States of matter with quasi-particle excitations that exhibit anyonic statisticsare of great theoretical interest, especially in those cases where the anyons arenon-Abelian. Two of the most promising states that could support non-Abeliananyons are the ν = 5/2 quantum Hall state and the two dimensional p-wavesuperconductor, and they can both be understood as p-wave paired states. Themotivation for the present thesis is to get a better understanding of the theo-retical description of p-wave paired states.In the accompanying paper we construct an effective field theory for the 2Dspin-less p-wave paired superconductor that faithfully describes the topologicalproperties of the bulk state, and also provides a model for the subgap statesat vortex cores and edges. In particular it captures the topologically protectedzero modes and has the correct ground state degeneracy on the torus. Wealso show that our effective field theory becomes a topological field theory in awell defined scaling limit and that the vortices have the expected non-Abelianbraiding statistics.

One effective tool to probe a system revealing topological order is to biparti- tion the system in some way and look at the properties of the reduced density operator corresponding to one part of the system. In this thesis we focus on a bipartition scheme known as the particle cut in which the particles in the system are divided into two groups and we look at the rank of the re- duced density operator. In the context of fractional quantum Hall physics it is conjectured that the rank of the reduced density operator for a model Hamiltonian describing the system is equal to the number of quasi-hole states. Here we consider the Laughlin wave function as the model state for the system and try to put this conjecture on a firmer ground by trying to determine the rank of the reduced density operator and calculating the number of quasi-hole states. This is done by relating this conjecture to the mathematical properties of symmetric polynomials and proving a theorem that enables us to find the lowest total degree of symmetric polynomials that vanish under some specific transformation referred to as clustering transformation.

<p>Ytterligare forskningsfinansiärer: Knut and Alice WallenbergFoundation for a Fellowship Grant and Project funding (KAW 2015.0043), Swedish Government Strategic Research Area in Materials Science on Functional Materials at Linköping University (Faculty Grant SFO MatLiUNo. 2009 00971), Swedish Research Council VR-RFI (#2017-00646_9), Swedish Foundation for Strategic Research(contract RIF14-0053)</p>

The recent decades of research in molecular biology have resulted in break-throughs concerning our knowledge of the genetic code, protein structures and functions of the different cellular components. With this new information follows an increased interest in constructing computational models of the biological systems. A computational model can range from a description of one specific protein to a complete cell or organism. The aim of a computational model is often to complement the experimental studies and help identify essential mechanisms of a system. All processes taking place in our cells, from general metabolic processes to cell specific actions, originates from information encoded in our DNA. The first step in transferring the genetic information to a functional protein or RNA, is through the transcription of a gene. The transcription process is controlled by cellular proteins binding to DNA regions called promoters. The term "genetic switch", used in the title of this thesis, refers to a specific change in transcription activity, where one or several promoters get activated or silenced. In this thesis, I present studies of the regulation mechanisms in two different genetic switches. The first is a switch between two central promoters in the Epstein- Barr virus. This human virus is mostly known for causing the ’kissing disease’, but is also coupled to several cancer types. Infected cells can change between a resting and a proliferating phenotype, depending on which viral promoter is active. In order to understand what causes uncontrolled proliferation in tumors, it is important to understand the regulation of these viral promoters. The other switch is present in the phage λ, a bacterial virus. This virus has one specific promoter region, controlling expression of two proteins that determine if the phage will remain silent (lysogenic) in the host cell, or start producing new viral particles (go lytic). For the Epstein- Barr virus we tested, and confirmed, the hypothesis that the regulation of the two central promoters can be obtained by only one viral and one human protein. Further, we studied the cooperative effects on one of the promoters, showing that steric hindrance at the promoter region results in a more effective switching than with only cooperative binding present. For the bacteriophage λ we studied the genetically altered λ- Lac mutants, presented by Little &amp; Atsumi in 2006. We demonstrate that the experimental results cannot, in terms of its equilibria, be explained by the mechanisms generally believed to be in control of the lysogenic/ lytic switch. / QC 20101119

Measurements of partial discharges are commonly used to diagnose the insulation system in high voltage components. Traditionally a single xed frequency of the applied voltage is used for such measurements as in the Phase Resolved Partial Discharge Analysis (PRPDA) technique. With the Variable Frequency Phase Resolved Partial Discharge Analysis (VF-PRPDA) technique the frequency of the applied voltage is instead variable. This technique provides more information about the condition of the insulation than the PRPDA technique. To extract the extra information a physical understanding of the frequency dependence of partial discharges is necessary. In this thesis partial discharges in cylindrical cavities in polycarbonate are measured using the VF-PRPDA technique in the frequency range 10 mHz { 100 Hz. It is studied how the cavity diameter and height inuence the frequency dependence of partial discharges. Insulated cavities are compared with cavities bounded by an electrode. It is shown that from measurements at variable applied frequency it is possible to distinguish between cavities of di erent dimensions and between insulated and metal bounded cavities. A two-dimensional eld model of partial discharges in a cylindrical cavity is developed. The sequence of discharges in the cavity is simulated by use of the eld computation program FEMLABR. Discharges are modeled with a voltage and current dependent streamer conductivity and are simulated dynamically to obtain charge and current consistency. It is shown that the frequency dependence of partial discharges is signi - cantly inuenced by the statistical time lag and by the two dielectric time constants related to charge movements on the cavity surface and in the bulk insulation. Simulation results are used to interpret the frequency dependent partial discharge activity in a cylindrical cavity. / QC 20101129

High-entropy alloys (HEAs) are composed of multi-principal elements with equal or near-equal concentrations, which open up a vast compositional space for alloy design. Based on first-principle theory, we focus on the fundamental characteristics of the reported HEAs, as well as on the optimization and prediction of alternative HEAs with promising technological applications. The ab initio calculations presented in the thesis confirm and predict the relatively structural stability of different HEAs, and discuss the composition and temperature-induced phase transformations. The elastic behavior of several HEAs are evaluated through the single-crystal and polycrystalline elastic moduli by making use of a series of phenomenological models. The competition between dislocation full slip, twinning, and martensitic transformation during plastic deformation of HEAs with face-centered cubic phase are analyzed by studying the generalized stacking fault energy. The magnetic moments and magnetic exchange interactions for selected HEAs are calculated, and then applied in the Heisenberg Hamiltonian model in connection with Monte-Carlo simulations to get further insight into the magnetic characteristics including Curie point. The Debye-Grüneisen model is used to estimate the temperature variation of the thermal expansion coefficient. This work provides specific theoretical points of view to try to understand the intrinsic physical mechanisms behind the observed complex behavior in multi-component systems, and reveals some opportunities for designing and optimizing the properties of materials / <p>QC 20171127</p>

<p>QC 20171219</p>

In this thesis, we aim to display characteristics of symmetry protected topological phases within quantum mechanics (QM). Building on well known aspects of QM, we relate the formalism to basic group representation theory, and review the connection between projective symmetries and protected vacuum degeneracies. Symmetries acting projectively on the Hilbert space, corresponding to non-trivial equivalence classes in group cohomology, guarantee degenerate vacua. Furthermore, considering QM in the framework of path integrals, we see that an SPT phase for the system consisting of a particle on a circle maps to a so-called "anomaly theory" in one dimension higher. / Uppsatsens ändamål är att presentera en grundläggande introduktion till symmetri bevarade topologiska faser (SPT) inom kvantmekanik. Med en genomgång av Kvantmekanikens formalism, påvisas ett samband mellan representationer av symmetrier och degenererade grundtillstånd. Mer specifikt, anmärker vi att G-symmetriska SPT faser har den besynnerliga egenskapen att parametriseras av ekvivalensklasser i G:s grupp kohomologi. Bevarade symmetrier med en icke-trivial projektiv fas, garanterar degenerarat vakuum. Vi undersöker även ett specifikt kvantmekaniskt system som består av en partikel på en ring. Under vägintegral-formalismen, uppenbaras då SPT fasen som en anomali för teorin.

The III-nitride semiconductors family includes gallium nitride (GaN), aluminum nitride (AlN), indium nitride (InN), and related ternary and quaternary alloys. The research interest on this group of materials is sparked by the direct bandgaps, and excellent physical and chemical properties. Moreover, the ternary alloys (InGaN, InAlN and AlGaN) present the advantage of bandgap tuning, giving access to the whole visible spectrum, from near infrared into deep ultraviolet wavelengths. The intrinsic properties of III-nitride materials can be combined with characteristical features of nanodimension and geometry in nanorod structures. Moreover, nanorods offer the advantage of avoiding problems arising from the lack of native substrates, like lattice and thermal expansion, film – substrate mismatch. The growth and characterization of group III-nitride semiconductos nanorods, namely InAlN and GaN nanorods, is presented in this thesis. All the nanostructures were grown by employing direct-current reactive magnetron sputter epitaxy. InxAl1−xN self-assembled, core-shell nanorods on Si(111) substrates were demonstrated. A comprehensive study of temperature effect upon the morphology and composition of the nanorods was realized. The radial nanorod heterostructure consists of In-rich cores surrounded by Al-rich shells with different thicknesses. The spontaneous formation of core-shell nanorods is suggested to originate from phase separation due to spinodal decomposition. As the growth temperature increase, In desorption is favored, resulting in thicker Al-rich shells and larger nanorod diameters. Both self-assembled and selective-area grown GaN nanorods are presented. Self-assembled growth of GaN nanorods on cost-effective substrates offers a cheaper alternative and simplifies device processing. Successful growth of high- quality GaN (exhibiting strong bandedge emission and high crystalline quality) on conductive templates/substrates such as Si, SiC, TiN/Si, ZrB2/Si, ZrB2/SiC, Mo, and Ti is supported by the possibility to be used as electrodes when integrated in optoelectronic devices. The self-assembled growth leads to mainly random nucleation, resulting in nanorods with large varieties of diameters, heights and densities within a single growth run. This translates into non-uniform properties and complicates device processing. These problems can be circumvented by employing selective-area growth. Pre-patterned substrates by nano-sphere lithography resulted in GaN nanorods with controlled length, diameter, shape, and density. Well-faceted c-axis oriented GaN nanorods were grown directly onto the native SiOx layer inside nano-opening areas, exhibiting strong bandedge emission at room- temperature and single-mode lasing. Our studies on the growth mechanism revealed a different growth behavior when compared with selective-area grown GaN nanorods by MBE and MOCVD. The time-dependent growth series helped define a comprehensive growth mechanism from the initial thin wetting layer formed inside the openings, to the well-defined, uniform, hexagonal NRs resulted from the coalescence of multiple initial nuclei.

In this thesis we have thermodynamically characterized finite time processes performed on a colloidal particle, kept in contact with thermal reservoir(s). Thermodynamic processes are implemented on the colloidal particle by systematically changing the confining potential in a time dependent way, according to an external driving protocol or by controlling the environmental conditions over a finite duration. First, we study two externally driven systems: one in which the driving is deterministic, and another where the driving is stochastic. These models have appeared in the literature as the building blocks of microscopic machines such as Brownian heat engines and are hence of interest to analyze. In particular, it is of interest to understand the distribution of work done by the colloidal particle as well as the distribution of heat dissipated. These distributions are known in all generality only in a very few cases. In the work we present here, we determine exactly the asymptotic forms of the work distributions (for a finite time duration of the process), which is shown to have non-Gaussian fluctuations. We also find a method to obtain the exact moment generating function of the work distribution, using which we can explicitly calculate aspects of a recently discovered relation for non-equilibrium systems, namely the thermodynamic uncertainty relation. To our knowledge, our model provides the only non-trivial example of a system where the uncertainty relation can be investigated exactly for all times. We have studied the system in various temporal regimes, and have found interesting features such as a time of minimum uncertainty, which may be relevant for the functioning of microscopic machines. Finally, we discuss, an experimentally realized colloidal heat engine model which consists of a single colloidal particle as the working substance. Exact finite time statistics can be obtained for this model using the methods we discuss in the thesis. We present our preliminary results illustrating this.