Browsing by study line "Teoreettinen fysiikka"
Now showing items 120 of 21

(2022)We study a system of cold highdensity 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 Fermisphere 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.

(2023)Certain topological phases of matter exhibit lowenergy quasiparticles that closely resemble relativistic Weyl fermions due to their linear dispersion. This notion leads to a quasirelativistic description for these nonrelativistic condensed matter quasiparticles. In relativistic quantum field theory, Weyl fermions are subject to chiral anomalies when coupled to gauge fields or nontrivial background geometries. Condensed matter Weyl quasiparticles similarly experience anomalies from their background fields, leading to anomalous transport phenomena. We review the field theory of relativistic fermions in curved spacetimes with torsion, and the macroscopic BCS theory of superconductors and superfluids. Using the example of p+ippaired superfluids and superconductors, we show how their gapless excitations are quasirelativistic Weyl fermions in an emergent spacetime determined by their background fields. With a simple Landau level argument, we then argue that the presence of torsion in this emergent spacetime leads to a chiral anomaly for the Weyl quasiparticles. In the context of relativistic theory, the torsional contribution to the chiral anomaly is controversial, not least because it depends on a nonuniversal UV cutoff. The Landau level calculation presented here is also ambiguous for relativistic Weyl fermions. However, as we will show, the quasirelativistic approximation we use and the properties of the underlying superfluid or superconductor lead to a natural cutoff for the quasiparticle anomaly. We match this emergent torsional anomaly to the hydrodynamic anomaly in the p+ipsuperfluid 3HeA.

(2022)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 meanfield description. In this thesis, we study the creation and evolution of a monopoleantimonopole pair in such a spin1 Bose–Einstein condensate by numerically solving the Gross–Pitaevskii equation. The creation of Dirac monopoleantimonopole pairs in a spin1 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 spin1 Bose–Einstein condensate. We found that the monopoleantimonopole pair created in the polar phase of the spin1 condensate is unstable against decay into a pair of Alice rings with oscillating radii. As a result of a rapid polartoferromagnetic transition, these Alice rings were observed to decay by expanding on a short timescale.

(2019)When the standard model gauge group SU(3) × SU(2) × U(1) is extended with an extra U(1) symmetry, the resulting Abelian U(1) × U(1) symmetry introduces a new kinetic mixing term into the Lagrangian. Such double U(1) symmetries appear in various extensions of the standard model and have therefore long been of interest in theoretical physics. Recently this kinetic mixing has received attention as a model for dark matter. In this thesis, a systematic review of kinetic mixing and its physical implications is given, some of the dark matter candidates relying on kinetic mixing are considered, and experimental bounds for kinetic mixing dark matter are discussed. In particular, the process of diagonalizing the kinetic and mass terms of the Lagrangian with a suitable basis choice is discussed. A rotational ambiquity arises in the basis choice when both U(1) fields are massless, and it is shown how this can be addressed. BBN bounds for a model with a fermion in the dark sector are also given based on the most recent value of the effective number of neutrino species, and it is found that a significant portion of the FIMP regime is excluded by this constraint.

(2023)The QCD axion arises as a necessary consequence of the popular PecceiQuinn 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 indepth exposition of common direct detection experiments and astrophysical and laboratory limits is given. Particular emphasis is placed on direct detection by using the axionphoton coupling as it is the only coupling in which experimental sensitivity is enough to probe the QCD axion. The benchmark experiments of lightshiningthroughwall (LSTW), helioscopes and cavity haloscopes are given a thorough theoretical treatment. Other couplings and related experiments are relevant when looking for axionlike 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 ALPsearches 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 PecceiQuinn 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 uptodate astrophysical and laboratory limits on the most prominent axion couplings along with projections of some nearfuture experiments are compiled into a set of exclusion plots.

(2022)We will review techniques of perturbative thermal quantum chromodynamics (QCD) in the imaginarytime formalism (ITF). The Infrared (IR)problems arising from the perturbative treatment of equilibrium thermodynamics of QCD and their phenomenological causes will be investigated in detail. We will also discuss the construction of two effective field theory (EFT) frameworks most often used in modern high precision calculations to overcome these. The EFTs are the dimensionally reduced theories EQCD and MQCD and Hard thermal loop effective theory (HTL). EQCD is threedimensional Euclidean YangMills theory coupled to an adjoint scalar field and MQCD is threedimensional Euclidean pure YangMills theory. The effective parameters in these theories are determined through matching calculations. HTL is based on resummation of hard thermal loops and uses effective propagators and vertex functions. We will also discuss the determination of the pressure of QCD perturbatively. In general, this thesis details calculations and the methodology.

(2019)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.

(2021)Matrix product states provide an efficient parametrisation of lowentanglement manybody quantum states. In this thesis, the underlying theory is developed from scratch, requiring only basic notions of quantum mechanics and quantum information theory. A full introduction to matrix product state algebra and matrix product operators is given, culminating in the derivation of the density matrix renormalisation group algorithm. The latter provides a simple variational scheme to determine the ground state of arbitrary onedimensional manybody quantum systems with supreme precision. As an application of matrixproduct state technology, the kernel polynomial method is introduced in detail as a stateofthe art numerical tool to find the spectral function or the dynamical correlator of a given quantum system. This in turn gives access to the elementary excitations of the system, such that the locations of the lowenergy eigenstates can be studied directly in real space. To illustrate those theoretical tools concretely, the ground state energy, the entanglement entropy and the elementary excitations of a simple interface model of a Heisenberg ferromagnet and a Heisenberg antiferromagnet are studied. By changing the location of the model in parameter space, the dependence of the abovementioned quantities on the transverse field and the coupling strength is investigated. Most notably, we find that the entanglement entropy characteristic to the antiferromagnetic ground state stretches across the interface into the ferromagnetic halfchain. The dependence of the physics on the value of the coupling strength is, overall, small, with exception of the appearance of a boundary mode whose eigenenergy grows with the coupling. A comparison with a localised edge field shows however that the boundary mode is a true interaction effect of the two halfchains. Various algorithmic and physics extensions of the present project are discussed, such that the code written as part of this thesis could be turned into a stateoftheart MPS library with managable effort. In particular, an application of the kernel polynomial method to calculate finitetemperature correlators is derived in detail.

(2021)We determine the leading thermal contributions to various selfenergies in finitetemperature and density quantum chromodynamics (QCD). The socalled hard thermal loop (HTL) selfenergies are calculated for the quark and gluon fields at oneloop order and for the photon field at twoloop order using the realtime formulation of thermal field theory. Inmedium screening effects arising at long wavelengths necessitate the reorganization of perturbative series of thermodynamic quantities. Our results may be directly applied in a reorganization called the HTL resummation, which applies an effective theory for the longwavelength modes in the medium. The photonic result provides a partial nexttoleading order correction to the current leadingorder result and can be later extended to pure QCD with the techniques we develop. The thesis is organized as follows. First, by considering a complex scalar field, we review the main aspects of the equilibrium realtime formalism to build a solid foundation for our thermal field theoretic calculations. Then, these concepts are generalized to QCD, and the properties of the QCD selfenergies are thoroughly studied. We discuss the longwavelength collective behavior of thermal QCD and introduce the HTL theory, outlining also the main motivations for our calculations. The explicit computations of selfenergies are presented in extensive detail to highlight the computational techniques we employ.

(2021)We begin by discussing the essential concepts within the standard cosmology where the dark matter is "cold" and collisionless. We consider the structure formation in the dark matter component and present problems faced by the standard cosmology as well as some prospects for the solutions to those. The main problem considered in this work is the tension in the value of the Hubble constant measured with different procedures. We present the theories behind the procedures, and conclude the study of the tension by considering the most notable interpretations for the reason behind it. We then set up a proposal for an alternative model describing the dark sector. It is a hidden copy of the visible sector electromagnetism, allowing for a radiative cooling in virializing structures. By assuming first an asymmetric particle content, we study which scales of the dark matter halos are eligible to collapse into dense structure. Acquiring a mass function then allows to conclude how much from the total dark matter component is expected to collapse. If instead the dark matter particle content is taken to be symmetric, the collapsed fraction is assumed to annihilate into dark radiation. With certain modifications to the freely available Boltzmann code CAMB, we construct to the code a representation of the cosmology defined by our model. Lastly we use the modified cosmology to create a fit to the data defining the Hubble constant, and see for the relief of the tension. We find that our model provides a reasonable history for the energy content of the universe, and a notable relief to the Hubble tension, although the improvement is only a minor one compared to some more modest modifications to the cosmology.

(2022)This thesis reviews stateoftheart topdown holographic methods used for modeling dense matter in neutron stars. This is done with the help of the WittenSakaiSugimoto (WSS) model, which attempts to construct a holographic version of quantum chromodynamics (QCD) to mimic its features. As a starting chapter, string theory is reviewed in a quick fashion for the reader to understand some of the (historical) developments behind this construction. Bosonic and superstrings are reviewed along conformal field theory, and focus is put on Dpbranes and compactifications of spacetime. This chapter will also explain much of the jargon used in the thesis, which otherwise easily obstructs the main message. After a sufficient understanding of string theory has been achieved, we will move on to holography and holographic dualities in the next chapter, focusing on AdS/CFT and actual computations using holography. Matching of theories is discussed to set up a holographic dictionary. After this, we need to choose either a topdown or a bottomup approach, from which we will use the former since we are going to use the WSS model. After this comes a brief review of QCD and its central features to be reproduced in holographic QCD. Immediately following this, we will review the WittenSakaiSugimoto model, which is qualitatively and sometimes also quantitatively a reasonable holographic version of QCD. We will discuss WSS’s successes and room for improvement, especially in places that might affect the analysis that we are about to perform on neutron stars. Finally, after all this theoretical development, we will delve into the world of neutron stars. A quick review of the basic features and astrophysical constraints of neutron stars, along with difficulties in modeling them, is given. After this, we will discuss two models of neutron stars, the first one being a toy model with simplified physics and the other a more realistic one. The basic workflow that is required to get to the equation of state data and other relevant observables from a string theoretic action is given stepbystep, and many recent results using this model are reviewed. In the end, the future of the development of the holographic duality, constructing models with it, and modeling of neutron stars is discussed.

(2024)Quantum computers utilize qubits to store and process quantum information. In superconducting quantum computers, qubits are implemented as quantum superconducting resonant circuits. The circuits are operated only at the two energy states, which form the computational basis for the qubit. To suppress leakage to uncomputational states, superconducting qubits are designed to be anharmonic oscillators, which is achieved using one or more Josephson junctions, a nonlinear superconducting element. One of the main challenges in developing quantum computers is minimizing the decoherence caused by environmental noise. Decoherence is characterized by two coherence times, T1 for depolarization processes and T2 for dephasing. This thesis reviews and investigates the decoherence properties of superconducting qubits. The main goal of the thesis is to analyze the tradeoff between anharmonicity and dephasing in a qubit unimon. Recently developed unimon incorporates a single Josephson junction shunted by a linear inductor and a capacitor. Unimon is tunable by external magnetic flux, and at the half flux quantum bias, the Josephson energy is partially canceled by the inductive energy, allowing unimon to have relatively high anharmonicity while remaining fully protected against lowfrequency charge noise. In addition, at the sweet spot with respect to the magnetic flux, unimon becomes immune to firstorder perturbations in the flux. The sweet spot, however, is relatively narrow, making unimon susceptible to dephasing through the quadratic coupling to the flux noise. In the first chapter of this thesis, we present a comprehensive look into the basic theory of superconducting qubits, starting with twostate quantum systems, followed by superconductivity and superconducting circuit elements, and finally combining these two by introducing circuit quantum electrodynamics (cQED), a framework for building superconducting qubits. We follow with a theoretical discussion of decoherence in twostate quantum systems, described by the BlochRedfield formalism. We continue the discussion by estimating decoherence using perturbation theory, with special care put into the dephasing due to the lowfrequency 1/f noise. Finally, we review the theoretical model of unimon, which is used in the numerical analysis. As a main result of this thesis, we suggest a design parameter regime for unimon, which gives the best ratio between anharmonicity and T2.

(2021)Quantum entanglement is one of the biggest mysteries in physics. In gauge field theories, the amount of entanglement can be measured with certain quantities. For an entangled system, there are correlations with these measured quantities in both time and spatial coordinates that do not fit into the understanding we currently hold about the locality of the measures and correlations. Difficulties in obtaining probes for entanglement in gauge theories arise from the problem of nonlocality. It can be stated as the problem of decomposing the space of the physical states into different regions. In this thesis, we focus on a particular supersymmetric YangMills theory that is holographically dual to a classical gravity theory in an asymptotically anti de Sitter spacetime. We introduce the most important holographic probes of entanglement and discuss the inequalities obtained from the dual formulation of the entanglement entropy. We introduce the subregion duality as an interesting conjecture of holography that remains under research. The understanding of the subregion duality is not necessarily solid in arbitrary geometries, as new results that suggest either a violation of the subregion duality or act against our common knowledge of the holography by reconstructing the bulk metric beyond the entanglement wedge. This thesis will investigate this aspect of subregion duality by evaluating the bulk probes such as Wilson loop for two different geometries (deconfining and confining). We aim to find whether or not these probes remain inside of the entanglement wedge. We find that, for both geometries in four dimensions, the subregion duality is not violated. In other words, the reduced CFT state does not encode information about the bulk beyond the entanglement wedge. However, we can not assume this is the case with arbitrary geometries and therefore, this topic will remain under our interest for future research.

(2024)Quantum Chromodynamics (QCD) is the quantum field theory of strong interaction and therefore describes one of the fundamental forces in the universe. Quarks and gluons, together called partons, interact via strong force, and their interactions can be observed in highenergy collisions involving hadrons. Hadrons always contain some composition of quarks. The simplest way to obtain a partonic outgoing state in a collision, is through an electronpositron annihilation that produces a photon, which scatters, forming a combination of partons. Partons, unlike leptons, have properties known as color and flavor. There are six different types of quarks, all of which can be produced in a collision at sufficiently high energies. The energy involved in a hard collision of an electron and a positron is carried through the entire process. Generally, the partons’ binding to each other, known as color confinement, is so strong that they are observed as hadrons. Hadrons are colorneutral, meaning that the colored quarks are arranged such that they result in a colorneutral particle. This thesis focuses on calculating partonic collision outcomes on a small scale using perturbative QCD. At high energies and short distances, quarks are weakly coupled, allowing them to be considered relatively free from partonparton interactions. By comparing the outcomes of electronpositron collisions, namely the electromagnetic and strong force (leptonic and partonic) outcomes, we can receive information on their differences when interacting. By constructing the process of leptonic annihilation, we can observe probabilities of charged particle outcomes that scatter from a photon. Furthermore, we calculate the crosssections of the processes resulting in several partonic configurations. One of the results of this thesis is the ratio between the hadronic and leptonic outcomes stemming from the same initial collision. With partonic outcome crosssection calculated up to nexttoleading order, the ratio exhibits the impact of color factors as well as the running coupling of the partonparton interaction.

(2023)Numerical techniques have become powerful tools for studying quantum systems. Eventually, quantum computers may enable novel ways to perform numerical simulations and conquer problems that arise in classical simulations of highly entangled matter. Simple one dimensional systems of low entanglement are efficiently simulatable on a classical computer using tensor networks. This kind of toy simulations also give us the opportunity to study the methods of quantum simulations, such as different transformation techniques and optimization algorithms that could be beneficial for the near term quantum technologies. In this thesis, we study a theoretical framework for a fermionic quantum simulation and simulate the realtime evolution of particles governed by the GrossNeveu model in onedimension. To simulate the GrossNeveu model classically, we use the Matrix Product State (MPS) method. Starting from the continuum case, we discretise the model by putting it on a lattice and encode the time evolution operator with the help of fermiontoqubit transformations, JordanWigner and BravyiKitaev. The simulation results are visualised as plots of probability density. The results indicate the expected flavour and spatial symmetry of the system. The comparison of the two transformations show better performance of the JordanWigner transformation before and after the gate reduction.

(2020)First order electroweak phase transitions (EWPTs) are an attractive area of research. This is mainly due to two reasons. First, they contain aspects that could help to explain the observed baryon asymmetry. Secondly, strong first order PTs could produce gravitational waves (GWs) that could be detectable by the Laser Interferometer Space Antenna (LISA), a future spacebased GW detector. However, the electroweak PT in the Standard Model (SM) is not a first order transition but a crossover. In socalled beyond the SM theories the first order transitions are possible. To investigate the possibility of an EWPT and the detection by LISA, we must be able to parametrise the nature of the PT accurately. We are interested in the calculation of the bubble nucleation rate because it can be used to estimate the properties of the possible GW signal, such as the duration of the PT. The nucleation rate essentially quantifies how likely it is for a point in space to tunnel from one phase to the other. The calculation can be done either using perturbation theory or simulations. Perturbative approaches however suffer from the socalled infrared problem and are not free of theoretical uncertainty. We need to perform a nonperturbative calculation so that we can determine the nucleation rate accurately and test the results of perturbation theory. In this thesis, we will explain the steps that go into a nonperturbative calculation of the bubble nucleation rate. We perform the calculation on the cubic anisotropy model, a theory with two scalar fields. This toy model is one of the simplest in which a radiatively induced transition occurs. We present preliminary results on the nucleation rate and compare it with the thinwall approximation.

(2024)Astronomical observations suggest that the cores of neutron stars may have high enough baryon densities to contain quark matter (QM). The unavailability of lattice field theory makes perturbative computations important for understanding the thermodynamics of quantum chromodynamics at high baryon densities. The gluon selfenergy contributes to many transport coefficients in QM, such as thermal conductivity and shear viscosity, through quarkquark scattering processes. The contribution of shortwavelength virtual gluons to the selfenergy of soft, longwavelength gluons, known as the hardthermalloop (HTL) selfenergy, was recently computed at nexttoleading order (NLO) in perturbation theory. In this thesis, we complete the evaluation of the NLO selfenergy of soft gluons in cold QM by computing the contribution from soft virtual gluons, known as the oneloop HTLresummed self energy. We use HTL effective theory, a reorganization of the perturbative series for soft gluons, within the imaginarytime formulation of thermal field theory. We present the result in terms of elementary functions and finite integrals that can be evaluated numerically. We show explicitly that the NLO selfenergy is finite and gauge dependent. The NLO selfenergy could be used to compute corrections to transport coefficients in cold QM, which may be relevant for neutronstar applications.

(2022)One of the main ways of physically realizing quantum bits for the purposes of quantum technology is to manufacture them as superconducting circuits. These qubits are artiﬁcially built twolevel systems that act as carriers of quantum information. They come in a variety of types but one of the most common in use is the transmon qubit. The transmon is a more stable, improved version of the earlier types of superconducting qubits with longer coherence times. The qubit cannot function properly on its own, as it needs other circuit elements around it for control and readout of its state. Thus the qubit is only a small part of a larger superconducting circuit interacting with the qubit. Understanding this interaction, where it comes from and how it can be modiﬁed to our liking, allows researchers to design better quantum circuits and to improve the existing ones. Understanding how the noise, travelling through the qubit drive lines to the chip, affects the time evolution of the qubit is especially important. Reducing the amount of noise leads to longer coherence times but it is also possible to engineer the noise to our advantage to uncover novel ways of quantum control. In this thesis the effects of a variable temperature noise source on the qubit drive line is studied. A theoretical model describing the time evolution of the quantum state is built. The model starts from the basic elements of the quantum circuit and leads to a master equation describing the qubit dynamics. This allows us to understand how the different choices made in the manufacturing process of the quantum circuit affect the time evolution. As a proof of concept, the model is solved numerically using QuTiP in the speciﬁc case of a ﬁxedfrequency, dispersive transmon qubit. The solution shows a decohering qubit with no dissipation. The model is also solved in a temperature range 0K < T ≤ 1K to show how the decoherence times behave with respect to the temperature of the noise source.

(2023)One of the main questions in nuclear astrophysics is whether deconfined quark matter exists inside neutron stars. In order to answer this, the equation of state (EoS) of cold and dense quark matter, which plays an essential role in finding the equation of state of strongly interacting matter (QCD matter) inside neutron stars, needs to be determined as accurately as possible [14, 25]. The equation of state, or the pressure, of cold and dense quark matter was evaluated to the full threeloop order in perturbation theory back in 1977 by Freedman and McLerran [9, 10] and recently the contributions of the soft momentum scale to the fourloop pressure were evaluated in [13, 14, 15]. What is missing from the full fourloop pressure is the contribution of the hard momentum scale μ. In this thesis we shall first evaluate the known result for one threeloop Feynman diagram contributing to the threeloop pressure. After this, we derive a new result for a fermionic fourloop master integral at zero temperature and finite quark chemical potentials, which directly contributes to the yet unknown hard sector of the fourloop pressure of cold and dense quark matter.

(2023)Fysikaalisten kenttien rakenteista solmittuja linkkejä ja solmuja on osoitettu esiintyvän useissa eri systeemeissä, optisista ja akustisista kentistä aina supranesteisiin. Tällaisten solmujen evoluutio ideaaleissa systeemeissä rajoittuu perinteisten solmujen, kuten kengännauhoista löytyvien, tyyppiseksi. Fysikaalisissa systeemeissä, joissa energiahäviöt ovat mahdollisia, mahdolliset evoluutiot ovat eksoottisempia; kentässä olevan solmun säikeet  kentän topologisten pyörteiden ytimet  voivat mahdollisesti kokea solmun topologiaa muuttavia evoluutioita ja purkautua erillisiksi solmuttomiksi silmukoiksi. Hyödyntämällä väritettyä linkkidiagrammiesitystä osoitamme yllä mainittuja evoluutioita välttävien topologisesti suojattujen pyörresolmujen olemassaolon spin2 BosenEinsteinin kondensaatin syklisessä faasissa. Nämä ovat ensimmäiset suojatut pyörresolmut, jotka on löydetty fysikaalisesti toteutettavasta systeemistä. Todistuksessa käytetty väritysformalismi on yleinen viitekehys. Sitä voidaan soveltaa useisiin muihin systeemeihin, kunhan näiden järjestysparametriavaruuksien toinen homotopiaryhmä on triviaali. Syklisen faasin pyörresolmut ja linkit mahdollistavat myös osittaisen luokittelun: jokainen solmu on ekvivalentti joukkoon irtonaisia apilasolmuja ja/tai kahdeksikkosolmuja, tai on triviaali. Kokonaislukuaskelin kvantittuneista pyörteistä muodostuvat linkit ovat ekvivalentteja joko Borromeon renkaisiin, suljettuun kolmen silmukan ketjuun tai triviaaliin silmukkaan.
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