56 research outputs found
Resolving phase transitions with Discontinuous Galerkin methods
We demonstrate the applicability and advantages of Discontinuous Galerkin
(DG) schemes in the context of the Functional Renormalization Group (FRG). We
investigate the -model in the large limit. It is shown that the flow
equation for the effective potential can be cast into a conservative form. We
discuss results for the Riemann problem, as well as initial conditions leading
to a first and second order phase transition. In particular, we unravel the
mechanism underlying first order phase transitions, based on the formation of a
shock in the derivative of the effective potential.Comment: 19 pages, 9 figures, corrected typos, updated references, extended
explanation
Towards the spectral properties and phase structure of QCD
In this thesis we explore a multitude of aspects concerning strongly coupled quantum field theories, with a special focus on QCD. The first part of the thesis is concerned with formal developments, with the noteworthy highlight of enabling the use of hydrodynamic numerical methods in Functional Renormalization Group equations. This lead to the subsequent discovery of discontinuous solutions for the effective potential in the vicinity of first order phase transitions
Dissipation dynamics of a scalar field
We investigate the dissipation rate of a scalar field in the vicinity of the
phase transition and the ordered phase, specifically within the universality
class of model A. This dissipation rate holds significant physical relevance,
particularly in the context of interpreting effective potentials as inputs for
dynamical transport simulations, such as hydrodynamics. To comprehensively
understand the use of effective potentials and other calculation inputs, such
as the functional renormalization group, we conduct a detailed analysis of
field dependencies. We solve the functional renormalization group equations on
the Schwinger-Keldysh contour to determine the effective potential and
dissipation rate for both finite and infinite volumes. Furthermore, we conduct
a finite-size scaling analysis to calculate the dynamic critical exponent z.
Our extracted value closely matches existing values from the literature
On the complex structure of Yang-Mills theory
We consider the coupled set of spectral Dyson-Schwinger equations in
Yang-Mills theory for ghost and gluon propagators, which gives us access to the
ghost and gluon spectral functions. The set-up is used for a systematic
analytic evaluation of the constraints on generalised spectral representations
in Yang-Mills theory that are most relevant for informed spectral
reconstructions. We also provide numerical results for the coupled set of
spectral functions for a large range of potential mass gaps of the gluon, and
discuss the limitations and extensions of the present work.Comment: 30 pages, 16 figure
On the quark spectral function in QCD
We calculate the spectral function of light quark flavours in 2+1 flavour
vacuum QCD in the isospin-symmetric approximation. We employ spectral
Dyson-Schwinger equations and compute the non-perturbative quark propagator
directly in real-time, using recent spectral reconstruction results from
Gaussian process regression of gluon propagator data in 2+1 flavour lattice
QCD. Our results feature a pole-like peak structure at time-like momenta larger
than the propagator's gapping scale as well as a negative scattering continuum,
which we exploit assuming an analytic pole-tail split during the iterative
solution. The computation is augmented with a general discussion of the impact
of the quark-gluon vertex and the gluon propagator on the analytic structure of
the quark propagator. In particular, we investigate under which conditions the
quark propagator shows unphysical complex poles. Our results offer a wide range
of applications, encompassing the ab-initio calculation of transport as well as
resonance properties in QCD.Comment: 17 pages, 7 figure
Ghost spectral function from the spectral Dyson-Schwinger equation
We compute the ghost spectral function in Yang-Mills theory by solving the
corresponding Dyson-Schwinger equation for a given input gluon spectral
function. The results encompass both scaling and decoupling solutions for the
gluon propagator input. The resulting ghost spectral function displays a
particle peak at vanishing momentum and a negative scattering spectrum, whose
infrared and ultraviolet tails are obtained analytically. The ghost dressing
function is computed in the entire complex plane, and its salient features are
identified and discussed.Comment: 15 pages, 11 figure
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