP. The increasing need for extended scaling in the neighborhood of special critical points has been noted earlier in several aqueous electrolyte solutions, in polymer-solvent systems, etc. However, the magnitudes of the correction amplitudes were not as large as that in the present case. Analysis of the effective susceptibility exponent γeff in terms of t indicate that, for the TL far away from the DCP, γeff displays a nonmonotonic crossover from its single limit 3D Ising value (~ 1.24) towards its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value (~ 2.39) towards its nearly doubled mean-field value (~ 1.84) with increase in t. For the in-between TL’s, the limiting value of γeff in the asymptotic as well as nonasymptotic regimes gradually increases towards the DCP. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend towards shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover behavior to the mean-field limit extends well beyond t > 10¯2 for the TL’s studied. The crossover behavior is discussed in terms of the emergence of a new lengthscale ξD associated with the enhanced ion-induced clustering seen in the mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover is discussed in terms of the varying influence of the DCP on the critical behavior along the TL line. The discussion is extended to explain the observed critical behavior in various re-entrant systems having other special critical points. The extended renormalized Ising regime towards the DCP is also reflected in a decrease in the correlation length amplitude (ξ0) as TL approaches the DCP. It is observed that the first-correction amplitude A1 corresponding to fit using two correction terms becomes more negative as TL approaches the DCP, implying an increase in the value of the parameter ū of the crossover model [by Anisimov et al., Phys. Rev. Lett. 75, 3146 (1995)] as the DCP is approached. This increase in reflected in a trend towards a relatively sharp crossover behavior of γeff as TL shifts towards the DCP, i.e., towards the high temperature critical points. The significance of the field variable tUL in understanding different aspects of reentrant phase transitions is manifested in the present system as well. Analysis of the data in terms of tUL led to the retrieval of universal values of the exponents for all TL’s. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1. The limited (TL _ T) range restricted such a behavior of the effective exponent (in terms of t as well as tUL) for the lowest TL. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic, high tUL region, as foreseen earlier in micellar systems. The effective susceptibility exponent in terms of tUL also indicates an increase in the sharpness of crossover towards the high temperature TL’s. An increase in the sharpness of crossover with polymer chain length has been observed in polymer solutions. Therefore, our results suggest the need for further composition and temperature-dependent study of molecular structuring in the present mixture. There is also a large decrease in the dielectric constant of the mixture towards the high temperature TL’s. In Chapter 5 the light-scattering measurements are performed on approaching the DCP along the line of the upper critical solution temperatures (i.e., TU’s), by varying t [ = (T - TU )/ TU ] from the high temperature one-phase region in the mixture. A trend towards shrinkage in the simple scaling region is observed as TU shifts away from the DCP. Such a trend was not visible in the data analysis of the TL’s using the correction terms, due to the varying (TL - T) ranges. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. As with the TL’s, for the TU closest to the DCP, γeff displays a nonmonotonic crossover from its 3D-Ising value towards its nearly doubled mean-field value with increase in t. While for that far away from the DCP, γeff displays a nonmonotonic crossover from its single limit Ising value towards a value slightly lower than its mean-field value of 1 with increase in t. The limited (TL – T) range restricted such a behavior of γeff for the TL far away from the DCP, This feature of γeff in the nonasymptotic, high t region is yet again interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from below. Unlike TL’s, the crossover behavior in the present case is pronounced and more sharp for all TU’s. However, the variation in the width of the renormalized Ising regime on approaching the DCP along the TU line is quite similar to that observed along the TL line. The crossover behavior is attributed to the strong ion-induced structuring seen in the mixture, while the observed trend in the crossover as TU shifts towards/away from the DCP is attributed to the varying influence of the DCP. The influence of the DCP on the critical behavior along the TU (or TL) line decreases as TU (or TL) shifts away from the DCP. Our observations indicate an increase in the sharpness of crossover as the critical temperature shifts from TL towards TU, or in other words, as the critical point shifts towards higher temperatures. SANS measurements on the present mixture indicate no difference in the growth of mesoscale clusters in the lower and upper one-phase regions in the mixture. Hence, the observed increase in the sharpness of crossover towards the TU’s is very puzzling. The dielectric constant of the major constituent (i.e., water, ~ 62 %) of the present mixture decreases from around 80 to 63 as the critical temperature shifts from TL towards TU. Therefore, our results suggest the need to look at the crossover phenomena probably from two perspectives, namely, the solvent or dielectric effect and the clustering effect. The increase in the sharpness of the crossover behavior on approaching the high temperature critical points is probably related to the macroscopic property of the mixture, i.e., to the decrease in the dielectric constant of the mixture, while the actual nonmonotonic character of the crossover behavior is related to the microscopic property of the mixture, i.e., to the clustering effects, the extent of which determines the width of the asymptotic critical domain. However, this conclusion is somewhat subtle and calls for rigorous theoretical and experimental efforts to unravel the exact dependence of the crossover behavior on the dielectric constant. Analysis using the field variable tUL in lieu of the conventional variable t led to the retrieval of unique, universal exponents for all TU’s irrespective of the ΔT value. For all TU’s, the effective susceptibility exponent in terms of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis of the effective exponent for the TU far away from the DCP. Like with the TL’s, the crossover behavior extends over nearly the same tUL range for the TU’s studied. However, the crossover is again sharper when compared to the TL’s. Chapter 6 reports light-scattering measurements (by heating as well as cooling) on a non phase-separating 1P + W + KCl mixture in the vicinity of the DCP. The results indicate that despite the lack of phase-separation or critical points, critical-phenomena-like fluctuations can still occur in homogeneous mixtures if they reside in some other direction than temperature or composition (like, pressure or salt concentration) of the phase diagram. Unlike earlier studies on non phase-separating mixtures, our results indicate a crossover behavior of the effective susceptibility exponent, in addition to the power-law behavior. Chapter 7 sums up the major findings of the work reported in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the exact dependence of dielectric constant of the mixture on the character of the crossover behavior.

We report experimentally results on the low temperature properties of two classes of materials with a special emphasizes near the QCP induced by substitution and magnetic 1.field: (1) the HF systems YbRh2(Si0.95Ge0.05)2, Yb1-yLayRh2Si2 (y = 0.05, 0.1),and YbIr2Si2 with tetragonal structures and CeIn3-xSnx (x = 0.55, 0.6, 0.65, 0.7, 0.8) with cubic structure; (2) the quantum spin systems: Cs2CuCl4 and Cs2CoCl4. In all the HF compounds we have observed NFL behavior in zero magnetic field close to the QCP. The La substituted system does not show an antiferromagnetic (AFM) transition down to the lowest accessible temperature (0.03 K) while in YbRh2(Si1-xGex)2 with x = 0 and x = 0.05 AFM transitions occur at TN =0.07 K and 0.02 K, respectively. For Yb0.9La0.1Rh2Si2 we observe below 0.07 K saturation of DeltaC/T indicating clearly a LFL state for this concentration. For YbIr2Si2, DeltaC/T saturates below 0.5 K. In contrast to the Yb based compounds in the vicinity of the QCP, CeIn3-xSnx shows no evidence of a divergence in Delta C/T, with B or with x. Furthermore, we used specic heat measurements in the mK temperature range and at high fields (up to 12 T) to probe the phase diagrams in the low dimensional quantum antiferromagnets Cs2CuCl4 and Cs2CoCl4. In applied magnetic field, we have presented experimental evidence that in Cs2CuCl4 the field dependence of the critical temperature Tc(B) ~ (Bc-B)^1-Phi close to the critical field Bc = 8.51 T is well described with Phi=1.5. This is in very good agreement with the exponent expected in the mean-field approximation and support the notion of a Bose-Einstein condensation of magnons in Cs2CuCl4.

Submitted by Johnny Rodrigues (johnnyrodrigues@ufcg.edu.br) on 2018-07-17T17:42:26Z No. of bitstreams: 1 LEOPOLDO MAURÍCIO TAVARES BARBOSA - DISSERTAÇÃO PPGMAT 2007..pdf: 712644 bytes, checksum: 6b24483b48b038e23d4ace377b04ece5 (MD5) / Made available in DSpace on 2018-07-17T17:42:27Z (GMT). No. of bitstreams: 1 LEOPOLDO MAURÍCIO TAVARES BARBOSA - DISSERTAÇÃO PPGMAT 2007..pdf: 712644 bytes, checksum: 6b24483b48b038e23d4ace377b04ece5 (MD5) Previous issue date: 2007-10 / CNPq / Capes / Neste trabalho usamos métodos variacionais para mostrar a existência de solução fraca para dois tipos de problema. O primeiro trata-se de uma Equação Diferencial Ordinária. O segundo é referente ao sistema Hamiltoniano. *Para Visualisar as equações ou formulas originalmente escritas neste resumo recomendamos o downloado do arquivo completo. / In this work we use variational methods to show the existence of weak solutions for two types problems. The first, is related with a following Ordinary Differential Equations. The second is relating at the Hamiltonian Systems. *To see the equations or formulas originally written in this summary we recommend downloading the complete file.

Les transitions de phase près d'un point critique - dites du second ordre - sont un sujet toujours d'actualité en raison des nombreux phénomènes critiques intéressants tels que la force de Casimir critique, les problèmes de confinements ou les phénomènes hors d'équilibre suivant une trempe au point critique. Cette thèse vise à étudier expérimentalement certains phénomènes engendrés près d'un point critique. La thèse est divisée en deux axes : le premier consiste à développer plusieurs systèmes expérimentaux qui permettront de mesurer essentiellement la viscosité, par l'intermédiaire des fluctuations thermiques à l'échelle micrométrique. Le deuxième axe consiste à trouver et caractériser des mélanges binaires présentant une transition de phase du second ordre dans lesquelles on souhaite faire des mesures. Les enjeux de ces systèmes expérimentaux sont d'avoir une régulation en température précise, une sonde de mesure sensible aux fluctuations thermiques et/ou à des forces de l'ordre du pN, et un échantillon fiable et reproductible présentant un point critique accessible expérimentalement. Nous avons ainsi monté à partir d'un microscope à force atomique (AFM) déjà présent au laboratoire, un système de mesure de viscosité à sonde AFM fibrée. Malgré sa faible efficacité en terme de sonde de mesure métrologique, nous avons pu décrire et développer un modèle de couplage de modes de vibration permettant de comprendre la mécanique de microleviers AFM fibrés. J'ai également développé au laboratoire la mesure de microscopie dynamique différentielle qui permet de faire des mesures à sondes multiples contrairement au premier montage. J'ai discuté de la précision de la mesure dans le cadre de notre objectif d'étude des fluctuations critiques. En ce qui concerne l'échantillon de mesure, nous avons étudié plusieurs mélanges binaires que nous avons caractérisés par des méthodes classiques de turbidité et diffusion statique de la lumière. Cette caractérisation nous a permis de connaître les mélanges binaires pour les utiliser dans un troisième système de mesure : billes micrométriques piégées dans des pinces optiques déjà monté au laboratoire. Nous y avons rajouté un système de régulation thermique fait maison pour être exploité avec les contraintes de la pince optique. Ces tests ont fait apparaître un phénomène inattendu d'oscillations de transition de phase induites par laser. Nous avons développé un modèle pour les décrire. Enfin, des expériences préliminaires - toujours avec les pinces optiques dans les mélanges binaires - nous ont permis d'observer qualitativement des effets de l'approche au point critique par des mesures de viscosité et d'interaction type force de Casimir critique. / Phase transitions near a critical point, or second order phase transitions, are still a recent object of studies because of the large amount of interesting critical phenomena as the critical Casimir force, confinements problems or out of equilibrium phenomena following a quench at the critical point. This thesis experimentally studies phenomena near a critical point. This manuscript is divided in two parts : the first one consists in building several experimental set-up which measure viscosity through thermal fluctuation at micrometric scale. The second part consists in finding and characterize binary mixtures which show a second order phase transition. Preliminary results have been done in these samples. One of the principal points of these experimental set-up are a well regulated temperature, a probe sensitive to thermal fluctuation and/or pN forces and a reproducible binary mixture which presents a critical point easy to reach experimentally. We mounted from an Atomic Force Microscope (AFM) already built in the laboratory, a hanging-fiber probe to measure viscosity of liquids. Despite its weak efficiency as a metrologic probe, we described and developed a mode coupling model which let us understand mechanics of hanging-fiber probes. I also developed in the lab the dynamic differential microscopy technique (DDM) which do measurements with several probes. I discussed about the measure precision with in mind the aim of studying critical fluctuations. For the choice of the sample, we studied several binary mixtures. We characterized them by classical methods as turbidity measurements and static light scattering. These characterizations let us learn about binary mixtures in order to use them in a third experimental set-up : beads trapped in an optical tweezers already built in the lab. We added to it a home-made thermal regulation which can be used with the constraints of optical tweezers. These tests showed an unexpected phenomenon of oscillating phase transition induce by laser. We developed a model to describe it. At last, preliminary experiments with optical tweezers in binary mixtures showed qualitative effects of an approach near a critical point on the viscosity and on interactions between beads as critical Casimir force.

Orientador: Francisco Odair Vieira de Paiva / Tese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática, Estatística e Computação Científica / Made available in DSpace on 2018-08-21T19:28:36Z (GMT). No. of bitstreams: 1 Malavazi_MazilioCoronel_D.pdf: 1741221 bytes, checksum: becbc428943851a9a63bba6d406db3ca (MD5) Previous issue date: 2013 / Resumo: O resumo poderá ser visualizado no texto completo da tese digital / Abstract: The abstract is available with the full electronic document / Doutorado / Matematica / Doutor em Matemática

The interplay of thermodynamic properties of strongly interacting matter and its emission of photons is investigated. For this purpose the Lagrangian of the quark meson model (in the literature also dubbed "linear sigma model" or "linear sigma model with quarks") is extended by an electromagnetic sector. Based on this extended Lagrangian both the grand-canonical potential and the generating functional of correlation functions are calculated in a consistent manner. From the former, the phase structure and various thermodynamical properties are determined. Especially, the dependence of certain landmarks (critical point, intersections of the phase boundary with the coordinate axes, etc.) of the phase diagram with respect to the model parameters is investigated in detail. With the help of the generating functional in turn, the photon propagator can be computed whose imaginary part is connected to the emission rate of photons. The leading order of the result with respect to the number of participating particles and the power of the quark-meson coupling is expressed in terms of tree level diagrams, which are calculated likewise. On this basis, the photon emissivity with respect to temperature, chemical potential and photon frequency is calculated and analyzed addressing various questions. The dependence of the particle masses with respect to temperature and chemical potential leaves notable imprints on the emissivities of the individual production processes. Especially a first-order phase transition can easily be identified, since, there, the emissivity may jump - depending on the temperature - by a factor of about ten. Contrarily, within our analysis, we do not find signatures in the photon emissivities that specifically mark a critical end point. Moreover, it is investigated on which parameters the photon emission rate depends in the low- and high-frequency regions. With these results the behavior of the emissivity with respect to temperature and chemical potential can be understood and many peculiarities of the emissivities can be explained. / Das Zusammenspiel der thermodynamischen Eigenschaften von stark wechselwirkender Materie und deren Emission von Photonen wird untersucht. Dazu wird die Lagrangedichte des Quark-Meson-Modells (auch: Linear-Sigma-Modell oder Linear-Sigma-Modell mit Quarks) um einen elektromagnetischen Sektor erweitert. Aus der so erweiterten Lagrangedichte werden auf konsistente Weise sowohl das großkanonische Potential als auch das erzeugende Funktional der Korrelationsfunktionen ermittelt. Aus ersterem werden die Phasenstruktur des Modells sowie zahlreiche thermodynamische Eigenschaften berechnet. Insbesondere wird die Abhänigkeit einiger Orientierungspunkte (kritischer Punkt, Schnittpunkte der Phasengrenze mit den Koordinatenachsen usw.) des Phasendiagramms von den Modellparametern detailiert untersucht. Mit Hilfe des erzeugenden Funktionals wiederum kann der Photonenpropagator bestimmt werden, dessen Imaginärteil mit der Emissionsrate von Photonen zusammenhängt. Die führende Ordnung in einer Entwicklung nach der Anzahl der beteiligten Teilchen und der Potenz der Quark-Meson-Kopplung lässt sich durch Baumgraphen-Diagramme darstellen, die ebenfalls berechnet werden. Auf dieser Basis wird die Photon-Emissivität in Abhängigkeit von Temperatur, chemischem Potential und Photon-Frequenz berechnet und unter verschiedenen Gesichtspunkten analysiert. Die Abhängigkeit der Teilchenmassen von Temperatur und chemischem Potential hinterlässt teilweise ausgeprägte Signaturen in den Emissivitäten der einzelnen sub-Prozesse. Insbesondere ein Phasenübergang erster Ordnung zeigt sich deutlich, da an diesem die Emissivität - abhänging von der Temperatur - um einen Faktor der Größenordnung zehn springen kann. Jedoch finden wir im Rahmen dieser Analyse keine spezifischen Signaturen in den Photonen-Emissivitäten, die einen kritischen Punkt auszeichnen. Des weiteren wird untersucht von welchen Parametern die Photonen-Emissionsrate in den Bereichen niedriger oder hoher Photonen-Frequenzen abhängt. Mit diesen Ergebnissen kann das Verhalten der Emissivität in Abhängigkeit von Temperatur und chemischem Potential gut verstanden und zahlreiche Auffälligkeiten in den Emissivitäten erklärt werden.

As a first aspect the thesis treats existence results of the perturbed eigenvalue problem of the 1-Laplace operator. This is done with the aid of a quite general critical point theory results with the genus as topological index. Moreover we show that the eigenvalues of the perturbed 1-Laplace operator converge to the eigenvalues of the unperturebed 1-Laplace operator when the perturbation goes to zero. As a second aspect we treat the eigenvalue problems of the vectorial 1-Laplace operator and the symmetrized 1-Laplace operator. And as a third aspect certain related parabolic problems are considered.

We report experimentally results on the low temperature properties of two classes of materials with a special emphasizes near the QCP induced by substitution and magnetic 1.field: (1) the HF systems YbRh2(Si0.95Ge0.05)2, Yb1-yLayRh2Si2 (y = 0.05, 0.1),and YbIr2Si2 with tetragonal structures and CeIn3-xSnx (x = 0.55, 0.6, 0.65, 0.7, 0.8) with cubic structure; (2) the quantum spin systems: Cs2CuCl4 and Cs2CoCl4. In all the HF compounds we have observed NFL behavior in zero magnetic field close to the QCP. The La substituted system does not show an antiferromagnetic (AFM) transition down to the lowest accessible temperature (0.03 K) while in YbRh2(Si1-xGex)2 with x = 0 and x = 0.05 AFM transitions occur at TN =0.07 K and 0.02 K, respectively. For Yb0.9La0.1Rh2Si2 we observe below 0.07 K saturation of DeltaC/T indicating clearly a LFL state for this concentration. For YbIr2Si2, DeltaC/T saturates below 0.5 K. In contrast to the Yb based compounds in the vicinity of the QCP, CeIn3-xSnx shows no evidence of a divergence in Delta C/T, with B or with x. Furthermore, we used specic heat measurements in the mK temperature range and at high fields (up to 12 T) to probe the phase diagrams in the low dimensional quantum antiferromagnets Cs2CuCl4 and Cs2CoCl4. In applied magnetic field, we have presented experimental evidence that in Cs2CuCl4 the field dependence of the critical temperature Tc(B) ~ (Bc-B)^1-Phi close to the critical field Bc = 8.51 T is well described with Phi=1.5. This is in very good agreement with the exponent expected in the mean-field approximation and support the notion of a Bose-Einstein condensation of magnons in Cs2CuCl4.