Studies in quantum field theory at finite temperature

The thesis deals with certain quantum field systems exhibiting spontaneous symmetry breaking and their response to temperature. These models find application in diverse branches such as particle physics, solid state physics and non~linear optics. The nature of phase transition that these systems may undergo is also investigated. The thesis contains seven chapters. The first chapter is introductory and gives a brief account of the various phenomena associated with spontaneous symmetry breaking. The chapter closes with anote on the effect of temperature on quantum field systems. In chapter 2, the spontaneous symmetry breaking phenomena are reviewed in more detail. Chapter 3, deals with the formulation of ordinary and generalised sine-Gordon field theories on a lattice and the study of the nature of phase transition occurring in these systems. In chapter 4, the effect of temperature on these models is studied, using the effective potential method. Chapter 5 is a continuation of this study for another model, viz, the m6 model. The nature of phase transition is also studied. Chapters 5 and 6 constitute a report of the investigations on the behaviour of coupling constants under thermal excitation D1 $4 theory, scalar electrodynamics, abelian and non-abelian gauge theories

Analysis discrete function theory

There is a recent trend to describe physical phenomena without the use of infinitesimals or infinites. This has been accomplished replacing differential calculus by the finite difference theory. Discrete function theory was first introduced in l94l. This theory is concerned with a study of functions defined on a discrete set of points in the complex plane. The theory was extensively developed for functions defined on a Gaussian lattice. In 1972 a very suitable lattice H: {Ci qmxO,I qnyo), X0) 0, X3) 0, O < q < l, m, n 5 Z} was found and discrete analytic function theory was developed. Very recently some work has been done in discrete monodiffric function theory for functions defined on H. The theory of pseudoanalytic functions is a generalisation of the theory of analytic functions. When the generator becomes the identity, ie., (l, i) the theory of pseudoanalytic functions reduces to the theory of analytic functions. Theugh the theory of pseudoanalytic functions plays an important role in analysis, no discrete theory is available in literature. This thesis is an attempt in that direction. A discrete pseudoanalytic theory is derived for functions defined on H.

Adsorption of element 112 on a Au surface

Während der letzten 20 Jahre hat sich das Periodensystem bis zu den Elementen 114 und 116 erweitert. Diese sind kernphysikalisch nachgewiesen, so dass jetzt die chemische Untersuchung an erster Selle steht. Nachdem sich das Periodensystem bis zum Element 108 so verhält, wie man es dem Periodensystem nach annimmt, wird in dieser Arbeit die Chemie des Elements 112 untersucht. Dabei geht es um die Adsorptionsenergie auf einer Gold-Ober fläche, weil dies der physikalisch/chemische Prozess ist, der bei der Analyse angewandt wird. Die Methode, die in dieser Arbeit angwandt wird, ist die relativistische Dichtefunktionalmethode. Im ersten Teil wird das Vielkörperproblem in allgemeiner Form behandelt, und im zweiten die grundlegenden Eigenschaften und Formulierungen der Dichtefunktionaltheorie. Die Arbeit beschreibt zwei prinzipiell unterschiedliche Ansätze, wie die Adsorptionsenergie berechnet werden kann. Zum einen ist es die sogenannte Clustermethode, bei der ein Atom auf ein relativ kleines Cluster aufgebracht und dessen Adsorptionsenergie berechnet wird. Wenn es gelingt, die Konvergenz mit der Größe des Clusters zu erreichen, sollte dies zu einem Wert für die Adsorptionsenergie führen. Leider zeigt sich in den Rechnungen, dass aufgrund des zeitlichen Aufwandes die Konvergenz für die Clusterrechnungen nicht erreicht wird. Es werden sehr ausführlich die drei verschiedenen Adsorptionsplätze, die Top-, die Brücken- und die Muldenposition, berechnet. Sehr viel mehr Erfolg erzielt man mit der Einbettungsmethode, bei der ein kleiner Cluster von vielen weiteren Atomen an den Positionen, die sie im Festkörpers auf die Adsorptionsenergie soweit sichergestellt ist, dass physikalisch-chemisch gute Ergebnisse erzielt werden. Alle hier gennanten Rechnungen sowohl mit der Cluster- wie mit der Einbettungsmethode verlangen sehr, sehr lange Rechenzeiten, die, wie oben bereits erwähnt, nicht zu einer Konvergenz für die Clusterrechnungen ausreichten. In der Arbeit wird bei allen Rechnungen sehr detailliert auf die Abhängigkeit von den möglichen Basissätzen eingegangen, die ebenfalls in entscheidender Weise zur Länge und Qualität der Rechnungen beitragen. Die auskonvergierten Rechnungen werden in der Form von Potentialkurven, Density of States (DOS), Overlap Populations sowie Partial Crystal Overlap Populations analysiert. Im Ergebnis zeigt sich, dass die Adsoptionsenergie für das Element 112 auf einer Goldoberfläche ca. 0.2 eV niedriger ist als die Adsorption von Quecksilber auf der gleichen Ober fläche. Mit diesem Ergebnis haben die experimentellen Kernchemiker einen Wert an der Hand, mit dem sie eine Anhaltspunkt haben, wo sie bei den Messungen die wenigen zu erwartenden Ereignisse finden können.

Many-body theory of laser-induced ultrafast demagnetization and angular momentum transfer in ferromagnetic transition metals

An electronic theory is developed, which describes the ultrafast demagnetization in itinerant ferromagnets following the absorption of a femtosecond laser pulse. The present work intends to elucidate the microscopic physics of this ultrafast phenomenon by identifying its fundamental mechanisms. In particular, it aims to reveal the nature of the involved spin excitations and angular-momentum transfer between spin and lattice, which are still subjects of intensive debate. In the first preliminary part of the thesis the initial stage of the laser-induced demagnetization process is considered. In this stage the electronic system is highly excited by spin-conserving elementary excitations involved in the laser-pulse absorption, while the spin or magnon degrees of freedom remain very weakly excited. The role of electron-hole excitations on the stability of the magnetic order of one- and two-dimensional 3d transition metals (TMs) is investigated by using ab initio density-functional theory. The results show that the local magnetic moments are remarkably stable even at very high levels of local energy density and, therefore, indicate that these moments preserve their identity throughout the entire demagnetization process. In the second main part of the thesis a many-body theory is proposed, which takes into account these local magnetic moments and the local character of the involved spin excitations such as spin fluctuations from the very beginning. In this approach the relevant valence 3d and 4p electrons are described in terms of a multiband model Hamiltonian which includes Coulomb interactions, interatomic hybridizations, spin-orbit interactions, as well as the coupling to the time-dependent laser field on the same footing. An exact numerical time evolution is performed for small ferromagnetic TM clusters. The dynamical simulations show that after ultra-short laser pulse absorption the magnetization of these clusters decreases on a time scale of hundred femtoseconds. In particular, the results reproduce the experimentally observed laser-induced demagnetization in ferromagnets and demonstrate that this effect can be explained in terms of the following purely electronic non-adiabatic mechanism: First, on a time scale of 10–100 fs after laser excitation the spin-orbit coupling yields local angular-momentum transfer between the spins and the electron orbits, while subsequently the orbital angular momentum is very rapidly quenched in the lattice on the time scale of one femtosecond due to interatomic electron hoppings. In combination, these two processes result in a demagnetization within hundred or a few hundred femtoseconds after laser-pulse absorption.

Theory of enhanced magnetic anisotropy induced by Pt adatoms on two-dimensional Co clusters supported on a Pt(111) substrate

Calculations are reported of the magnetic anisotropy energy of two-dimensional (2D) Co nanostructures on a Pt(111) substrate. The perpendicular magnetic anisotropy (PMA) of the 2D Co clusters strongly depends on their size and shape, and rapidly decreases with increasing cluster size. The PMA calculated is in reasonable agreement with experimental results. The sensitivity of the results to the Co-Pt spacing at the interface is also investigated and, in particular, for a complete Co monolayer we note that the value of the spacing at the interface determines whether PMA or in-plane anisotropy occurs. We find that the PMA can be greatly enhanced by the addition of Pt adatoms to the top surface of the 2D Co clusters. A single Pt atom can induce in excess of 5 meV to the anisotropy energy of a cluster. In the absence of the Pt adatoms the PMA of the Co clusters falls below 1 meV/Co atom for clusters of about 10 atoms whereas, with Pt atoms added to the surface of the clusters, a PMA of 1 meV/Co atom can be maintained for clusters as large as about 40 atoms. The effect of placing Os atoms on the top of the Co clusters is also considered. The addition of 5d atoms and clusters on the top of ferromagnetic nanoparticles may provide an approach to tune the magnetic anisotropy and moment separately.

Low-lying excited states and primary photoproducts of [Os-3(CO)(10)-(s-cis-L)] (L = cyclohexa-1,3-diene, buta-1,3-diene)] clusters studied by picosecond time-resolved UV/Vis and IR spectroscopy and by density functional theory

Combined picosecond transient absorption and time-resolved infrared studies were performed, aimed at characterising low-lying excited states of the cluster [Os-3(CO)(10)(s-cis-L)] (L= cyclohexa-1,3-diene, 1) and monitoring the formation of its photoproducts. Theoretical (DFT and TD-DFT) calculations on the closely related cluster with L=buta-1,3-diene (2') have revealed that the low-lying electronic transitions of these [Os-3(CO)(10)(s-cis-1,3-diene)] clusters have a predominant sigma(core)pi*(CO) character. From the lowest sigmapi* excited state, cluster 1 undergoes fast Os-Os(1,3-diene) bond cleavage (tau=3.3 ps) resulting in the formation of a coordinatively unsaturated primary photoproduct (1a) with a single CO bridge. A new insight into the structure of the transient has been obtained by DFT calculations. The cleaved Os-Os(1,3-diene) bond is bridged by the donor 1,3-diene ligand, compensating for the electron deficiency at the neighbouring Os centre. Because of the unequal distribution of the electron density in transient la, a second CO bridge is formed in 20 ps in the photoproduct [Os-3(CO)(8)(mu-CO)(2)- (cyclohexa-1,3-diene)] (1b). The latter compound, absorbing strongly around 630 nm, mainly regenerates the parent cluster with a lifetime of about 100 ns in hexane. Its structure, as suggested by the DFT calculations, again contains the 1,3-diene ligand coordinated in a bridging fashion. Photoproduct 1b can therefore be assigned as a high-energy coordination isomer of the parent cluster with all Os-Os bonds bridged.

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.

The signature of dark energy perturbations in galaxy cluster surveys

Models of dynamical dark energy unavoidably possess fluctuations in the energy density and pressure of that new component. In this paper we estimate the impact of dark energy fluctuations on the number of galaxy clusters in the Universe using a generalization of the spherical collapse model and the Press-Schechter formalism. The observations we consider are several hypothetical Sunyaev-Zel`dovich and weak lensing (shear maps) cluster surveys, with limiting masses similar to ongoing (SPT, DES) as well as future (LSST, Euclid) surveys. Our statistical analysis is performed in a 7-dimensional cosmological parameter space using the Fisher matrix method. We find that, in some scenarios, the impact of these fluctuations is large enough that their effect could already be detected by existing instruments such as the South Pole Telescope, when priors from other standard cosmological probes are included. We also show how dark energy fluctuations can be a nuisance for constraining cosmological parameters with cluster counts, and point to a degeneracy between the parameter that describes dark energy pressure on small scales (the effective sound speed) and the parameters describing its equation of state.

SPECTRUM OF SCREENING MASSES FOR SU(2) GAUGE THEORY: UNIVERSALITY CLASS

In this work we study the spectrum of the lowest screening masses for Yang-Mills theories on the lattice. We used the SU(2) gauge group in (3 + 1) dmensions. We adopted the multiple exponential method and the so-called ""variational"" method, in order to detect possible excited states. The calculations were done near the critical temperature of the confinement-deconfinement phase transition. We obtained values for the ratios of the screening masses consistent with predictions from universality arguments. A Monte Carlo evolution of the screening masses in the gauge theory confirms the validity of the predictions.

Supramolecular Approach to Gold Nanoparticle/Triruthenium Cluster Hybrid Materials and Interfaces

A systematic and comprehensive study of the interaction of citrate-stabilized gold nanoparticles with triruthenium cluster complexes of general formula [Ru(3)(CH(3)COO)(6)(L)](+) [L = 4-cyanopyridine (4-CNpy), 4,4`-bipyridine (4,4`-bpy) or 4,4`-bis(pyridyl)ethylene (bpe)] has been carried out. The cluster-nanoparticle interaction in solution and the construction of thin films of the hybrid materials were investigated in detail by electronic and surface plasmon resonance (SPR) spectroscopy, Raman scattering spectroscopy and scanning electron microscopy (SEM). Citrate-stabilized gold nanoparticles readily interacted with [Ru(3)O(CH(3)COO)(6)(L)(3)](+) complexes to generate functionalized nanoparticles that tend to aggregate according to rates and extents that depend on the bond strength defined by the characteristics of the cluster L ligands following the sequence bpe > 4,4`-bpy >> 4-CNpy. The formation of compact thin films of hybrid AuNP/[Ru(3)O(CH(3)COO)(6)(L)(3)](+) derivatives with L = bpe and 4,4`-bpy indicated that the stability/lability of AuNP-cluster bonds as well as their solubility are important parameters that influence the film contruction process. Fluorine-doped tin oxide electrodes modified with thin films of these nanomaterials exhibited similar electrocatalytic activity but much higher sensitivity than a conventional gold electrode in the oxidation of nitrite ion to nitrate depending on the bridging cluster complex, demonstrating the high potential for the development of amperometric sensors.

Investigating the Nature of Noble Gas-Copper Bonds by the Quantum Theory of Atoms in Molecules

We investigated noble gas copper bonds in linear complexes represented by the NgCuX general formula in which Ng and X stand for a noble gas (neon, argon, krypton, or xenon) and a halogen (fluorine, chlorine or bromine), respectively, by coupled cluster methods and modified cc-pVQZ basis sets. The quantum theory of atoms in molecules (QTAIM) shows a linear relation between the dissociation energy or noble gas-copper bonds and the amount of electronic charge transferred mainly from the noble gas to copper during complexation. Large changes in the QTAIM quadrupole moments of copper and noble gases resulting from this bonding and a comparison between NgCuX and NgNaCl systems indicate that these noble gas-copper bonds should be better interpreted as predominantly covalent. Finally, QTAIM atomic dipoles of noble gases in NgNaCl systems agree satisfactorily with atomic dipoles given by a simple model for these NgNa van der Waals bonds.

The Quasi-lattice of Indiscernible Elements

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)