Browsing by discipline "Teoretisk fysik"
Now showing items 61-80 of 96
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(2012)In this thesis we consider extending the standard model of particle physics (SM) to include a fourth generation of elementary particles (SM4). The fourth generation would have to be sufficiently heavy to have escaped detection; specifically, its neutrino is required to be kinematically inaccessible to the Z boson in order to agree with the very precise LEP measurements of the Z width. This extension is appealing since the current theory (the SM) exhibits tension with some phenomena observed in nature. Such phenomena are, for example, the replication and number of fermion families, the ratio of matter to antimatter in the observable universe, charge-parity violation and the mixings between the fermions. Up to very recently the issue of the origin of mass, that is, the mechanism of electroweak symmetry breaking in the SM, was lacking experimental verification. However, during the writing of this thesis there have been some very exciting advances in this domain. In July 2012 the CMS and ATLAS collaborations at the LHC have reported the observation of a resonance at ∼ 125 GeV, an observation confirmed by experiments at another high-energy particle collider, the Tevatron. This resonance seems to correspond to the Higgs particle, the quantum of the scalar field responsible for the breaking of the electroweak symmetry. Besides verifying the answer to the theoretically fundamental question about the origin of mass, the experimental discovery also serves as a constraint for any theory of particle physics. The goodness of models describing particle physics are generally tested by performing global fits to the data, with the data set usually taken to be the most precisely measured quantities available — the electroweak precision observables. When the recent Higgs signal strengths are included in the data set, it is seen that the SM4 is not a correct theory of nature. Specifically, the Higgs signals predicted by the SM4 are not in agreement with the data, and the model has in September 2012 been quite decisively excluded at the statistical significance of 5.3σ. Following the developments in the field we next consider the phenomenological effects of adding another scalar doublet to the previously considered SM4. In the SM and SM4 there is just one scalar (Higgs) doublet: the models have a minimal scalar sector. The fermion sector, however, is not minimal: there are at least three replicas of a fermion family and so it is possible that the scalar sector is not minimal either. There are in fact arguments in favor of several Higgs doublets, for example supersymmetry and the baryon asymmetry of the universe. Two doublets give rise to five physical particles and so the phenomenology of such models is much richer than in the minimal scenario. Four family-models have received a great deal of interest in the last decade: some 500 articles are reported to have been published concerning their phenomenology during this time. This thesis is a review of the recent developments is this field.
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(2016)A quantum computer is a promising addition to a classical computer due to increase in performance on certain computational problems. A classical computer computes by manipulating bits, which assume a value either 0 or 1, using logical gates. Similarly, a quantum computation is carried out by manipulating quantum bits, so-called qubits, using quantum gates. The main advantage of qubits is that they can be not only in the states representing 0 and 1, but also in any superposition of these two states. Many different physical realizations for qubits have been proposed. One of the most promising candidates for the hardware of quantum computing are superconducting circuits. Here, the qubit can be represented in number of ways. For example, the two different states can be the direction of current circulating in a superconducting loop, or presence and absence of a photon in a transmission line. In this thesis, we study a tunable phase gate for microwave photons. The gate is implemented by a transmission line interrupted by three superconducting quantum interference devices (SQUIDs), which we model as inductors. We theoretically show that this system fulfills the requirements of a phase gate and that the tunability of the phase shift is frequency dependent. In addition, we consider a non-ideal system by including the effects of the capacitance associated with the SQUIDs. We find that the capacitance has no adverse effects, and in the best case, it may even increase the range of tunability. We also measure the phase shift at frequency of 6.3 GHz and find that the system is well described by the theory. To our knowledge, similar phase gate has not been experimentally studied before.
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(2015)The phase of accelerating expansion of the early universe is called cosmological inflation. It is believed that the acceleration was driven by a scalar field called the inflaton, which in the simplest inflationary models was slowly rolling down its potential (slow-roll inflation). As an extension of these simple models, in this work we study a model in which the rolling of the inflaton field was fast (fast-roll inflation). From the inflationary phase we can detect density fluctuations which are usually thought to be created from quantum fluctuations of the inflaton field. In the case of the fast-rolling inflaton field, the evolution of the perturbations may differ significantly from the simpler slow-roll models. In addition to the inflaton, there might have also been other quantum fields in the early universe acting on the perturbation evolution. In this work, we study a case in which the perturbations are partly created from the inflaton field fluctuations and partly from another scalar field named the curvaton. This kind of scenario is called the mixed model. In the investigation of the early universe, it is essential to be able to estimate to what extent the observed perturbations tell us directly of the inflaton dynamics – and not of other phenomena. From the inflationary model-building point of view, freeing the inflaton from often somewhat unnatural observational constraints gives us new possibilities to develop more plausible models of inflation. In this thesis, we introduce briefly the simplest inflation and curvaton models and study analytically the perturbation evolution in the mixed model and fast-roll inflation. The research part of the thesis contains a numerical investigation of the perturbation evolution, as well as the inflaton and curvaton dynamics, in these models.
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(2013)We study the possible initial conditions of the universe and the possibility of isocurvature perturbations in the early universe through CMB data. We consider three isocurvature modes; Cold Dark Matter Density Isocurvature (CDI) mode, Neutrino Density Isocurvature (NDI) mode and Neutrino Velocity Isocurvature (NVI) mode. We use three CMB datasets WMAP, QUaD and ACBAR data to constrain the (possibly) correlated adiabatic and isocurvature models. For CDI and NDI models we use both a phenomenological approach, where primordial perturbations are parametrized in terms of amplitudes at two different scales, and a slow-roll two-field inflation approach. For the NVI model we only use the phenomenological approach, since NVI mode would occur only after neutrino decoupling, i.e., after inflation. We find that larger isocurvature fractions are allowed in NDI and NVI models than in corresponding CDI models. For generally correlated perturbations, we find the upper limit to the CDM density, neutrino density and neutrino velocity isocurvature fraction to be 4.5%, 9.8% and 12.4% respectively at k = 0.002 Mpc−1 . Analysis has also been done for the special cases of uncorrelated and fully (anti) correlated perturbations. We find no clear preference for non-zero isocurvature fraction for the models considered. We find that the odds for a correlated isocurvature model compared to the standard adiabatic model are very low. We conclude that the present data does support the standard adiabatic model.
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(2018)Kerrin metriikka kuvaa pyörivän mustan aukon aiheuttamaa aika-avaruuden kaareutumaa. Käytännössä kaikki mustat aukot pyörivät jonkin verran joten Kerrin metriikka on olennainen osa kosmologiaa. Viime vuosina pyörivät mustat aukot ovat nousseet valokeilaan gravitaatioaaltojen löytämisen vuoksi. Nämä gravitaatioaaltohavainnot on tehty nimenomaan mustien aukkojen yhdistymisen seurauksena. Tässä työssä tulen käsittelemään Kerrin metriikkaan liittyvää teoriaa sekä selvittämään gravitaatioaaltojen linkittymistä pyöriviin mustiin aukkoihin.
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(2016)In this thesis we introduce the Coleman-Weinberg mechanism through sample calculations. We calculate the effective potential in the massless scalar theory and massless quantum electrodynamics. After sample calculations, we walk through simple model in which the scalar particle, that breaks the scale invariance, resides at the hidden sector. Before we go into calculations we introduce basic concepts of the quantum field theory. In that context we discuss interaction of the fields and the Feynman rules for the Feynman diagrams. Afterwards we introduce the thermal field theory and calculate the effective potential in two cases, massive scalar theory and the Standard Model without fermions. We introduce the procedure how to calculate the effective potential, which contains ring diagram contributions. Motivation for this is knowledge of that sometimes the spontaneously broken symmetries are restored in the high temperature regime. If the phase transition between broken-symmetry and full-symmetry phase is first order phase transition baryogenesis can happen. Using the methods introduced in this thesis the Standard Model extensions that contain hidden sectors can be analyzed.
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(Helsingin yliopistoUniversity of HelsinkiHelsingfors universitet, 2004)
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(2018)This thesis presents a ray-tracing based method for performing polarized radiative transfer in arbitrary spacetimes and a numerical implementation of said method. This method correctly accounts for general relativistic effects on the propagation of radiation, and the polarized im- ages and spectra it produces can be directly compared with observations. Thus it is well suited for studying systems where relativistic effects are significant, such as compact astrophysical objects. The ray-tracing method is based on several approximations, which are discussed in depth. The most important one of these is the geometric optics approximation, which is derived starting from Maxwell’s equations. In the geometric optics approximation, high frequency radiation is described as amplitudes or intensities which are propagated along geodesic rays. Additional assumptions about the properties of the radiation field allow describing it and its interaction with matter using the formalism of kinetic theory, which leads to a simple transfer equation along rays. This transfer equation is valid in arbitrary spacetimes, and forms the basis for the ray-tracing method. The ray-tracing method presented in this work and various similar methods described in the literature are not suited for analytic computations using realistic models. Instead numerical methods are needed. Such numerical methods are implemented in a general fashion in the Arcmancer library (paper in preparation), of which large parts were implemented as a part of this work. The implementation details of Arcmancer are described and its features are compared to those available in other similar codes. Tests of the accuracy of the numerical methods as well as example applications are also presented, including a novel computation of a gravitational lensing event in a binary black hole system. The implementation is found to be correct and easily applicable to a variety of problems.
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(2018)The fundamental building blocks of quantum computers, called qubits, can be physically realized through any quantum system that is restricted to two possible states. The power of qubits arises from their ability to be in a superposition of these two states, allowing for the development of quantum algorithms that are impossible for classical computers. However, interactions with the surrounding environment destroy the superposition in a process called decoherence, which makes it important to find ways to model these interactions and mitigate them. In this thesis we derive a non-Markovian master equation for the spin-boson model, with a time-dependent two-level system, using the reaction coordinate representation. We show numerically that in the superconducting qubit regime this master equation maintains the positivity of the density operator for relevant parameter ranges, and is able to model non-Markovian effects between the system and the environment. We also compare the reaction coordinate master equation to a Markovian master equation with parameters taken from real superconducting qubits. We demonstrate that the Markovian master equation fails to capture the system–bath correlations for short times, and in many cases overestimates relaxation and coherence times. Finally, we test how a time-dependent bias affects the evolution of the two-level system. The bias is assumed to be constant with an additive term arising from an externally applied time-dependent plane wave control field. We show that an amplitude, angular frequency, and phase shift for the plane wave can be chosen such that the control field improves the coherence time of the two-level system.
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(2017)Conformal blocks are building blocks of correlation functions in conformal field theories (CFTs). They neatly encode the universal information dictated by conformal symmetry and separate it from the dynamical information which depends on the particular theory. Conformal blocks merit an in-depth study as is evidenced by their extensive applications in the study of bulk locality in the AdS/CFT correspondence and the recent conformal bootstrap program. The vacuum Virasoro blocks in the semi-classical (large central charge) limit is known to compute the leading order contribution to the Rényi entropy. Moreover, the semi-classical Virasoro blocks along with conformal bootstrap feature in a proof of the cluster decomposition principle for AdS3/CFT2. In this thesis, conformal field theory and its necessary ingredients are briefly reviewed. Conformal blocks from the exchange of a spinless operator are evaluated by holographic computations of geodesic Witten diagrams for AdSd+1/CFTd. The results are verified against the Casimir operator method of Dolan and Osborn. Virasoro blocks in various semi-classical limits are discussed, and holographic Virasoro blocks are calculated in the global, heavy-light, and perturbative heavy, and the results are verified using the monodromy method. Finally, defect conformal field theories (dCFTs) are introduced and, as an original contribution, an integral expression for defect conformal blocks is obtained, which is expected to precisely match the corresponding result in dCFT literature.
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(Helsingin yliopistoHelsingfors universitetUniversity of Helsinki, 2005)Planeettainvälisessä avaruudessa havaitaan runsaasti Auringosta peräisin olevia korkeaenergiaisia hiukkasia. Havainnot voidaan jakaa karkeasti lyhyt- ja pitkäkestoisiin. Yleisin selitys jälkimmäisille on diffusiivinen shokkikiihdytys koronan massapurkausten edellään työntämissä shokkiaalloissa. Hiukkaset siroavat shokin turbulentista sähkömagneettisesta kentästä ja saavat lisää energiaa ylittäessään shokkirintaman monta kertaa. Kiihdytys alkaa koronassa ja jatkuu useiden päivien ajan massapurkauksen liikkuessa poispäin Auringosta. Havaintojen mukaan koronassa tapahtuva kiihdytys, jossa protonit voivat saavuttaa jopa 1 GeV suuruusluokkaa olevan energian, tapahtuu minuuttien aikaskaaloissa. Korkeaenergiaisten hiukkasten energiaspektri on tyypillisesti potenssilaki dN/dE ~ E^{-sigma}, missä sigma on lähellä ykköstä oleva vakio. Opinnäytteessä esitellään diffusiivisen shokkikiihdytyksen teoria ja tutkitaan kiihdytystä testihiukkassimulaatiolla. Koronan aktiivista aluetta mallinnetaan yksinkertaistetulla magneettikentällä. Simulaatiossa lasketaan tasomaisen shokin eteen injektoitujen protonien ratoja siihen asti, kun ne joko osuvat Auringon pintaan tai karkaavat planeettainväliseen avaruuteen. Lopputuloksista lasketuista statistiikoista etsitään kiihdytykseen vaikuttavia tekijöitä. Saatujen tuloksien perusteella koronan magneettikentän geometrialla on suuri merkitys saavutettavaan energiaan. Tehokkainta kiihdytys on geometrioissa, joissa shokki on lähes poikittainen. Erityisesti sironnan ei tarvitse olla voimakasta suurten energioiden saavuttamiseksi. Sen vaikutus näyttäisi olevan enneminkin jakaumafunktion isotropisointi, jolloin energiaspektristä tulee potenssilakimuotoinen.
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(2013)This thesis presents a method to simulate scalar electrodynamics on the lattice in a dual representation which avoids the sign problem arising at finite density in conventional simulations. We first introduce the model as a classical field theory and canonically quantize it paying special attention to the role of conserved charges. We then derive the path integral formulation of the grand canonical partition function, and formulate a lattice regulated version of the model. The dual representation used in the simulations is based on well known high temperature expansion techniques. We discuss these methods in order to give the reader a general picture of their applicability to spin models and abelian lattice field theory. The existing literature on simulations of lattice models in dual representations is also reviewed. We find that, besides solving some sign problems, a dual representation often alleviates the inefficiency of Monte Carlo simulations near phase transitions. This is partly due to the availability of efficient update algorithms, such as the worm algorithm. Using the expansion techniques introduced earlier we derive a dual formulation of lattice regulated scalar electrodynamics. We show that the dynamical variables of the dual model can be intuitively interpreted as field strengths and current densities. The dual representation of other observables, such as general correlation functions, is also discussed. Finally, we present an algorithm to simulate the dual model. This algorithm is based on simple local updates combined with a worm algorithm that updates the current densities. By comparing simulation results at vanishing density with a conventional simulation we show that the algorithm is working correctly. We find that the worm algorithm behaves very differently in different phases of the system, and argue that this phenomenon is directly linked with the presence or absence of long range order. We also perform simulations at nonzero chemical potential where the system exhibits the silver blaze phenomenon and a transition to a finite density phase.
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(2013)In recent years statistical physics and computational complexity have found mutually interesting subjects of research. The theory of spin glasses from statistical physics has been successfully applied to the boolean satisfiability problem, which is the canonical topic of computational complexity. The study of spin glasses originated from experimental studies of the magnetic properties of impure metallic alloys, but soon the study of the theoretical models outshone the interest in the experimental systems. The model studied in this thesis is that of Ising spins with random interactions. In this thesis we discuss two analytical derivations on spin glasses: the famous replica trick on the Sherrington-Kirkpatrick model and the cavity method on a Bethe lattice spin glass. Computational complexity theory is a branch of theoretical computer science that studies how the running time of algorithms scales with the size of the input. Two important classes of algorithms or problems are P and NP, or colloquially easy and hard problems. The first problem to be proven to belong to the class of NP-complete problems is that of boolean satisfiability, i.e., the study of whether there is an assignment of variables for a random boolean formula so that the formula is satisfied. The boolean satisfiability problem can be tackled with spin glass theory; the cavity method can be applied to it. Boolean satisfiability exhibits a phase transition. As one increases the ratio of constraints to variables the probability of a random formula being satisfiable drops from unity to zero. This transition of random formulas from satisfiable to unsatisfiable is continuous for small formulas. It grows sharper with increasing problem size and becomes discrete at the limit of an infinite number of variables. The cavity method gives a value for the location of the phase transition that is in agreement with the numerical value. The cavity method is an analytical tool for studying average values over a distribution, but it introduces so called surveys that can also be calculated numerically for a single instance. These surveys inspire the survey propagation algorithm that is implemented as a numerical program to efficiently solve large instances of random boolean satisfiability problems. In this thesis I present a parallel version of survey propagation that achieves a speedup by a factor of 3 with 4 processors. With the improved version we are able to gain further knowledge on the detailed workings of survey propagation. It is found, firstly, that the number of iterations needed for one convergence of survey propagation depends on the number of variables, seemingly as ln(N). Secondly, it is found that the constraint to variable ratio for which survey propagation succeeds is dependent on the number of variables.
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(2014)The spin-orbit (SO) coupling gives rise to a large splitting of the subband energy levels in semiconducting heterostructures. Both theoretical and experimental interest towards SO interactions in superconductors and superconducting heterostructures has been on the rise due to new experimental findings on the field. The zero-energy peak in the local density of states in the experiment suggests that Majorana fermions appear in superconductor-semiconductor nanowires. In this thesis, I study the effects of SO coupling in superconductor-normal metal-superconductor (SNS) junctions in the presence of an exchange field. We adopt the quasiclassical Green's function approach and implement the Rashba SO interaction into the Usadel equation, which is the equation of motion for the quasiclassical Green's functions. We solve the Usadel equation numerically as the analytic solution in the general case is not possible. We find that the Rashba SO coupling has a finite effect on the physical properties of the junction only if there is also an exchange field along the SNS junction. When both are present, two interesting phenomena occur. Contrary to the case without Rashba SO coupling, supercurrent through the SNS junction stays finite even with a very large exchange field strength along the junction. Also, the local density of states peaks up in the normal metal at zero energy when both, the exchange field and the Rashba SO coupling, are present. The peak persists almost throughout the normal metal regime vanishing only at the edges near the superconductors. Therefore, the peak cannot be explained as Majorana fermions as they would appear as a peak near the edges and an alternative explanation is needed.
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(Helsingin yliopistoUniversity of HelsinkiHelsingfors universitet, 2004)
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(2017)In this thesis, we discuss the Sachdev-Ye-Kitaev (SYK) model and tensor models with similar properties. The SYK model is a quantum field theoretical model describing N interacting fermions, whose coupling constants are drawn from a Gaussian ensemble. Noteworthy properties of the SYK model include that it is analytically solvable in the large N limit, that it exhibits conformal symmetry at low energies and that it is maximally chaotic. These properties are remarkably similar to those of a 1 + 1 dimensional Schwarzschild black hole. It has been conjectured the SYK model is a holographic dual to the black hole. We introduce a set of Feynman rules for the SYK model. Using these rules, we show that in the large N limit the diagrams that contribute to the two-point function are all so-called iterated melonic diagrams. This allows us to derive a Schwinger-Dyson equation for the two-point function, which, in turn, can be solved exactly in the infrared limit. We also consider the four-point function. In the large N limit, the leading-order correction to the four-point function is given by so-called ladder diagrams. This allows us to derive an explicit expression for the four-point function. The SYK model can be generalized in a few different ways. In this thesis, we consider the generalization where the fermions act through q-fold interactions instead of quartic interactions present in the original SYK model. In particular, considerable simplifications can be achieved in the q → ∞ limit or q = 2 case, which we study. While the SYK model has many interesting properties, its random couplings limit its usability especially as a dual to a Schwarzschild black hole. We therefore also consider tensor models which do not have this drawback but manage to preserve the interesting properties of the SYK model. In the last chapter, we briefly inspect the chaotic behaviour of the SYK and tensor models and derive Lyapunov exponent for them. It can be shown that the expression saturates an upper bound for Lyapunov exponents of a large class of quantum systems, including large N systems.
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(2016)Tässä tutkielmassa tarkastellaan tähtienvälisen pölyn dynamiikkaa, joka kytkeytyy sähkömagneettisen säteilyn sirontaan. Klassisen mekaniikan perustavanlaatuisimpiin pyörimisyhtälöihin perustuva pölyhiukkasen dynamiikka ja sirontatapahtuman Maxwellin yhtälöistä juontuva dynaaminen perusta kytketään tutkielmassa uudella tavalla ratkaisemalla ongelmassa keskeinen sirontatapahtuma sironnan integraaliyhtälömenetelmän avulla. Lukija johdatellaan myös esiteltyyn teoriaan pohjautuvan numeerisen menetelmän äärelle. Erään olemassa olevan sironnan integraaliyhtälöesityksen toteutuksen ympärille laaditaan viitekehys Fortran-ohjelmistolle, joka laskee hilaverkon avulla mallinnetun homogeenisen hiukkasen dynamiikkaa. Tutkielman teoreettisessa osuudessa luodaan teoreettinen viitekehys mielivaltaisen muotoisen hiukkasen dynamiikalle, jossa liikeyhtälöiden voimatermit ovat seurausta sähkömagneettisesta sirontatapahtumasta. Lisäksi sirontatapahtumaan liittyvät elektrodynamiikan perusteet sekä itse sirontaongelman ratkaisu pintaintegraaliyhtälöformalismilla esitellään teoreettisessa osuudessa. Numeerisessa osuudessa esitellään hiukkasen mallinnus sekä luonnehditaan teoreettisen viitekehyksen sekä olemassa olevan pintaintegraalimenetelmän yhdistävän Fortran-ohjelmiston rakenne. Osuudessa käsitellään myös ohjelmiston toiminnan kannalta oleellisimmat algoritmit. Liikeyhtälöitä ratkaisevan Runge-Kutta-integraattorin oikea toiminta varmennetaan työssä asettamalla tunnettuja tuloksia tuottavia sidosehtoja ja vääntöjä. Kosmista ympäristöä mallintavilla alkuehdoilla pintaintegraaliyhtälömenetelmällä lasketun sirontavuorovaikutuksen määräämä dynamiikka tuottaa odotettuja tuloksia. Tulosten perusteella voidaan tulkita työssä esitetyn viitekehyksen olevan kehityskelpoinen, kun tavoitteena on mallintaa hiukkasdynamiikkaa erilaisissa kosmisissa ympäristöissä.
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(2016)Sähkömagneettisen aallon käyttäytymisen simuloimisesta on tullut tärkeä työkalu nykyaikana. Laskentaresurssien kasvu on mahdollistanut Maxwellin yhtälöiden ratkaisemisen mitä monimutkaisemmille systeemeille ilman, että systeemiä tarvittaisiin fyysisesti rakentaa. Tästä on hyötyä tähtitieteelle, sillä kaukaisten kohteiden ominaisuuksia voidaan tutkia vertaamalla kohteesta sironnutta valoa laskennalliseen dataan. Ongelmana laskennallisen datan tuottamisessa on, että sähkömagneettisen aallon käyttäytymistä kuvaavia Maxwellin yhtälöitä ei pystytä ratkaisemaan nykyisillä menetelmillä eksaktisti, kun mallinnettava kohde on suuri. Tästä syystä ongelmaa pitää yksinkertaistaa, kuten tehdään säteilynkuljetusohjelmissa. Säteilynkuljetusohjelmissa seurataan sähkömagneettisen aallon kulkua aineessa ja näin pyritään ratkaisemaan, kuinka aine sirottaa säteilyä. Säteilynkuljetusohjelmat onnistuvat ratkaisemaan harvojen aineiden sirontaongelmia, koska sirottajien väliset vuorovaikutusten oletetaan tapahtuvan kaukokenttien kautta, mikä on pätevä approksimaatio harvojen aineiden tapauksessa. Tiheiden aineiden sirontaongelmissa lähikenttien vaikutusta ei voi kuitenkaan sivuuttaa ja siksi säteilynkuljetuksen tulokset tiheille aineille eroavat eksaktista ratkaisusta huomattavasti. Tässä pro gradu -tutkielmassa on esitetty uudenlaisen säteilynkuljetusohjelma R²T² (Radiative Transfer with Reciprocal Transactions) kehitystyötä. Oletamme, että käyttämällä niin sanottua vapaan avaruuden sirontakenttää kaukokenttien sijaan, pystymme laskemaan säteilynkuljetusohjelma R²T²:lla myös tiheiden aineiden sirontaongelmia. Sähkökentät esitetään palloharmonisilla funktioilla ja säteilynkuljetuksessa yksittäiset sirottajat korvataan palloklustereilla, joiden väliset vuorovaikutukset lasketaan käyttämällä superpositio T-matriisimenetelmää. Tutkielmassa perehdytään säteilynkuljetusyhtälön johtoon, sähkömagneettisen kentän esittämiseen palloharmonisilla funktioilla ja superpositio T-matriisimenetelmään. Tutkielmassa käydään läpi R²T²:n algoritmia, jatkosuunnitelmia ja näytetään, että R²T² onnistuu kelvollisesti ratkaisemaan absorboimattomien aineiden ongelmia. Absorption huomioiminen vaatii kuitenkin vielä menetelmän jatkokehitystä.
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(Helsingin yliopistoHelsingfors universitetUniversity of Helsinki, 2008)In technicolor theories the scalar sector of the Standard Model is replaced by a strongly interacting sector. Although the Standard Model has been exceptionally successful, the scalar sector causes theoretical problems that make these theories seem an attractive alternative. I begin my thesis by considering QCD, which is the known example of strong interactions. The theory exhibits two phenomena: confinement and chiral symmetry breaking. I find the low-energy dynamics to be similar to that of the sigma models. Then I analyze the problems of the Standard Model Higgs sector, mainly the unnaturalness and triviality. Motivated by the example of QCD, I introduce the minimal technicolor model to resolve these problems. I demonstrate the minimal model to be free of anomalies and then deduce the main elements of its low-energy particle spectrum. I find the particle spectrum contains massless or very light technipions, and also technibaryons and techni-vector mesons with a high mass of over 1 TeV. Standard Model fermions remain strictly massless at this stage. Thus I introduce the technicolor companion theory of flavor, called extended technicolor. I show that the Standard Model fermions and technihadrons receive masses, but that they remain too light. I also discuss flavor-changing neutral currents and precision electroweak measurements. I then show that walking technicolor models partly solve these problems. In these models, contrary to QCD, the coupling evolves slowly over a large energy scale. This behavior adds to the masses so that even the light technihadrons are too heavy to be detected at current particle accelerators. Also all observed masses of the Standard Model particles can be generated, except for the bottom and top quarks. Thus it is shown in this thesis that, excluding the masses of third generation quarks, theories based on walking technicolor can in principle produce the observed particle spectrum.
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(2013)In this thesis we give self-sufficient introduction to the complex Langevin method, which is a promising simulation method for the quantum field theories with finite chemical potential. We begin by revising the the stochastic methods needed for mathematical understanding of Langevin equation. This revision is done trough the examples of a Brownian motion. After the stochastical preliminaries are deled with, we also give a short introduction to quantum field theories on the lattice and with both finite temperature and chemical potential. We show that introduction of chemical potential can cause a sign problem, which can yield traditional Monte Carlo simulations non usable for this problem. We notice a similarity of form between the stochastic path integrals and the Feynman path integrals. We use this similarity to define a stochastic quantization method, that lets us to use stochastic evolution equations to find the correlation function in quantum field theory. This method is then expanded for complex actions that arise from the use of the finite chemical potential in the quantum field theory. We discuss the possible problems with this expansion and deduct that there is no complete mathematical understanding of complex Langevin equation. After all these theoretical considerations we do our own simulations to inspect if this model works. We find out, that for the U(1) one link model and for the SU(3) spin model, the method works as long as we are not using imaginary noise. Unfortunately we also find out that three dimensional XY-model converges to wrong results. We find no reason for this behavior.
Now showing items 61-80 of 96