arXiv subjects

Mario Mitter

Publications and source records attributed to Mario Mitter.

At least 19 recordsLinked to original sources

arXiv2022

Unsupervised energy disaggregation via convolutional sparse coding

In this work, a method for unsupervised energy disaggregation in private households equipped with smart meters is proposed. This method aims to classify power consumption as active or passive, granting the ability to report on the residents' activity and presence without direct interaction. This lays the foundation for applications like non-intrusive health monitoring of private homes. The proposed method is based on minimizing a suitable energy functional, for which the iPALM (inertial proximal alternating linearized minimization) algorithm is employed, demonstrating that various conditions guaranteeing convergence are satisfied. In order to confirm feasibility of the proposed method, experiments on semi-synthetic test data sets and a comparison to existing, supervised methods are provided.

math.OC↗

arXiv2019

Partial bosonisation for the two-dimensional Hubbard model: How well does it work?

Partial bosonisation of the two-dimensional Hubbard model focuses the functional renormalisation flow on channels in which interactions become strong and local order sets in. We compare the momentum structure of the four-fermion vertex, obtained on the basis of a patching approximation, to an effective bosonic description. For parameters in the antiferromagnetic phase near the onset of local antiferromagnetic order, the interaction of the electrons is indeed well described by the exchange of collective bosonic degrees of freedom. The residual four-fermion vertex after the subtraction of the bosonic exchange contribution is small. We propose that similar partial bosonisation techniques can improve the accuracy of renormalisation flow studies also for the case of competing order.

cond-mat.str-el↗

arXiv2019

Low-energy limit of the O(4) quark-meson model

We study the generation of low-energy couplings induced by quantum fluctuations within the O(4)-symmetric quark-meson model. To this end, we compute the functional renormalization group flow of the linearly realized quark-meson model including higher-derivative interactions and subsequently transform the resulting effective action into a nonlinear effective pion action. The latter is referred to as the low-energy limit of the O(4) quark-meson model. The present study may be considered as a preparatory work for the dynamical generation of low-energy couplings from functional QCD fluctuations in order to determine meaningful renormalization scales for purely pionic models.

hep-ph↗

arXiv2019

Dynamical generation of low-energy couplings from quark-meson fluctuations

We extend our recent computation of the low-energy limit of the linear O(4) Quark-Meson Model. The present analysis focuses on the transformation of the resulting effective action into a nonlinearly realized effective pion action, whose higher-derivative interaction terms are parametrized by so-called low-energy couplings. Their counterparts in the linear model are determined from the Functional Renormalization Group flow of the momentum-dependent four-pion vertex, which is calculated in a fully O(4)-symmetric approximation by including also momentum-dependent {\sigma}{\pi} interactions as well as {\sigma} self-interactions. Consequently, these higher-derivative couplings are dynamically generated solely from quark and meson fluctuations, initialized at a hadronic scale. Despite our restriction to low-energy degrees of freedom, we find that the qualitative features of the fluctuation dynamics allow us to comment on the range of validity and on appropriate renormalization scales for purely pionic effective models.

hep-ph↗

arXiv2018

Bound state properties from the Functional Renormalisation Group

We discuss an approach for accessing bound state properties, like mass and decay width, of a theory within the functional renormalisation group approach. An important cornerstone is the dynamical hadronization technique for resonant interaction channels. The general framework is exemplified and put to work within the two-flavour quark-meson model. This model provides a low-energy description of the dynamics of two-flavour QCD with quark and hadronic degrees of freedom. We compare explicitly the respective results for correlation functions and observables with first principle QCD results in a quantitative manner. This allows us to estimate the validity range of low energy effective models. We also present first results for pole masses and decay widths. Next steps involving real-time formulations of the functional renormalisation group are discussed.

hep-ph↗

arXiv2018

Low-energy limit of the $O(4)$ quark-meson model from the functional renormalization group approach

We compute the low-energy limit of the $O(4)$-symmetric quark-meson model as an effective field theory for Quantum Chromodynamics within the Functional Renormalization Group (FRG) approach. In particular, we analyze the renormalization group flow of momentum-dependent pion self-interactions beyond the local potential approximation. The numerical results for these couplings obtained from the FRG are confronted with a recent tree-level study. Additionally, their effect on the wave-function renormalization and the curvature masses is investigated.

hep-ph↗

arXiv2018

Correlation functions of three-dimensional Yang-Mills theory from the FRG

We compute correlation functions of three-dimensional Landau-gauge Yang-Mills theory with the Functional Renormalisation Group. Starting from the classical action as only input, we calculate the non-perturbative ghost and gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon, and four-gluon vertices in a comprehensive truncation scheme. Compared to the physical case of four spacetime dimensions, we need more sophisticated truncations due to significant contributions from non-classical tensor structures. In particular, we apply a special technique to compute the tadpole diagrams of the propagator equations, which captures also all perturbative two-loop effects, and compare our correlators with lattice and Dyson-Schwinger results.

hep-ph↗

arXiv2017

Non-perturbative finite-temperature Yang-Mills theory

We present non-perturbative correlation functions in Landau-gauge Yang-Mills theory at finite temperature. The results are obtained from the functional renormalisation group within a self-consistent approximation scheme. In particular, we compute the magnetic and electric components of the gluon propagator, and the three- and four-gluon vertices. We also show the ghost propagator and the ghost-gluon vertex at finite temperature. Our results for the propagators are confronted with lattice simulations and our Debye mass is compared to hard thermal loop perturbation theory.

hep-ph↗

arXiv2017

Non-perturbative quark, gluon and meson correlators of unquenched QCD

We present non-perturbative first-principle results for quark-, gluon- and meson $1$PI correlation functions of two-flavour Landau-gauge QCD in the vacuum. These correlation functions carry the full information about the theory. They are obtained by solving their Functional Renormalisation Group equations in a systematic vertex expansion, aiming at apparent convergence. This work represents a crucial prerequisite for quantitative first-principle studies of the QCD phase diagram and the hadron spectrum within this framework. In particular, we have computed the gluon, ghost, quark and scalar-pseudoscalar meson propagators, as well as gluon, ghost-gluon, quark-gluon, quark, quark-meson, and meson interactions. Our results stress the crucial importance of the quantitatively correct running of different vertices in the semi-perturbative regime for describing the phenomena and scales of confinement and spontaneous chiral symmetry breaking without phenomenological input.

hep-ph↗

arXiv2016

FormTracer - A Mathematica Tracing Package Using FORM

We present FormTracer, a high-performance, general purpose, easy-to-use Mathematica tracing package which uses FORM. It supports arbitrary space and spinor dimensions as well as an arbitrary number of simple compact Lie groups. While keeping the usability of the Mathematica interface, it relies on the efficiency of FORM. An additional performance gain is achieved by a decomposition algorithm that avoids redundant traces in the product tensors spaces. FormTracer supports a wide range of syntaxes which endows it with a high flexibility. Mathematica notebooks that automatically install the package and guide the user through performing standard traces in space-time, spinor and gauge-group spaces are provided.

hep-ph↗

arXiv2016

Landau gauge Yang-Mills correlation functions

We investigate Landau gauge $SU(3)$ Yang-Mills theory in a systematic vertex expansion scheme for the effective action with the functional renormalisation group. Particular focus is put on the dynamical creation of the gluon mass gap at non-perturbative momenta and the consistent treatment of quadratic divergences. The non-perturbative ghost and transverse gluon propagators as well as the momentum-dependent ghost-gluon, three-gluon and four-gluon vertices are calculated self-consistently with the classical action as only input. The apparent convergence of the expansion scheme is discussed and within the errors, our numerical results are in quantitative agreement with available lattice results.

hep-ph↗

arXiv2015

Pion and $\eta$-meson mass splitting at the two-flavour chiral crossover

We study the splitting in the screening mass of pions and the $\eta$-meson across the chiral crossover. This splitting is determined by the 't Hooft determinant. We use results for the renormalisation group scale dependence of the 't Hooft determinant obtained within the functional renomalisation group in quenched QCD with two flavours. The scale dependence of the 't Hooft determinant is mapped to its temperature dependence with the help of a Polyakov-quark-meson model. As a result we obtain the temperature dependence of the splitting in the screening mass of pions and the $\eta$-meson.

hep-ph↗

arXiv2014

Chiral symmetry breaking in continuum QCD

We present a quantitative analysis of chiral symmetry breaking in two-flavour continuum QCD in the quenched limit. The theory is set-up at perturbative momenta, where asymptotic freedom leads to precise results. The evolution of QCD towards the hadronic phase is achieved by means of dynamical hadronisation in the non-perturbative functional renormalisation group approach. We use a vertex expansion scheme based on gauge-invariant operators and discuss its convergence properties and the remaining systematic errors. In particular we present results for the quark propagator, the full tensor structure and momentum dependence of the quark-gluon vertex, and the four-fermi scatterings.

hep-ph↗

arXiv2014

On propagators and vertices of Landau gauge Yang-Mills theory

We calculate the three-point functions of pure Landau gauge QCD and investigate their influence on the propagators. As expected, the ghost-gluon vertex leads only to minor modifications, while the three-gluon vertex has a sizeable impact on the mid-momentum regime of the gluon propagator. We describe an effective model of the three-gluon vertex that includes contributions from the neglected two-loop diagrams and thus allows to obtain propagators in good agreement with lattice results. We also determine the three-gluon vertex from these propagators and find good agreement with lattice results as well. In turn, these results allow us to assess the effect of the missing two-loop diagrams in the gluon propagator equation. Finally, we present the first self-consistent calculation that includes all two-and three-point functions.

hep-ph↗

arXiv2014

Exploring the Phase Structure and Thermodynamics of QCD

We put forward a Polyakov-loop extended quark meson model, where matter as well as glue fluctuations are taken into account, cf. [1]. The latter are included via a Polyakov-loop potential. Usually such a glue potential is based on Yang-Mills lattice data only. We show that a parametrisation of unquenching effects as proposed in [2], together with the inclusion of fluctuations via the functional renormalisation group [3,4], accounts for the relevant dynamics. This is demonstrated by a comparison of order parameters and thermodynamic observables to recent lattice results at vanishing chemical potential, where we find very good agreement.

hep-ph↗

arXiv2014

Gluonic three-point correlations in pure Landau gauge QCD

We report on the first self-consistent solution of the Dyson-Schwinger equation (DSE) for the three-gluon vertex. Based on earlier results for the propagators which match data from lattice Monte-Carlo simulations, we obtain results for the three-gluon vertex that are in very good agreement with available lattice data likewise. Feeding these results back into the propagator DSEs leads to some changes especially in the gluon propagator. These changes allow us to assess previously used models for the three-gluon vertex and to systematically estimate the influence of neglected two-loop diagrams with four-gluon interactions. In the final step, a full iterative solution to the coupled DSEs of pure Landau gauge QCD without quarks is then obtained for the first time in an extended truncation which now dynamically includes the complete set of three-point vertex functions.

hep-ph↗

arXiv2013

Three-flavor chiral phase transition and axial symmetry breaking with the functional renormalization group

The interplay of mesonic fluctuations with an axial $U(1)_A$-symmetry breaking and resulting effects on the location of a possibly existing critical endpoint in the QCD phase diagram are investigated in a framework of the functional renormalization group within a $N_f = 2 + 1$ flavor quark-meson model truncation. The axial $U(1)_A$-symmetry breaking is imposed by a mesonic Kobayashi-Maskawa-'t Hooft determinant. The quark mass sensitivity of the chiral phase transition with and without the $U(1)_A$-symmetry breaking is studied.

hep-ph↗

arXiv2013

Thermodynamics of QCD at vanishing density

We study the phase structure of QCD at finite temperature within a Polyakov-loop enhanced quark-meson model. Such a model describes the chiral as well as the confinement-deconfinement dynamics. In the present investigation, based on the approach and results put forward in [1-4], both, matter as well as glue fluctuations are included. We present results for the order parameters as well as some thermodynamic observables and find very good agreement with recent results from lattice QCD.

hep-ph↗