QUASI-TOPOLOGICAL QUANTUM FIELD THEORIES AND Z(2) LATTICE GAUGE THEORIES

We consider a two-parameter family of Z(2) gauge theories on a lattice discretization T(M) of a three-manifold M and its relation to topological field theories. Familiar models such as the spin-gauge model are curves on a parameter space Gamma. We show that there is a region Gamma(0) subset of Gamma where the partition function and the expectation value h < W-R(gamma)> i of the Wilson loop can be exactly computed. Depending on the point of Gamma(0), the model behaves as topological or quasi-topological. The partition function is, up to a scaling factor, a topological number of M. The Wilson loop on the other hand, does not depend on the topology of gamma. However, for a subset of Gamma(0), < W-R(gamma)> depends on the size of gamma and follows a discrete version of an area law. At the zero temperature limit, the spin-gauge model approaches the topological and the quasi-topological regions depending on the sign of the coupling constant.

Relaxation of Adaptive Evolution during the HIV-1 Infection Owing to Reduction of CD4+T Cell Counts

Background: The first stages of HIV-1 infection are essential to establish the diversity of virus population within host. It has been suggested that adaptation to host cells and antibody evasion are the leading forces driving HIV evolution at the initial stages of AIDS infection. In order to gain more insights on adaptive HIV-1 evolution, the genetic diversity was evaluated during the infection time in individuals contaminated by the same viral source in an epidemic cluster. Multiple sequences of V3 loop region of the HIV-1 were serially sampled from four individuals: comprising a single blood donor, two blood recipients, and another sexually infected by one of the blood recipients. The diversity of the viral population within each host was analyzed independently in distinct time points during HIV-1 infection. Results: Phylogenetic analysis identified multiple HIV-1 variants transmitted through blood transfusion but the establishing of new infections was initiated by a limited number of viruses. Positive selection (d(N)/d(S)>1) was detected in the viruses within each host in all time points. In the intra-host viruses of the blood donor and of one blood recipient, X4 variants appeared respectively in 1993 and 1989. In both patients X4 variants never reached high frequencies during infection time. The recipient, who X4 variants appeared, developed AIDS but kept narrow and constant immune response against HIV-1 during the infection time. Conclusion: Slowing rates of adaptive evolution and increasing diversity in HIV-1 are consequences of the CD4+ T cells depletion. The dynamic of R5 to X4 shift is not associated with the initial amplitude of humoral immune response or intensity of positive selection.

Exercise training improves relaxation response and SOD-1 expression in aortic and mesenteric rings from high caloric diet-fed rats

Abstract Background Obesity has been associated with a variety of disease such as type II diabetes mellitus, arterial hypertension and atherosclerosis. Evidences have shown that exercise training promotes beneficial effects on these disorders, but the underlying mechanisms are not fully understood. The aim of this study was to investigate whether physical preconditioning prevents the deleterious effect of high caloric diet in vascular reactivity of rat aortic and mesenteric rings. Methods Male Wistar rats were divided into sedentary (SD); trained (TR); sedentary diet (SDD) and trained diet (TRD) groups. Run training (RT) was performed in sessions of 60 min, 5 days/week for 12 weeks (70–80% VO2max). Triglycerides, glucose, insulin and nitrite/nitrate concentrations (NOx-) were measured. Concentration-response curves to acetylcholine (ACh) and sodium nitroprusside (SNP) were obtained. Expression of Cu/Zn superoxide dismutase (SOD-1) was assessed by Western blotting. Results High caloric diet increased triglycerides concentration (SDD: 216 ± 25 mg/dl) and exercise training restored to the baseline value (TRD: 89 ± 9 mg/dl). Physical preconditioning significantly reduced insulin levels in both groups (TR: 0.54 ± 0.1 and TRD: 1.24 ± 0.3 ng/ml) as compared to sedentary animals (SD: 0.87 ± 0.1 and SDD: 2.57 ± 0.3 ng/ml). On the other hand, glucose concentration was slightly increased by high caloric diet, and RT did not modify this parameter (SD: 126 ± 6; TR: 140 ± 8; SDD: 156 ± 8 and TRD 153 ± 9 mg/dl). Neither high caloric diet nor RT modified NOx- levels (SD: 27 ± 4; TR: 28 ± 6; SDD: 27 ± 3 and TRD: 30 ± 2 μM). Functional assays showed that high caloric diet impaired the relaxing response to ACh in mesenteric (about 13%), but not in aortic rings. RT improved the relaxing responses to ACh either in aortic (28%, for TR and 16%, to TRD groups) or mesenteric rings (10%, for TR and 17%, to TRD groups) that was accompanied by up-regulation of SOD-1 expression and reduction in triglycerides levels. Conclusion The improvement in endothelial function by physical preconditioning in mesenteric and aortic arteries from high caloric fed-rats was directly related to an increase in NO bioavailability to the smooth muscle mostly due to SOD-1 up regulation.

Dynamical Elastic Moduli of the Ti-13Nb-13Zr biomaterial alloy by mechanical spectroscopy

Dynamical Elastic Moduli of the Ti-13Nb-13Zr biomaterial alloy were obtained using the mechanical spectroscopy technique. The sample with heat treatment at 1170K for 30 minutes and water quenched with subsequent aging treatment at 670 K for 3 hours (TNZ + WQ + 670 K/3 h), was characterized through decay of free oscillations of the sample in the flexural vibration mode. The spectra of anelastic relaxation (internal friction and frequency) in the temperature range from 300 K to 625 K not revealed the presence of relaxation process. As shown in the literature, the hcp structure usually does not exhibit any relaxation due to the symmetry of the sites in the crystalline lattice, but if there is some relaxation, this only occurs in special cases such as low concentration of zirconium or saturation of the stoichiometric ratio of oxygen for zirconium. Dynamical elastic modulus obtained for TNZ + WQ + 670 K/3 h alloy was 87 GPa at room temperature, which is higher than the value for Ti-13Nb-13Zr alloy (64 GPa) of the literature. This increment may be related to the change of the proportion of α and β phases. Besides that, the presence of precipitates in the alloy after aging treatment hardens the material and reduces its ductility.

Stochastic lattice model describing a vector-borne disease

We employ the approach of stochastic dynamics to describe the dissemination of vector-borne diseases such as dengue, and we focus our attention on the characterization of the threshold of the epidemic. The coexistence space comprises two representative spatial structures for both human and mosquito populations. The human population has its evolution described by a process that is similar to the Susceptible-Infected-Recovered (SIR) dynamics. The population of mosquitoes follows a dynamic of the type of the Susceptible Infected-Susceptible (SIS) model. The coexistence space is a bipartite lattice constituted by two structures representing the human and mosquito populations. We develop a truncation scheme to solve the evolution equations for the densities and the two-site correlations from which we get the threshold of the disease and the reproductive ratio. We present a precise deØnition of the reproductive ratio which reveals the importance of the correlations developed in the early stage of the disease. According to our deØnition, the reproductive rate is directed related to the conditional probability of the occurrence of a susceptible human (mosquito) given the presence in the neighborhood of an infected mosquito (human). The threshold of the epidemic as well as the phase transition between the epidemic and the non-epidemic states are also obtained by performing Monte Carlo simulations. References: [1] David R. de Souza, T^ania Tom∂e, , Suani R. T. Pinho, Florisneide R. Barreto and M∂ario J. de Oliveira, Phys. Rev. E 87, 012709 (2013). [2] D. R. de Souza, T. Tom∂e and R. M. ZiÆ, J. Stat. Mech. P03006 (2011).

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Study of surface free energy on a lattice-gas model applied to Liquid bridge

The pulmonary crackling and the formation of liquid bridges are problems that for centuries have been attracting the attention of scientists. In order to study these phenomena, it was developed a canonical cubic lattice-gas­ like model to explain the rupture of liquid bridges in lung airways [A. Alencar et al., 2006, PRE]. Here, we further develop this model and add entropy analysis to study thermodynamic properties, such as free energy and force. The simulations were performed using the Monte Carlo method with Metropolis algorithm. The exchange between gas and liquid particles were performed randomly according to the Kawasaki dynamics and weighted by the Boltzmann factor. Each particle, which can be solid (s), liquid (l) or gas (g), has 26 neighbors: 6 + 12 + 8, with distances 1, √2 and √3, respectively. The energy of a lattice's site m is calculated by the following expression: Em = ∑k=126 Ji(m)j(k) in witch (i, j) = g, l or s. Specifically, it was studied the surface free energy of the liquid bridge, trapped between two planes, when its height is changed. For that, was considered two methods. First, just the internal energy was calculated. Then was considered the entropy. It was fond no difference in the surface free energy between this two methods. We calculate the liquid bridge force between the two planes using the numerical surface free energy. This force is strong for small height, and decreases as the distance between the two planes, height, is increased. The liquid-gas system was also characterized studying the variation of internal energy and heat capacity with the temperature. For that, was performed simulation with the same proportion of liquid and gas particle, but different lattice size. The scale of the liquid-gas system was also studied, for low temperature, using different values to the interaction Jij.

Reduced endothelium-dependent relaxation to anandamide in mesenteric arteries from young obese Zucker rats

Impaired vascular function, manifested by an altered ability of the endothelium to release endothelium-derived relaxing factors and endothelium-derived contracting factors, is consistently reported in obesity. Considering that the endothelium plays a major role in the relaxant response to the cannabinoid agonist anandamide, the present study tested the hypothesis that vascular relaxation to anandamide is decreased in obese rats. Mechanisms contributing to decreased anandamide-induced vasodilation were determined. Resistance mesenteric arteries from young obese Zucker rats (OZRs) and their lean counterparts (LZRs) were used. Vascular reactivity was evaluated in a myograph for isometric tension recording. Protein expression and localization were analyzed by Western blotting and immunofluorescence, respectively. Vasorelaxation to anandamide, acetylcholine, and sodium nitroprusside, as well as to CB1, CB2, and TRPV1 agonists was decreased in endothelium-intact mesenteric arteries from OZRs. Incubation with an AMP-dependent protein kinase (AMPK) activator or a fatty acid amide hydrolase inhibitor restored anandamide-induced vascular relaxation in OZRs. CB1 and CB2 receptors protein expression was decreased in arteries from OZRs. Incubation of mesenteric arteries with anandamide evoked endothelial nitric oxide synthase (eNOS), AMPK and acetyl CoA carboxylase phosphorylation in LZRs, whereas it decreased phosphorylation of these proteins in OZRs. In conclusion, obesity decreases anandamide-induced relaxation in resistance arteries. Decreased cannabinoid receptors expression, increased anandamide degradation, decreased AMPK/eNOS activity as well as impairment of the response mediated by TRPV1 activation seem to contribute to reduce responses to cannabinoid agonists in obesity.

Resistance exercise acutely enhances mesenteric artery insulin-induced relaxation in healthy rats

AIMS: We evaluated the mechanisms involved in insulin-induced vasodilatation after acute resistance exercise in healthy rats. MAIN METHODS: Wistar rats were divided into 3 groups: control (CT), electrically stimulated (ES) and resistance exercise (RE). Immediately after acute RE (15 sets with 10 repetitions at 70% of maximal intensity), the animals were sacrificed and rings of mesenteric artery were mounted in an isometric system. After this, concentration-response curves to insulin were performed in control condition and in the presence of LY294002 (PI3K inhibitor), L-NAME (NOS inhibitor), L-NAME+TEA (K(+) channels inhibitor), LY294002+BQ123 (ET-A antagonist) or ouabain (Na(+)/K(+) ATPase inhibitor). KEY FINDINGS: Acute RE increased insulin-induced vasorelaxation as compared to control (CT: Rmax=7.3 ± 0.4% and RE: Rmax=15.8 ± 0.8%; p<0.001). NOS inhibition reduced (p<0.001) this vasorelaxation from both groups (CT: Rmax=2.0 ± 0.3%, and RE: Rmax=-1.2 ± 0.1%), while PI3K inhibition abolished the vasorelaxation in CT (Rmax=-0.1±0.3%, p<0.001), and caused vasoconstriction in RE (Rmax=-6.5 ± 0.6%). That insulin-induced vasoconstriction on PI3K inhibition was abolished (p<0.001) by the ET-A antagonist (Rmax=2.9 ± 0.4%). Additionally, acute RE enhanced (p<0.001) the functional activity of the ouabain-sensitive Na(+)/K(+) ATPase activity (Rmax=10.7 ± 0.4%) and of the K(+) channels (Rmax=-6.1±0.5%; p<0.001) in the insulin-induced vasorelaxation as compared to CT. SIGNIFICANCE: Such results suggest that acute RE promotes enhanced insulin-induced vasodilatation, which could act as a fine tuning to vascular tone.

Enhanced Mixed Integer Programming Techniques and Routing Problems

Mixed integer programming is up today one of the most widely used techniques for dealing with hard optimization problems. On the one side, many practical optimization problems arising from real-world applications (such as, e.g., scheduling, project planning, transportation, telecommunications, economics and finance, timetabling, etc) can be easily and effectively formulated as Mixed Integer linear Programs (MIPs). On the other hand, 50 and more years of intensive research has dramatically improved on the capability of the current generation of MIP solvers to tackle hard problems in practice. However, many questions are still open and not fully understood, and the mixed integer programming community is still more than active in trying to answer some of these questions. As a consequence, a huge number of papers are continuously developed and new intriguing questions arise every year. When dealing with MIPs, we have to distinguish between two different scenarios. The first one happens when we are asked to handle a general MIP and we cannot assume any special structure for the given problem. In this case, a Linear Programming (LP) relaxation and some integrality requirements are all we have for tackling the problem, and we are ``forced" to use some general purpose techniques. The second one happens when mixed integer programming is used to address a somehow structured problem. In this context, polyhedral analysis and other theoretical and practical considerations are typically exploited to devise some special purpose techniques. This thesis tries to give some insights in both the above mentioned situations. The first part of the work is focused on general purpose cutting planes, which are probably the key ingredient behind the success of the current generation of MIP solvers. Chapter 1 presents a quick overview of the main ingredients of a branch-and-cut algorithm, while Chapter 2 recalls some results from the literature in the context of disjunctive cuts and their connections with Gomory mixed integer cuts. Chapter 3 presents a theoretical and computational investigation of disjunctive cuts. In particular, we analyze the connections between different normalization conditions (i.e., conditions to truncate the cone associated with disjunctive cutting planes) and other crucial aspects as cut rank, cut density and cut strength. We give a theoretical characterization of weak rays of the disjunctive cone that lead to dominated cuts, and propose a practical method to possibly strengthen those cuts arising from such weak extremal solution. Further, we point out how redundant constraints can affect the quality of the generated disjunctive cuts, and discuss possible ways to cope with them. Finally, Chapter 4 presents some preliminary ideas in the context of multiple-row cuts. Very recently, a series of papers have brought the attention to the possibility of generating cuts using more than one row of the simplex tableau at a time. Several interesting theoretical results have been presented in this direction, often revisiting and recalling other important results discovered more than 40 years ago. However, is not clear at all how these results can be exploited in practice. As stated, the chapter is a still work-in-progress and simply presents a possible way for generating two-row cuts from the simplex tableau arising from lattice-free triangles and some preliminary computational results. The second part of the thesis is instead focused on the heuristic and exact exploitation of integer programming techniques for hard combinatorial optimization problems in the context of routing applications. Chapters 5 and 6 present an integer linear programming local search algorithm for Vehicle Routing Problems (VRPs). The overall procedure follows a general destroy-and-repair paradigm (i.e., the current solution is first randomly destroyed and then repaired in the attempt of finding a new improved solution) where a class of exponential neighborhoods are iteratively explored by heuristically solving an integer programming formulation through a general purpose MIP solver. Chapters 7 and 8 deal with exact branch-and-cut methods. Chapter 7 presents an extended formulation for the Traveling Salesman Problem with Time Windows (TSPTW), a generalization of the well known TSP where each node must be visited within a given time window. The polyhedral approaches proposed for this problem in the literature typically follow the one which has been proven to be extremely effective in the classical TSP context. Here we present an overall (quite) general idea which is based on a relaxed discretization of time windows. Such an idea leads to a stronger formulation and to stronger valid inequalities which are then separated within the classical branch-and-cut framework. Finally, Chapter 8 addresses the branch-and-cut in the context of Generalized Minimum Spanning Tree Problems (GMSTPs) (i.e., a class of NP-hard generalizations of the classical minimum spanning tree problem). In this chapter, we show how some basic ideas (and, in particular, the usage of general purpose cutting planes) can be useful to improve on branch-and-cut methods proposed in the literature.

Dielektrische Relaxation und Retardation lokaler Prozesse in glasbildenden Materialien

Lokale sekundäre Prozesse in glasbildenden Materialien sind wegen ihrer Wechselwirkung mit der primären Relaxation von besonderem Interesse. Für D-Sorbitol wurde die beta-Relaxation mit drei verschiedenen dielektrischen Meßtechniken untersucht und die Ergebnisse miteinander verglichen. Im Gegensatz zu konventionellen Messungen der dielektrischen Retardation, detektiert eine echte dielektrische Relaxationsmessung den Zerfall des elektrischen Feldes unter der Bedingung einer konstanten dielektrischen Verschiebung. Eine weitere dielektrische Relaxationsmethode ist die Solvatationsdynamik. Sie detektiert die dielektrische Relaxation in der direkten Umgebung eines Farbstoffmoleküls. Die Übereinstimmung der lokal ermittelten und der makroskopisch gemittelten Ergebnisse für den Glaszustand weisen darauf hin, daß die Sekundärrelaxation in D-Sorbitol eine räumlich homogene Eigenschaft ist. Im Gegensatz zu beta-Prozessen anderer Materialien, zeigt nur der abgeschreckte Glaszustand von ortho-Terphenyl einen sekundären Prozeß. Es wurde beobachtet, daß die beta-Amplitude beim Ausheilen langsam abnimmt und im Gleichgewichtszustand der Flüssigkeit oberhalb der Glasübergangstemperatur völlig verschwindet. Viele glasbildende Materialien, wie z. B. Salol zeigen keinen dielektrischen beta-Prozeß. Im Gegensatz zu Messungen mit Standardkühlraten, zeigt eine stark abgeschreckte Salol-Probe eine symmetrische dielektrische Sekundärrelaxation. Diese neuartige Eigenschaft von Salol verschwindet irreversibel, wenn sich die Temperatur der Glasübergangstemperatur nähert.

Trasporto di materia in membrane polimeriche e nanocomposite per la separazione di gas

Membrane-based separation processes are acquiring, in the last years, an increasing importance because of their intrinsic energetic and environmental sustainability: some types of polymeric materials, showing adequate perm-selectivity features, appear rather suitable for these applications, because of their relatively low cost and easy processability. In this work have been studied two different types of polymeric membranes, in view of possible applications to the gas separation processes, i.e. Mixed Matrix Membranes (MMMs) and high free volume glassy polymers. Since the early 90’s, it has been understood that the performances of polymeric materials in the field of gas separations show an upper bound in terms of permeability and selectivity: in particular, an increase of permeability is often accompanied by a decrease of selectivity and vice-versa, while several inorganic materials, like zeolites or silica derivates, can overcome this limitation. As a consequence, it has been developed the idea of dispersing inorganic particles in polymeric matrices, in order to obtain membranes with improved perm-selectivity features. In particular, dispersing fumed silica nanoparticles in high free volume glassy polymers improves in all the cases gases and vapours permeability, while the selectivity may either increase or decrease, depending upon material and gas mixture: that effect is due to the capacity of nanoparticles to disrupt the local chain packing, increasing the dimensions of excess free volume elements trapped in the polymer matrix. In this work different kinds of MMMs were fabricated using amorphous Teflon® AF or PTMSP and fumed silica: in all the cases, a considerable increase of solubility, diffusivity and permeability of gases and vapours (n-alkanes, CO2, methanol) was observed, while the selectivity shows a non-monotonous trend with filler fraction. Moreover, the classical models for composites are not able to capture the increase of transport properties due to the silica addition, so it has been necessary to develop and validate an appropriate thermodynamic model that allows to predict correctly the mass transport features of MMMs. In this work, another material, called poly-trimethylsilyl-norbornene (PTMSN) was examined: it is a new generation high free volume glassy polymer that, like PTMSP, shows unusual high permeability and selectivity levels to the more condensable vapours. These two polymer differ each other because PTMSN shows a more pronounced chemical stability, due to its structure double-bond free. For this polymer, a set of Lattice Fluid parameters was estimated, making possible a comparison between experimental and theoretical solubility isotherms for hydrocarbons and alcoholic vapours: the successfully modelling task, based on application of NELF model, offers a reliable alternative to direct sorption measurement, which is extremely time-consuming due to the relevant relaxation phenomena showed by each sorption step. For this material also dilation experiments were performed, in order to quantify its dimensional stability in presence of large size, swelling vapours.

Simulation studies of correlation functions and relaxation in polymeric systems

We investigate the statics and dynamics of a glassy,non-entangled, short bead-spring polymer melt with moleculardynamics simulations. Temperature ranges from slightlyabove the mode-coupling critical temperature to the liquidregime where features of a glassy liquid are absent. Ouraim is to work out the polymer specific effects on therelaxation and particle correlation. We find the intra-chain static structure unaffected bytemperature, it depends only on the distance of monomersalong the backbone. In contrast, the distinct inter-chainstructure shows pronounced site-dependence effects at thelength-scales of the chain and the nearest neighbordistance. There, we also find the strongest temperaturedependence which drives the glass transition. Both the siteaveraged coupling of the monomer and center of mass (CM) andthe CM-CM coupling are weak and presumably not responsiblefor a peak in the coherent relaxation time at the chain'slength scale. Chains rather emerge as soft, easilyinterpenetrating objects. Three particle correlations arewell reproduced by the convolution approximation with theexception of model dependent deviations. In the spatially heterogeneous dynamics of our system weidentify highly mobile monomers which tend to follow eachother in one-dimensional paths forming ``strings''. Thesestrings have an exponential length distribution and aregenerally short compared to the chain length. Thus, arelaxation mechanism in which neighboring mobile monomersmove along the backbone of the chain seems unlikely.However, the correlation of bonded neighbors is enhanced. When liquids are confined between two surfaces in relativesliding motion kinetic friction is observed. We study ageneric model setup by molecular dynamics simulations for awide range of sliding speeds, temperatures, loads, andlubricant coverings for simple and molecular fluids. Instabilities in the particle trajectories are identified asthe origin of kinetic friction. They lead to high particlevelocities of fluid atoms which are gradually dissipatedresulting in a friction force. In commensurate systemsfluid atoms follow continuous trajectories for sub-monolayercoverings and consequently, friction vanishes at low slidingspeeds. For incommensurate systems the velocity probabilitydistribution exhibits approximately exponential tails. Weconnect this velocity distribution to the kinetic frictionforce which reaches a constant value at low sliding speeds. This approach agrees well with the friction obtaineddirectly from simulations and explains Amontons' law on themicroscopic level. Molecular bonds in commensurate systemslead to incommensurate behavior, but do not change thequalitative behavior of incommensurate systems. However,crossed chains form stable load bearing asperities whichstrongly increase friction.

Thermal relaxation for particle systems in interaction with several bosonic heat reservoirs

The present thesis is concerned with the study of a quantum physical system composed of a small particle system (such as a spin chain) and several quantized massless boson fields (as photon gasses or phonon fields) at positive temperature. The setup serves as a simplified model for matter in interaction with thermal "radiation" from different sources. Hereby, questions concerning the dynamical and thermodynamic properties of particle-boson configurations far from thermal equilibrium are in the center of interest. We study a specific situation where the particle system is brought in contact with the boson systems (occasionally referred to as heat reservoirs) where the reservoirs are prepared close to thermal equilibrium states, each at a different temperature. We analyze the interacting time evolution of such an initial configuration and we show thermal relaxation of the system into a stationary state, i.e., we prove the existence of a time invariant state which is the unique limit state of the considered initial configurations evolving in time. As long as the reservoirs have been prepared at different temperatures, this stationary state features thermodynamic characteristics as stationary energy fluxes and a positive entropy production rate which distinguishes it from being a thermal equilibrium at any temperature. Therefore, we refer to it as non-equilibrium stationary state or simply NESS. The physical setup is phrased mathematically in the language of C*-algebras. The thesis gives an extended review of the application of operator algebraic theories to quantum statistical mechanics and introduces in detail the mathematical objects to describe matter in interaction with radiation. The C*-theory is adapted to the concrete setup. The algebraic description of the system is lifted into a Hilbert space framework. The appropriate Hilbert space representation is given by a bosonic Fock space over a suitable L2-space. The first part of the present work is concluded by the derivation of a spectral theory which connects the dynamical and thermodynamic features with spectral properties of a suitable generator, say K, of the time evolution in this Hilbert space setting. That way, the question about thermal relaxation becomes a spectral problem. The operator K is of Pauli-Fierz type. The spectral analysis of the generator K follows. This task is the core part of the work and it employs various kinds of functional analytic techniques. The operator K results from a perturbation of an operator L0 which describes the non-interacting particle-boson system. All spectral considerations are done in a perturbative regime, i.e., we assume that the strength of the coupling is sufficiently small. The extraction of dynamical features of the system from properties of K requires, in particular, the knowledge about the spectrum of K in the nearest vicinity of eigenvalues of the unperturbed operator L0. Since convergent Neumann series expansions only qualify to study the perturbed spectrum in the neighborhood of the unperturbed one on a scale of order of the coupling strength we need to apply a more refined tool, the Feshbach map. This technique allows the analysis of the spectrum on a smaller scale by transferring the analysis to a spectral subspace. The need of spectral information on arbitrary scales requires an iteration of the Feshbach map. This procedure leads to an operator-theoretic renormalization group. The reader is introduced to the Feshbach technique and the renormalization procedure based on it is discussed in full detail. Further, it is explained how the spectral information is extracted from the renormalization group flow. The present dissertation is an extension of two kinds of a recent research contribution by Jakšić and Pillet to a similar physical setup. Firstly, we consider the more delicate situation of bosonic heat reservoirs instead of fermionic ones, and secondly, the system can be studied uniformly for small reservoir temperatures. The adaption of the Feshbach map-based renormalization procedure by Bach, Chen, Fröhlich, and Sigal to concrete spectral problems in quantum statistical mechanics is a further novelty of this work.

Lattice preferred orientation in omphacite: Examples from the Tauern Window, Austria and the Western Gneiss Region, Norway

It is lively debated how eclogites find their way from deep to mid-crustal levels during exhumation. Different exhumation models for high-pressure and ultrahigh-pressure rocks were suggested in previous studies, based mainly on field observations and less on microstructural studies on the exhumed rocks. The development and improvement of electron microscopy techniques allows it, to focus interest on direct investigations of microstructures and crystallographic properties in eclogites. In this case, it is of importance to study the applicability of crystallographic measurements on eclogites for exhumation processes and to unravel which processes affect eclogite textures. Previous studies suggested a strong relationship between deformation and lattice preferred orientation (LPO) in omphacite but it is still unclear if the deformation is related to the exhumation of eclogites. This study is focused on the questions which processes affect omphacite LPO and if textural investigations of omphacite are applicable for studying eclogite exhumation. Therefore, eclogites from two examples in the Alps and in the Caledonides were collected systematically and investigated with respect to omphacite LPO by using the electron backscattered diffraction (EBSD) technique. Omphacite textures of the Tauern Window (Austria) and the Western Gneiss Region (Norway) were studied to compare lattice preferred orientation with field observations and suggested exhumation models from previous studies. The interpretation of omphacite textures, regarding the deformation regime is mainly based on numerical simulations in previous studies. Omphacite LPO patterns of the Eclogite Zone are clearly independent from any kind of exhumation process. The textures were generated during omphacite growth on the prograde path of eclogite development until metamorphic peak conditions. Field observations in the Eclogite Zone show that kinematics in garnet mica schist, surrounding the eclogites, strongly indicate an extrusion wedge geometry. Stretching lineations show top-N thrusting at the base and a top-S normal faulting with a sinistral shear component at the top of the Eclogite Zone. The different shear sense on both sides of the unit does not affect the omphacite textures in any way. The omphacite lattice preferred orientation patterns of the Western Gneiss Region can not be connected with any exhumation model. The textures were probably generated during the metamorphic peak and reflect the change from subduction to exhumation. Eclogite Zone and Western Gneiss Region differ significantly in size and especially in metamorphic conditions. While the Eclogite Zone is characterized by constant P-T conditions (600-650°C, 20-25 kbar), the Western Gneiss Region contains a wide P-T range from high- to ultrahigh pressure conditions (400-800°C, 20-35 kbar). In contrast to this, the omphacite textures of both units are very similar. This means that omphacite LPO is independent from P-T conditions and therefore from burial depth. Further, in both units, omphacite LPO is independent from grain and subgrain size as well as from any shape preferred orientation (SPO) on grain and subgrain scale. Overall, omphacite lattice preferred orientation are generated on the prograde part of omphacite development. Therefore, textural investigations on omphacite LPO are not applicable to study eclogite exhumation.