Browsing by discipline "Teoreettinen fysiikka"

We apply the modern effective field theory framework to study the nucleation rate in high-temperature first-order phase transitions. With this framework, an effective description for the critical bubble can be constructed, and the exponentially large contributions to the nucleation rate can then be computed from the effective description. The results can be used to make more accurate predictions relating to cosmological first-order phase transitions, for example, the gravitational wave spectrum from a transition, which is important for the planned experiment LISA. We start by reviewing a nucleation rate calculation for a classical scalar field to understand, how the critical bubble arises, via a saddle-point approximation, as the central object of the nucleation rate calculation. We then focus on the statistical part of the nucleation rate coming from the Boltzmann suppression of nucleating bubbles. This is done by the creation of an effective field theory from a thermal field theory that can describe the critical bubble. We give an example calculation with the renormalizable model of two $\mathbb{Z}_2$-symmetric scalar fields. The critical bubbles of the model and their Boltzmann suppression are studied numerically, for which we further develop a recently proposed method.

The one-dimensional method of characteristics is a forward method for determining ionospheric currents from electric and magnetic field measurements. In this work the applicability of the method was studied with respect to polar electrojet and shear flow events as these are the predominant ionospheric current situations and are often one-dimensional, the fields thus having only dependence on the latitude. In this work the characteristic equations are derived from Maxwell's equations and Ohm's law. A program was developed with an algorithm applying the one-dimensional method of characteristics to ionospheric electric field measurements by the STARE radars and ground- based magnetic field measurements by the IMAGE magnetometer network. The magnetic field was upward continued to the ionospheric horizontal current altitude (100km). The applicability of the one-dimensional method of characteristics was shown by analyzing the results from three electric current events. The length of these events varied between 10 and 40 minutes and the study area was limited to STARE and IMAGE measurement area over Scandinavia and part of the Arctic Ocean. The results were accurate and relatively detailed and gave insight to e.g. the origin of the features of the field-aligned currents. The estimated ratio of the Hall and Pedersen conductances, or the alpha parameter, is needed in the method. It was shown that the alpha dependence follows the theoretical predictions, and thus the Hall conductance and the East-West component of the horizontal currents (the Hall current, that dominated the horizontal currents) have practically no dependence on alpha. Also the general features of the conductance and current profiles were not dependent of alpha. Field-aligned current (FAC) results obtained during one of the events were compared with concurrent Cluster satellite measurements at a high altitude orbit above the area of study. Two maxima and a minimum of FAC occurred simultaneously in the results with very comparable numerical values after the mapping down of the results from the satellite. The one-dimensional method of characteristics was found very successful in determining ionospheric conductances and currents in detail from ionospheric electric and magnetic field measurements when the assumption of the one-dimensionality of the event is valid. It seems quite feasible to develop the algorithm for application of the method during longer time periods, where as here only singular events were studied.

Quantum computers store and manipulate information in individual quantized energy levels. These devices, not yet realized in their full potential, have the ability to perform certain computational tasks more efficiently than any classical computer. One possible way to implement a quantum computer is to use superconducting circuits controlled by single-mode electromagnetic fields. These circuits constitute the physical quantum bits, or qubits, that are used to store quantum information. A complete, fault-tolerant quantum computer potentially consists of at least millions of physical qubits which are grouped to form fault-tolerant logical qubits. Controlling each physical qubit individually requires a great amount of energy, and hence a future challenge is to reduce the energy consumption in qubit control while maintaining the high precision. In this thesis, we derive a fundamental upper bound for the gate fidelity of a single-qubit not gate implemented with a single resonant driving pulse. It is shown that the upper bound approaches unity inversely proportionally to the increasing mean photon number of the pulse. Furthermore, we find that the upper bound is achieved with an optimal superposition of squeezed states. The typically employed coherent state produces twice as high gate error as the corresponding optimal state. In addition, we present and numerically study a correction protocol that allows using the same drive state for multiple qubit operations. This sustained state is refreshed by sequentially coupling ancillary qubits to it, effectively resetting it and removing entanglement with the previously operated qubits. Thus our protocol allows using the same drive state to implement not gates for different qubits indefinitely, and hence provides a possible route to energy-efficient large-scale quantum computing.

Cold quark matter is matter consisting of free quarks in high energy density, and it can be formed when the energy density of ordinary hadronic matter increases to a region of 1 GeV/fm3. At such high energies, hadronic matter undergoes a phase transition and quarks that would normally be in color confinement break free to form a new phase. It is assumed that similar process happened in the very early universe, but in the opposite direction, when high temperature quark-gluon plasma cooled down significantly. With the cooling, the quark and gluon degrees of freedom switched to hadrons and ordinary matter began to form. Opposed to the hot quark-gluon plasma, there are no direct observations of cold quark matter and its existence is still speculative. Still, it is suspected that cold quark matter can be found in dense neutron star cores or even as stable quark matter in strange quark stars. Theoretically, cold quark matter and quark-gluon plasma can be studied in finite-temperature field theory. Finite-temperature field theory combines the field formalism of quantum field theory and the thermodynamical and statistical methods utilized in quantum statistics. The asymptotic freedom of the theory of strong interactions, quantum chromodynamics (QCD), provides an opportunity to expand the equation of state of high-energy quark matter in the limit of weak coupling, and thus opens a door to implement the tools of finite-temperature field theory perturbatively. Along with the perturbative analysis, it is useful to look at the possibilities offered by effective theories. Two of which are important in the study of finite-temperature QCD, dimensional reduction and hard thermal loop effective theory. Both effective theories address the issue of infrared divergences that arise in finite-temperature field theory efficiently compared to the naïve loop expansion. In dimensional reduction, scales that are defined as hard by the scale hierarchy are integrated out of the theory, after which the infrared problems of gluonic Matsubara zero-modes can be studied in a simpler three-dimensional setting. Hard thermal loop effective theory, on the other hand, examines the infrared divergences that appear in loop-level corrections of soft gluons. When the magnitude of the loop-momentum corresponds to the hard scale, the correction that contains the loop becomes proportional to a tree-level amplitude and breaks the perturbative expansion. The effective theory answers this problem by resumming the propagators and vertex functions and using the new quantities in place of the ordinary ones. With perturbation theory and the effective descriptions, the equation of state of cold quark matter and the pressure extracted from it, have been solved partially up to and including order g6ln2g2 in coupling. The meaning of this thesis is to present the methods of finite-temperature field theory and the supporting effective theories and their implementation to study the equation of state of cold quark matter. The results for QCD pressure will be presented to the last known order in coupling. Also, the effect of a massive strange quark and the role of cold quark matter in solving the neutron star equation of state will be discussed briefly.

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.

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.

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.

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.

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.

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.