Browsing by master's degree program "Magisterprogrammet i teoretiska och beräkningsmetoder"

Many beyond the Standard Model theories include a first order phase transition in the early universe. A phase transition of this kind is presumed to be able to source gravitational waves that might be be observed with future detectors, such as the Laser Interferometer Space Antenna. A first order phase transition from a symmetric (metastable) minimum to the broken (stable) one causes the nucleation of broken phase bubbles. These bubbles expand and then collide. It is of importance to examine how the bubbles collide in depth, as the events during the collision affect the gravitational wave spectrum. We assume the field to interact very weakly or not at all with the particle fluid in the early universe. The universe also experiences fluctuations due to thermal or quantum effects. We look into how these background fluctuations affect the field evolution and bubble collisions during the phase transition in O(N) scalar field theory. Specifically, we numerically simulate two colliding bubbles nucleated on top of the background fluctuations, with the field being a N-dimensional vector in the O(N) group. Due to the symmetries present, the system can be examined in cylindrical coordinates, lowering the number of simulated spatial dimensions. In this thesis, we perform the calculation of initial state fluctuations and simulate them and two bubbles numerically. We present results of the simulation of the field, concentrating on the effects of fluctuations on the O(N) scalar field theory.

Resonant inelastic X-ray scattering (RIXS) is one of the most powerful synchrotron based methods for attaining information of the electronic structure of materials. Novel ultra-brilliant X-ray sources, X-ray free electron lasers (XFEL), offer new intriguing possibilities beyond the traditional synchrotron based techniques facilitating the transition of X-ray spectroscopic methods to the nonlinear intensity regime. Such nonlinear phenomena are well known in the optical energy range, less so in X-ray energies. The transition of RIXS to the nonlinear region could have significant impact on X-ray based materials research by enabling more accurate measurements of previously observed transitions, allowing the detection of weakly coupled transitions on dilute samples and possibly uncovering completely unforeseen information or working as a platform for novel intricate methods of the future. The nonlinear RIXS or stimulated RIXS (SRIXS) on XFEL has already been demonstrated in the simplest possible proof of concept case. In this work a comprehensive introduction to SRIXS is presented from a theoretical point of view starting from the very beginning, thus making it suitable for anyone with the basic understanding of quantum mechanics and spectroscopy. To start off, the principles of many body quantum mechanics are revised and the configuration interactions method for representing molecular states is introduced. No previous familiarity with X-ray matter interaction or RIXS is required as the molecular and interaction Hamiltonians are carefully derived, based on which a thorough analysis of the traditional RIXS theory is presented. In order to stay in touch with the real world, the basic experimental facts are recapped before moving on to SRIXS. First, an intuitive picture of the nonlinear process is presented shedding some light onto the term \textit{stimulated} while introducing basic terminology and some X-ray pulse schemes along with futuristic theoretical examples of SRIXS experiments. After this, a careful derivation of the Maxwell-Liouville-von Neumann theory up to quadrupole order is presented for the first time ever. Finally, the chapter is concluded with a short analysis of the experimental status quo on XFELs and some speculation on possible transition metal samples where SRIXS in its current state could be applied to observe quadrupole transitions advancing the field remarkably.

LHC is the highest energy particle collider ever built and it is employed to study elementary particles by colliding protons together. One intriguing study subject at LHC is the stability of the electroweak vacuum in our universe. The current prediction suggests that the vacuum is in the metastable state. The stability of the vacuum is dependent on the mass of the top quark, and it is possible that more precise measurement of the mass could shift the prediction to the border of the metastable and stable states. In order to measure the mass of the top quark more precisely, we need to measure the bottom (b) quarks decaying from it at high precision, as top quark decays predominantly into a W boson and a b quark. Due to the phenomenon called hadronisation, we can not measure the quarks directly, but rather as sprays of collimated particles called jets. The jets originating from b quarks (b jet) can be identified by b-tagging. The precise measurement and calibration of the b jet energy is crucial for top quark mass measurement. This thesis studies the b jets and their energy calibration at the CMS, which is one of the general purpose detectors along the LHC. Especially the b jet energy scale (bJES) is under the investigation and the various phenomena affecting to it. For example, large fraction of b jets contain neutrinos, which cannot be measured directly. This increases uncertainties related to the energy measurement. Also there are problems how precisely the formation and evolution of the b jets can be modelled by Monte Carlo event generators, such as Pythia8, which was utilized in this thesis. The aim of this thesis is to evaluate how big effect on the bJES is caused by the various different phenomena, which presumably weaken the precision of the b jet measurements. The studied phenomena are the semileptonic branching ratios of b hadrons, branching ratios of b hadron to c hadron decays, b hadron production fraction and parameterization of the b quark fragmentation function. The combined effect of all four different rescaling features mentioned above, suggests that bJES is known at 0.2% level. A small shift of -0.1% in the Missing transverse energy Projection Fraction (MPF) response scale is detected at low pt values, which vanishes as the pt increases. This improves remarkably 0.4-0.5% JES accuracy achieved during at CMS during Run 1 of the LHC. However, there are still many ways we can improve the performance presented here. Definitely there is a need for further studies of the rescaling methods before results could be utilized in the corrections of bJES to do precision measurement of the top quark mass.

We study a system of cold high-density matter consisting purely of quarks and gluons. The mathematical construction of Quantum Chromodynamics (QCD) introduces interactions between the fields, which modify the thermodynamic properties of the system. In the presence of interactions, we can not solve the thermodynamic properties of the system analytically. The method is to expand the result in a series in terms of the QCD coupling constant. This is referred to as the perturbation theory in the context of thermal field theory (TFT). The coupling constant describes the strength of the interaction. We introduce the basic calculation methods used in the QCD and the TFTs in general. We will also include the chemical potential associated with the number of quarks in the system in the calculation. In the case of zero temperature, quarks form a Fermi-sphere such that energy states lower than the chemical potential will be Pauli blocked. The resulting fermionic momentum integrals are modified as a consequence. We can split these integrals into two parts, referred to as the vacuum and matter parts. We can split the calculation of the pressure into two distinct contributions: one from skeleton diagrams and one from ring diagrams. The ring diagrams have unphysical IR divergences that we can not cancel using the counterterms. This is why hard thermal loop (HTL) effective field theory (EFT) is introduced. We will discuss this HTL framework, which requires the computation of the matter part of the gluon polarization tensor, which we will also evaluate in this thesis.

Stacking of antiaromatic molecules leads to enhanced stability and higher conductivity due to reversed antiarotmaticity. It has been shown that cyclophenes consisting of antiaromatic Ni(II) norrcorrole subunits have a vertical current-density flux between the two metal ions. The Ni(II) meso- substituted dibenzotetraaza[14]annulene complex fulfills the Hückel rule for being antiaromatic. Upon increasing the temperature above 13 K, the effective magnetic moment of solid state Ni(II) meso-substituted dibenzotetraaza[14]annulene changes from being diamagnet to paramagnetic. A suggested explanation for this is that there might be weak interaction between the Ni atoms. In this study the possibility of the existence of vertical current-density flux between the two metal ions in the Ni(II) meso-substituted dibenzotetraaza[14]annulene is investigated. In addition, the effect of the Ni and N atoms in Ni(II) 1,5,9,13-tetraaza[16]annulene was studied by replacing Ni and Zn and N with O. Electronic motion in molecules that are under the influence of a magnetic field is investigated computationally, since at present there is no routine experimental method for doing that. TURBOMOLE, the Gauge-including Magnetically Induced Currents method and Paraview were employed in this study for structure optimization of the molecules, calculation of current-density flux and current strength in the molecules and visualisation of the current-density pathways respectively. The results of this study does not show any current transport between the subunits in the Ni(II) meso-substituted dibenzotetraaza[14]annulene complex. Both the Ni(II) 1,5,9,13-tetraaza[16]annulene and the Zn(II) 1,5,9,13-tetraaza[16]annulene are aromatic but they were not stacked due to their distorted structure. The (2Z,7Z,10Z,14Z)-1,9-dioxa-5,13-diazacyclohexadeca-2,7,10,14-tetraene-5,13-diide complexes with either Zn(II) or Ni(II) were both non-aromatic as well as the Ni(II) (2Z,7Z,10Z,14Z)-1,9-dioxa-5,13-diazacyclohexadeca-2,7,10,14-tetraene-5,13-diide dimer.

Topological defects and solitons are nontrivial topological structures that can manifest as robust, nontrivial configurations of a physical field, and appear in many branches of physics, including condensed matter physics, quantum computing, and particle physics. A fruitful testbed for experimenting with these fascinating structures is provided by dilute Bose–Einstein condensates. Bose–Einstein condensation was first predicted in 1925, and Bose–Einstein condensation was finally achieved in a dilute atomic gas for the first time in 1995 in a breakthrough experiment. Since then, the study of Bose–Einstein condensates has expanded to the study of a variety of nontrivial topological structures in condensates of various atomic species. Bose–Einstein condensates with internal spin degrees of freedom may accommodate an especially rich variety of topological structures. Spinor condensates realized in optically trapped ultracold alkali atom gases can be conveniently controlled by external fields and afford an accurate mean-field description. In this thesis, we study the creation and evolution of a monopole-antimonopole pair in such a spin-1 Bose–Einstein condensate by numerically solving the Gross–Pitaevskii equation. The creation of Dirac monopole-antimonopole pairs in a spin-1 Bose–Einstein condensate was numerically demonstrated and a method for their creation was proposed in an earlier study. Our numerical results demonstrate that the proposed creation method can be used to create a pair of isolated monopoles with opposite topological charges in a spin-1 Bose–Einstein condensate. We found that the monopole-antimonopole pair created in the polar phase of the spin-1 condensate is unstable against decay into a pair of Alice rings with oscillating radii. As a result of a rapid polar-to-ferromagnetic transition, these Alice rings were observed to decay by expanding on a short timescale.

The QCD axion arises as a necessary consequence of the popular Peccei-Quinn solution to the strong CP problem in particle physics. The axion turns out to very naturally possesses all the usual qualities of a good dark matter (DM) candidate. Having the potential to solve two major problems in particle cosmology in one fell swoop makes the axion a very attractive prospect. In recent years, the weakening of the traditional WIMP dark matter paradigm and axion search experiments just beginning to reach the sensitivities required to look for the QCD axion have further increased interest in axion physics. In this thesis, the basics of axion physics are reviewed, and an in-depth exposition of common direct detection experiments and astrophysical and laboratory limits is given. Particular emphasis is placed on direct detection by using the axion-photon coupling as it is the only coupling in which experimental sensitivity is enough to probe the QCD axion. The benchmark experiments of light-shining-through-wall (LSTW), helioscopes and cavity haloscopes are given a thorough theoretical treatment. Other couplings and related experiments are relevant when looking for axion-like particles (ALPs), which are postulated by various extensions of the Standard Model but which do not solve the strong CP problem. A general overview of the prevalent ALP-searches is given. Most of the described experimental setups, with some exceptions, are actually searches for very general weakly interacting particles, WISPs, with a certain coupling. The searches are thus well motivated regardless of the future standing of the QCD axion. A chapter is dedicated to axion dark matter and its creation mechanisms, in particular the misalignment mechanism. Two scenarios are mapped out, depending on whether the Peccei-Quinn symmetry spontaneously breaks before or after inflation. Both cases have experimental implications, which are compared. These considerations motivate an axion dark matter window which should be prioritized by experiments. A significant part of this thesis is dedicated to mapping out the experimental landscape of axions today. The up-to-date astrophysical and laboratory limits on the most prominent axion couplings along with projections of some near-future experiments are compiled into a set of exclusion plots.

In this thesis, the sputtering of tungsten surfaces is studied under ion irradiation using molecular dynamics simulations. The focus of this work is on the effect of surface orientation and incoming angle on tungsten sputtering yields. We present a simulation approach to simulate sputtering yields of completely random surface orientations. This allows obtaining the total sputtering yields averaged over a large number of arbitrary surface orientations, which are representative to the sputtering yield of a polycrystalline sample with random grain orientations in a statistically meaningful way. In addition, a completely different method was utilised to simulate sputtering yields of tungsten fuzz surfaces with various fuzz structure heights. We observe that the total sputtering yield of the investigated surfaces are clearly dependent on the surface orientation and the sputtering yields of average random surfaces are different compared to the results of any of the low index surfaces or their averages. The low index surfaces and the random surface sputtering yields also show a dependence of the incoming angle of the projectile ions. In addition, we calculate the outgoing angular distribution of sputtered tungsten atoms in every bombardment case, which likewise shows to be a sensitive to the surface orientation. Finally, the effect of fuzz height on the sputtering yield of tungsten fuzz surfaces is discussed. We see that tungsten fuzz significantly reduces the sputtering yield compared to a pristine tungsten surface and the effect is already seen when the fuzz pillar height is a few atom layers.

Sijoitusten markkinariskin suuruutta tarkastellaan usein riskimittojen avulla. Riskimitta on kuvaus mahdollisia tappioita kuvaavien satunnaismuuttujien joukosta reaalilukuihin. Riski- mittojen avulla erilaisten sijotusten riskillisyyttä pystytään vertailemaan helposti. Pankki- valvojat hyödyntävät riskimittoja pankkien vakavaraisuuden valvonnassa. Pisimpään ylei- sessä käytössä on ollut VaR (Value-at-Risk) niminen riskimitta. VaR kertoo suurimman tappion, joka koetaan jollain asetetulla luottamustasolla α eli se on tappiojakauman α- kvantiili. Baselin uusimassa ohjeistuksessa (Minimum capital requirements of market risk) odotettu vaje niminen riskimitta korvaa VaR-riskimitan pääomavaateen laskennassa. Odotet- tu vaje kertoo, mikä on tappion odotusarvo silloin, kun tappio on suurempi kuin VaR- riskimitan antama luku. Riskimittaa ollaan vaihtamassa, koska VaR ei ole teoreettisilta ominaisuuksiltaan yhtä hyvä kuin odotettu vaje. Tämä johtuu siitä, että VaR ei ole sub- additiivinen, mikä tarkoittaa sitä, että positioiden yhteenlaskettu riski voi olla joissain ta- pauksissa suurempi kuin yksittäisten positioiden riskien summa. Tämä johtaa siihen, että hajauttamattoman sijoitussalkun riski voi olla pienempi kuin hajautetun. Odotettu vaje-riskimitta ei kuitenkaan ole täysin ongelmaton, koska se ei ole konsistentisti pisteytyvä, mikä tarkoittaa, että sille ei ole olemassa pisteytysfunktiota, jonka avulla voi- taisiin verrata estimoituja ja toteutuneita arvoja konsistentisti. Lisäksi se, että odotetun vajeen suuruus riippuu kaikista häntään jäävistä tappioista, tekee siitä herkän hännässä olevien tappioiden virheille. Tämä ei ole kovin hyvä ominaisuus, koska tappiojakaumien häntien estimointiin liittyy paljon epävarmuutta. Koska riskien estimointiin liittyy epävarmuutta, sääntely velvoittaa pankkeja toteumates- taamaan regulatiivisen pääomavaateen laskennassa käytettyjä riskiestimaatteja. Toteuma- testaamisella tarkoitetaan prosessia, jossa estimoituja riskilukuja verrataan toteutuneisiin tappioihin. VaR-estimaattien toteumatestaus perustuu niiden päivien lukumäärälle tes- tausjaksolla, joina tappio ylittää VaR-estimaatin antaman tappiotason. Odotetulle vajeelle ei ole vielä olemassa yhtä vakiintuneita toteumatestausmenetelmiä kuin VaR-estimaateille. Tässä tutkielmassa esitellään kolme erilaista tapaa toteumatestata odotettu vaje estimaat- teja, nämä tavat esittelivät Kratz kollegoineen, Moldenhauer ja Pitera sekä Costanzino ja Curran. Menetelmissä tarkastellaan useamman VaR-tason yhtäaikaisia ylityksiä, suojatun position eli tappion ja riskiestimaatin erotuksen positiiviseen lukuun kumuloitu- vasti summautuvien havaintojen määrää ja VaR-ylityksien keskimääräistä suuruutta. Tutkielman laskennallisessa osuudessa tutkittiin antavatko VaR- ja odotettu vaje- toteumatestit samanlaisia tuloksia ja vaikuttaako riskin estimointiin käytetyn havainto- jakson pituus estimaattien suoriutumiseen toteumatesteissä. Laskelmissa havaittiin, että odotettu vaje- ja VaR-toteumatestit antoivat samanlaisia tuloksia. Markkinadatasta eri kokoisilla estimointi-ikkunoilla lasketut estimaatit saivat toteumatestissä erikokoisia tes- tisuureiden arvoja, ja hyväksyivät väärän mallin tai hylkäsivät oikean malli eri todennä- köisyyksillä. Kun käytettiin puhtaasti simuloitua dataa, eri kokoisilla estimointi-ikkunoilla laskettujen estimaattien tuloksissa ei ollut eroja. Näin voidaan päätellä, että testitulosten erot eri mittaisilla havaintojaksoilla laskettujen estimaattien välillä eivät johdu pelkästään havaintojen määrästä vaan myös laadusta.

Coagulation equations are evolution equations that model the time-evolution of the size-distribution of particles in systems where colliding particles stick together, or coalesce, to form one larger particle. These equations arise in many areas of science, most prominently in aerosol physics and the study of polymers. In the former case, the colliding particles are small aerosol particles that form ever larger aerosol particles, and in the latter case, the particles are polymers of various sizes. As the system evolves, the density of particles of a specified size changes. The rate of change is specified by two competing factors. On one hand there is a positive contribution coming from smaller particles coalescing to form particles of this specific size. On the other hand, particles of this size can coalesce with other particles to form larger particles, which contributes negatively to the density of particles of this size. Furthermore, if there is no addition of new particles into the system, then the total mass of the particles should remain constant. From these considerations, it follows that the time-evolution of the coagulation equation is specified for every particle size by a difference of two terms which preserve the total mass of the system. The physical properties of the system affect the time evolution via a coagulation kernel, which determines the rate at which particles of different sizes coalesce. A variation of coagulation equations is achieved when we add an injection term to the evolution equation to account for new particles injected into the system. This results in a new evolution equation, a coagulation equation with injection, where the total mass of the system is no longer preserved, as new particles are added into the system at each point in time. Coagulation equations with injection may have non-trivial solutions that are independent of time. The existence of non-trivial stationary solutions has ramifications in aerosol physics, since these might map to observations that the particle size distribution in the air stays approximately constant. In this thesis, it will be demonstrated, following Ferreira et al. (2019), that for any good enough injection term and for suitably picked, compactly supported coagulation kernels, there exists a stationary solution to a regularized version of the coagulation equation. This theorem, which relies heavily on functional analytic tools, is a central step in the proof that certain asymptotically well-behaved kernels have stationary solutions for any prescribed compactly supported injection term.