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Neutron stars are very dense objects. One teaspoon of their material would have a mass of five billion tons. Their gravitational force is so strong that if an object were to fall from just one meter high it would hit the surface of the respective neutron star at two thousand kilometers per second. In such dense bodies, different particles from the ones present in atomic nuclei, the nucleons, can exist. These particles can be hyperons, that contain non-zero strangeness, or broader resonances. There can also be different states of matter inside neutron stars, such as meson condensates and if the density is height enough to deconfine the nucleons, quark matter. As new degrees of freedom appear in the system, different aspects of matter have to be taken into account. The most important of them being the restoration of the chiral symmetry. This symmetry is spontaneously broken, which is a fact related to the presence of a condensate of scalar quark-antiquark pairs, that for this reason is called chiral condensate. This condensate is present at low densities and even in vacuum. It is important to remember at this point that the modern concept of vacuum is far away from emptiness. It is full of virtual particles that are constantly created and annihilated, being their existence allowed by the uncertainty principle. At very high temperature/density, when the composite particles are dissolved into constituents, the chiral consensate vanishes and the chiral symmetry is restored. To explain how and when chiral symmetry is restored in neutron stars we use a model called non-linear sigma model. This is an effective quantum relativistic model that was developed in order to describe systems of hadrons interacting via meson exchange. The model was constructed from symmetry relations, which allow it to be chiral invariant. The first consequence of this invariance is that there are no bare mass terms in the lagrangian density, causing all, or most of the particles masses to come from the interactions with the medium. There are still other interesting features in neutron stars that cannot be found anywhere else in nature. One of them is the high isospin asymmetry. In a normal nucleus, the amount of protons and neutrons is more or less the same. In a neutron star the amount of neutrons is much higher than the protons. The resulting extra energy (called Fermi energy) increases the energy of the system, allowing the star to support more mass against gravitational collapse. As a consequence of that in early stages of the neutron star evolution, when there are still many trapped neutrinos, the proton fraction is higher than in later stages and consequently the maximum mass that the star can support against gravity is smaller. This, between many other features, shows how the microscopic phenomena of the star can reflect into the macroscopic properties. Another important property of neutron stars is charge neutrality. It is a required assumption for stability in neutron stars, but there are others. One example is chemical equilibrium. It means that the number of particles from each kind is not conserved, but they are created and annihilated through specific reactions that happen at the same rate in both directions. Although to calculate microscopic physics of neutron stars the space-time of special relativity, the Minkowski space, can be used, this is not true for the global properties of the star. In this case general relativity has to be used. The solution of Einstein's equations simplified to static, spherical and isotropic stars correspond to the configurations in which the star is in hydrostatic equilibrium. That means that the internal pressure, coming mainly from the Fermi energy of the neutrons, balances the gravity avoiding the collapse. When rotation is included the star becomes more stable, and consequently, can be more massive. The movement also makes it non-spherical, what requires the metric of the star to also be a function of the polar coordinate. Another important feature that has to be taken into account is the dragging of the local inertial frame. It generates centrifugal forces that are not originated in interactions with other bodies, but from the non-rotation of the frame of reference within which observations are made. These modifications are introduced through the Hartle's approximation that solves the problem by applying perturbation theory. In the mean field approximation, the couplings as well as the parameters of the non-linear sigma model are calibrated to reproduce massive neutron stars. The introduction of new degrees of freedom decreases the maximum mass allowed for the neutron star, as they soften the equation of state. In practice, the only baryons present in the star besides the nucleons are the Lambda and Sigma-, in the case in which the baryon octet is included, and Lambda and Delta-,0,+,++, in the case in which the baryon decuplet is included. The leptons are included to ensure charge neutrality. We choose to proceed our calculations including the baryon octet but not the decuplet, in order to avoid uncertainties in the couplings. The couplings of the hyperons were fitted to the depth of their potentials in nuclei. In this case the chiral symmetry restoration can be observed through the behavior of the related order parameter. The symmetry begins to be restored inside neutron stars and the transition is a smooth crossover. Different stages of the neutron star cooling are reproduced taking into account trapped neutrinos, finite temperature and entropy. Finite-temperature calculations include the heat bath of hadronic quasiparticles within the grand canonical potential of the system. Different schemes are considered, with constant temperature, metric dependent temperature and constant entropy. The neutrino chemical potential is introduced by fixing the lepton number in the system, that also controls the amount of electrons and protons (for charge neutrality). The balance between these two features is delicate and influenced mainly by the baryon number conservation. Isolated stars have a fixed number of baryons, which creates a link between different stages of the cooling. The maximum masses allowed in each stage of the cooling process, the one with high entropy and trapped neutrinos, the deleptonized one with high entropy, and the cold one in beta equilibrium. The cooling process is also influenced by constraints related to the rotation of the star. When rotation is included the star becomes more stable, and consequently, can be more massive. The movement also deforms it, requiring the metric of the star to include modifications that are introduced through the use of perturbation theory. The analysis of the first stages of the neutron star, when it is called proto-neutron star, gives certain constraints on the possible rotation frequencies in the colder stages. Instability windows are calculated in which the star can be stable during certain stages but collapses into black holes during the cooling process. In the last part of the work the hadronic SU(3) model is extended to include quark degrees of freedom. A new effective potential to the order parameter for deconfinement, the Polyakov loop, makes the connection between the physics at low chemical potential and hight temperature of the QCD phase diagram with the height chemical potential and low temperature part. This is done through the introduction of a chemical potential dependency on the already temperature dependent potential. Analyzing the effect of both order parameters, the chiral condensate and the Polyakov loop, we can drawn a phase diagram for symmetric as well as for star matter. The diagram contains a crossover region as well as a first order phase transition line. The new couplings and parameters of the model are chosen mainly to fit lattice QCD, including the position of the critical point. Finally, this matter containing different degrees of freedom (depending on which phase of the diagram we are) is used to calculate hybrid star properties.
We explain how fluctuations of ratios can constrain and falsify the statistical model of particle production in heavy ion collisions, using K/p fluctuations as an example. We define an observable capable of determining which statistical model, if any, governs freeze-out in ultrarelativistic heavy ion collisions. We calculate this observable for K/p fluctuations, and show that it should be the same for RHIC and LHC energies, as well as independent of centrality, if the Grand-Canonical statistical model is an appropriate description and chemical equilibrium applies. We describe variations of this scaling for deviations from this scenario, such as light quark chemical non-equilibrium, strange quark over-saturation and local conservation (canonical ensemble) for strange quarks. We also introduce a similar observable capable, together with the published K*/K measurement, of ascertaining if an interacting hadron gas phase governs the system between thermal and chemical freeze-out, and of ascertaining its duration and impact on hadronic chemistry.
In this thesis the first fully integrated Boltzmann+hydrodynamics approach to relativistic heavy ion reactions has been developed. After a short introduction that motivates the study of heavy ion reactions as the tool to get insights about the QCD phase diagram, the most important theoretical approaches to describe the system are reviewed. To model the dynamical evolution of the collective system assuming local thermal equilibrium ideal hydrodynamics seems to be a good tool. Nowadays, the development of either viscous hydrodynamic codes or hybrid approaches is favoured. For the microscopic description of the hadronic as well as the partonic stage of the evolution transport approaches have beeen successfully applied, since they generate the full phse-space dynamics of all the particles. The hadron-string transport approach that this work is based on is the Ultra-relativistic Quantum Molecular Dynamics (UrQMD) approach. It constitutes an effective solution of the relativistic Boltzmann equation and is restricted to binary collisions of the propagated hadrons. Therefore, the Boltzmann equation and the basic assumptions of this model are introduced. Furthermore, predictions for the charged particle multiplicities at LHC energies are made. The next step is the development of a new framework to calculate the baryon number density in a transport approach. Time evolutions of the net baryon number and the quark density have been calculated at AGS, SPS and RHIC energies and the new approach leads to reasonable results over the whole energy range. Studies of phase diagram trajectories using hydrodynamics are performed as a first move into the direction of the development of the hybrid approach. The hybrid approach that has been developed as the main part of this thesis is based on the UrQMD transport approach with an intermediate hydrodynamical evolution for the hot and dense stage of the collision. The initial energy and baryon number density distributions are not smooth and not symmetric in any direction and the initial velocity profiles are non-trivial since they are generated by the non-equilibrium transport approach. The fulll (3+1) dimensional ideal relativistic one fluid dynamics evolution is solved using the SHASTA algorithm. For the present work, three different equations of state have been used, namely a hadron gas equation of state without a QGP phase transition, a chiral EoS and a bag model EoS including a strong first order phase transition. For the freeze-out transition from hydrodynamics to the cascade calculation two different set-ups are employed. Either an in the computational frame isochronous freeze-out or an gradual freeze-out that mimics an iso-eigentime criterion. The particle vectors are generated by Monte Carlo methods according to the Cooper-Frye formula and UrQMD takes care of the final decoupling procedure of the particles. The parameter dependences of the model are investigated and the time evolution of different quantities is explored. The final pion and proton multiplicities are lower in the hybrid model calculation due to the isentropic hydrodynamic expansion while the yields for strange particles are enhanced due to the local equilibrium in the hydrodynamic evolution. The elliptic flow values at SPS energies are shown to be in line with an ideal hydrodynamic evolution if a proper initial state is used and the final freeze-out proceeds gradually. The hybrid model calculation is able to reproduce the experimentally measured integrated as well as transverse momentum dependent $v_2$ values for charged particles. The multiplicity and mean transverse mass excitation function is calculated for pions, protons and kaons in the energy range from $E_{\rm lab}=2-160A~$GeV. It is observed that the different freeze-out procedures have almost as much influence on the mean transverse mass excitation function as the equation of state. The experimentally observed step-like behaviour of the mean transverse mass excitation function is only reproduced, if a first order phase transition with a large latent heat is applied or the EoS is effectively softened due to non-equilibrium effects in the hadronic transport calculation. The HBT correlation of the negatively charged pion source created in central Pb+Pb collisions at SPS energies are investigated with the hybrid model. It has been found that the latent heat influences the emission of particles visibly and hence the HBT radii of the pion source. The final hadronic interactions after the hydrodynamic freeze-out are very important for the HBT correlation since a large amount of collisions and decays still takes place during this period.
We calculate low-energymeson decay processes and pion-pion scattering lengths in a two-flavour linear sigma model with global chiral symmetry, exploring the scenario in which the scalar mesons f0(600) and a0(980) are assumed to be ¯qq states.
We argue that Clustering in heavy ion collisions could be the missing element in resolving the socalled HBT puzzle, and briefly discuss the different physical situations where clustering could be present. We then propose a method by which clustering in heavy ion collisions could be detectedin a model-independent way.
We calculate leading-order dilepton yields from a quark-gluon plasma which has a time-dependent anisotropy in momentum space. Such anisotropies can arise during the earliest stages of quark-gluon plasma evolution due to the rapid longitudinal expansion of the created matter. A phenomenological model for the proper time dependence of the parton hard momentum scale, p_hard, and the plasma anisotropy parameter, xi, is proposed. The model describes the transition of the plasma from a 0+1 dimensional collisionally-broadened expansion at early times to a 0+1 dimensional ideal hydrodynamic expansion at late times. We find that high-energy dilepton production is enhanced by pre-equilibrium emission up to 50% at LHC energies, if one assumes an isotropization/thermalization time of 2 fm/c. Given sufficiently precise experimental data this enhancement could be used to determine the plasma isotropization time experimentally.
This study addresses the structure-function relationships of three essential membrane proteins: Porin from Paracoccus denitrificans, Porin OmpG from Eschericia coli and BetP from Corynobacterium glutamicum using Fourier transform infrared (FT-IR) spectroscopy and Attenuated Total Reflection (ATR) techniques. The structure of porin from P. denitrificans is known for more than a decade; however, the mechanism for loss of functionality together with the monomerization was not clear. In this study we have addressed the role of lipids for the functionality of porin using FT-IR. OmpF porin was found to interact with the lipid molecules via the aromatic girdles surrounding the protein for functionality. In this study, molecular bonds and groups of the lipids were established as reporter groups probing at different depths of the bilayer in order to understand the interaction partner of the aromatic girdles of porins. Monomerization of the trimeric assembly of OmpF porin reconstituted in lipids is induced by increasing the temperature. Porin (OmpF) was found to be extremely stable: The secondary structure of the protein was unaltered up to the temperature-induced main transition, around 80-90 °C, above which it is denatured. However, the interaction of the aromatic girdle with the lipid molecules exhibited distinct changes at much lower temperature values (40 - 50°) where, according to the previous functional studies, monomerization and the loss of function occurs. The results are compared with OmpG porin from E.coli, for which the functional unit is a monomer. The aromatic girdle-lipid interaction was monitored by the tyrosine aromatic ring C=C vibrational mode, a universal marker for the protein stability and interaction. We have also found that the aromatic girdles of porins are interacting with the interfacial region of the lipid bilayer instead of lipid headgroups. Lipid-protein interaction was found to be not only essential for the structural stability, but also for the functionality of OmpF porin. We have also studied the structural properties of OmpG from E.coli. The structure of OmpG at two pH values has been resolved using X-ray crystallography and the channel has been proposed to attain different states at different pH values as closed (pH < 5.5) and open (pH >7.5). This study, using IR spectroscopy, revealed that the pH-induced opening and closing of the channel is reflected by the frequency shifts of the ? sheet structure. OmpG has more rigid ? barrel properties upon opening of the channel. IR spectral analysis revealed multiple ? sheet signals with different hydrogen bond strengths. This enabled us to monitor the formation of hydrogen bridges between the extracellular loops upon opening of the channel. The conclusion that OmpG porin having two states at different pH values was also confirmed by the three mutants where the role of the histidine pair (H231 & H261) and loop 6 has been addressed. Temperature-profiling of the wild type (WT) protein and the mutants did not show pH dependent structural stability differences in detergent solution. However, the WT protein was found to be more stable in the open form in 2D crystals than the closed form. Reconstitution into lipids has increased the transition temperature value by ~20 °C in the closed state and ~25 °C in the open state. Therefore we conclude that the open and closed state of OmpG has structural stability differences that are only revealed in the lipid environment. A comparison of the transition temperature values of OmpG WT and the mutants suggested that the hydrogen bond network among S218-H231-H261-D267, together with the formation of 12 residue-long ?-sheet contributes to the structural stability of the open channel. In the process of closing and opening of the channel, the globular structure of the protein remains mainly unchanged, while there are changes in the side chain moieties. In addition to the role of the histidine pair and the loop L6, in situ opening/closing experiments showed that the negatively charged amino acids, i.e. Asp and Glu, and Arg residues also play an active role; possibly by interacting with each other inside the pore lumen. Therefore it could be concluded that the closure of the channel at acidic pH values is not only via closing the channel entrance by loop 6, but also via changing the electric potential inside the lumen due to the different states of charged amino acids in order to effectively block the gateway. BetP from C.glutamicum attains an active and inactive state in order to adjust its glycine betaine uptake rate to the osmotic conditions that the cell encounters. The structure of BetP is not yet available. The WT protein exhibited structural differences in the presence of excess K+, which is one of the activation conditions. In 2D crystals, increasing the ionic strength to 700 mM K+ was shown to induce changes in the ?-helical moiety with contributions from the ester groups and one Tyr residue using ATR-FTIR. An increase in ionic strength to 220 mM K+ was found to be the threshold value of potassium concentration ([K+]) where the protein exhibits structural alterations in detergent solution. The determined [K+] values are in good agreement with the previous functional studies. However, there are differences in the activation profile of BetP in 2D crystals and in detergent solution, which points out that the lipids are involved in the conformational transition from the inactive to the active state and their absence can lead to different structural properties. BetP WT was found to have ~65% alpha-helix, ~25% random coil and ~10% turn structure in detergent solution. In the presence of excess K+, the WT protein is found to adapt more unordered structure. Secondary structure analysis of the mutants revealed that both the N- and C-terminus are in ?-helical conformation. Reconstitution of WT protein in 2D crystals increased the main transition (denaturation) temperature value from ~62 °C to ~85 °C, a clear indication that the protein is more stable in lipid environment. Temperature-profiling of the two forms of the WT protein revealed that the structural breakdown is preceeded by monomerization of the trimeric assembly. Comparing the two forms of the WT protein and the mutant BetA, we conclude that the oligomeric status is stabilized via the interactions among hydrophilic regions involving the N terminus. H/D exchange and activation with excess K+ in D2O-buffer revealed that activation of the protein involves the interaction of Arg and Asp/Glu residues in the cytoplasmic region of the protein. BetP WT and the two mutants tested, i.e. BetA and BetP?C45, showed differences in protein packing upon activation. The WT protein and BetP?C45 mutant also show changes in the hydrogen bonding properties of turns. Since BetA does not show such a property in activation, we conclude that the N-terminus interacts with the loops in the inactive state via the interaction of charged amino acids for the WT protein and that this interaction is altered during the activation. It could be argued that the protein packing is affected via the changes in turns upon activation. We also have found experimental evidence that one Tyr residue has different orientations in the active and inactive state of BetP. Based on the previous functional studies, it could be one of the five Tyr residues in the cytoplasmic region of the protein (in loop 3, 6, 7 or C-terminus). The mutant BetP?C45, on the other hand, showed fewer differences between the active and inactive state conditions and based on the H/D exchange rates, the mutant shows the properties of an active WT protein, proving that the C-terminal truncation impairs the conformational transition between the active and inactive states.
The characterization of microscopic properties in correlated low-dimensional materials is a challenging problem due to the effects of dimensionality and the interplay between the many different lattice and electronic degrees of freedom. Competition between these factors gives rise to interesting and exotic magnetic phenomena. An understanding of how these phenomena are driven by these degrees of freedom can be used for rational design of new materials, to control and manipulate these degrees of freedom in order to obtain desired properties. In this work, we study these effects in materials with small exchange interaction between the magnetic ions such as metal-organic and inorganic dilute compounds. We overcome the dfficulties in studying these kind of materials by combining classical and quantum mechanical ab initio methods and many-body theory methods in an effective theoretical approach. To treat metal-organic compounds we elaborate a novel two-step methodology which allows one to include quantum effects while reducing the computational cost. We show that our approach is an effective procedure, leading at each step, to additional insights into the essential features of the phenomena and materials under study. Our investigation is divided into two parts, the first one concerning the exploration of the fundamental physical properties of novel Cu(II) hydroquinone-based compounds. We have studied two representatives of this family, a polymeric system Cu(II)-2,5-bis(pyrazol-1-yl)-1,4-dihydroxybenzene (CuCCP) and a coupled system Cu2S2F6N8O12 (TK91). The second part concerns the study of magnetic phenomena associated with the interplay between different energy scales and dimensionality in zero-, one- and two-dimensional compounds. In the zero-dimensional case, we have performed a comprehensive study of Cu4OCl6L4 with L=diallylcyanamide=NC-N-(CH2-CH=CH2)2 (Cu4OCl6daca4). Interpretations of the magnetic properties for this tetrameric compound have been controversial and inconsistent. From our studies, we conclude that the common models usually applied to this and other representatives in the same family of cluster systems fail to provide a consistent description of their low temperature magnetic properties and we thus postulate that in such systems it is necessary to take into account quantum fluctuations due to possible frustrated behavior. In the one-dimensional case, we studied polymeric Fe(II)-triazole compounds, which are of special relevance due to the possibility of inducing a spin transition between low and high spin state by applying a external perturbation. A long standing problem has been a satisfactory microscopic explanation of this large cooperative phenomenon. A lack of X-ray data has been one mitigating reason for the absence of microscopic studies. In this work, we present a novel approach to the understanding of the microscopic mechanism of spin crossover in such systems and show that in these kind of compounds magnetic exchange between high spin Fe(II) centers plays an important role. The correct description of the underlying physics in many materials is often hindered by the presence of anisotropies. To illustrate this difficulty, we have studied a two dimensional dilute compound K2V3O8 which exhibits an unusual spin reorientation effect when applying magnetic fields. While this effect can be understood when considering anisotropies in the system, it is not sufficient to reproduce experimental observations. Based on our studies of the electronic and magnetic properties in this system, we predict an extra exchange interaction and the presence of an additional magnetic moment at the non-magnetic V site. This sheds a new light into the controversial recent experimental data for the magnetic properties of this material.