arXiv subjects
Publications and source records attributed to Jan M. Pawlowski.
The Polyakov loop potential serves to distinguish between the confined hadronic and the deconfined quark-gluon plasma phases of QCD. For Nf=2+1 quark flavors with physical masses we determine the Polyakov loop potential at finite temperature and density and extract the location of the deconfinement transition. We find a cross-over at small values of the chemical potential running into a critical end-point at mu/T > 1.
We consider a generalized Thirring model in 0+1 dimensions at finite density. In order to deal with the resulting sign problem we employ stochastic quantization, i.e., a complex Langevin evolution. We investigate the convergence properties of this approach and check in which parameter regions complex Langevin evolutions are applicable in this setting. To this end we derive numerous analytical results and compare directly with numerical results. In addition we employ indirect indicators to check for correctness. Finally we interpret and discuss our findings.
We consider a generalization of the Thirring model in 2+1 dimensions at finite density. We employ stochastic quantization and check for the applicability in the finite density case to circumvent the sign problem. To this end we derive analytical results in the heavy dense limit and compare with numerical ones obtained from a complex Langevin evolution. Furthermore we make use of indirect indicators to check for incorrect convergence of the underlying complex Langevin evolution. The method allows the numerical evaluation of observables at arbitrary values of the chemical potential. We evaluate the results and compare to the (0+1)-dimensional case.
We investigate the quark backreaction on the Polyakov loop and its impact on the thermodynamics of quantum chromodynamics. The dynamics of the gluons generating the Polyakov-loop potential is altered by the presence of dynamical quarks. However, this backreaction of the quarks has not yet been taken into account in Polyakov-loop extended model studies. In the present work, we show within a 2+1 flavour Polyakov-quark-meson model that a quark-improved Polyakov-loop potential leads to a smoother transition between the low-temperature hadronic phase and the high-temperature quark-gluon plasma phase. In particular, we discuss the dependence of our results on the remaining uncertainties that are the critical temperature and the parametrisation of the Polyakov-loop potential as well as the mass of the sigma-meson.
We analyse the role of the quark backreaction on the gauge-field dynamics and its impact on the Polyakov-loop potential. Based on our analysis we construct an improved Polyakov-loop potential that can be used in future model studies. In the present work, we employe this improved potential in a study of a 2+1 flavour Polyakov-quark-meson model and show that the temperature dependence of the order parameters and thermodynamics is closer to full QCD. We discuss the results for QCD thermodynamics and outline briefly the dependence of our results on the critical temperature and the parametrisation of the Polyakov-loop potential as well as the mass of the sigma-meson.
The sign problem at nonzero chemical potential prohibits the use of importance sampling in lattice simulations. Since complex Langevin dynamics does not rely on importance sampling, it provides a potential solution. Recently it was shown that complex Langevin dynamics fails in the disordered phase in the case of the three-dimensional XY model, while it appears to work in the entire phase diagram in the case of the three-dimensional SU(3) spin model. Here we analyse this difference and argue that it is due to the presence of the nontrivial Haar measure in the SU(3) case, which has a stabilizing effect on the complexified dynamics. The freedom to modify and stabilize the complex Langevin process is discussed in some detail.
We derive the universal high momentum factorization of the fermion self-energy in the BCS-BEC crossover of ultracold atoms using nonperturbative quantum field theoretical methods. This property is then employed to compute the Tan contact as a function of interaction strength, temperature, chemical potential and Fermi momentum. We clarify the mechanism of the factorization from an analysis of the self-consistent Schwinger-Dyson equation for the fermion propagator, and compute the perturbative contact on the BCS and BEC sides within this framework. A Functional Renormalization Group approach is then put forward, which allows to determine the contact over the whole crossover and, in particular, for the Unitary Fermi gas. We present numerical results from an implementation of the Renormalization Group equations within a basic truncation scheme.
We study quark confinement by computing the Polyakov loop potential in Yang--Mills theory within different non-perturbative functional continuum approaches [1]. We extend previous studies in the formalism of the functional renormalisation group and complement those with findings from Dyson--Schwinger equations and two-particle-irreducible functionals. These methods are formulated in terms of low order Green functions. This allows to identify a criterion for confinement solely in terms of the low-momentum behaviour of correlators.
We present a strategy for estimating the error of truncated functional flow equations. While the basic functional renormalization group equation is exact, approximated solutions by means of truncations do not only depend on the choice of the retained information, but also on the precise definition of the truncation. Therefore, results depend on specification parameters that can be used to quantify the error of a given truncation. We demonstrate this for the BCS-BEC crossover in ultracold atoms. Within a simple truncation the precise definition of the frequency dependence of the truncated propagator affects the results, indicating a shortcoming of the choice of a frequency independent cutoff function.
We compute the Polyakov loop potential in Yang--Mills theory from the fully dressed primitively divergent correlation functions only. This is done in a variety of functional approaches ranging from functional renormalisation group equations over Dyson--Schwinger equations to two-particle irreducible functionals. We present a confinement criterion that links the infrared behaviour of propagators and vertices to the Polyakov loop expectation value. The present work extends the works of [1-3] to general functional methods and sharpens the confinement criterion presented there. The computations are based on the thermal correlation functions in the Landau gauge calculated in [4-6].
The phase diagram of four-dimensional Einstein-Hilbert gravity is studied using Wilson's renormalization group. Smooth trajectories connecting the ultraviolet fixed point at short distances with attractive infrared fixed points at long distances are derived from the non-perturbative graviton propagator. Implications for the asymptotic safety conjecture and further results are discussed.
We give a self-contained introduction to the physics of ultracold atoms using functional integral techniques. Based on a consideration of the relevant length scales, we derive the universal effective low energy Hamiltonian describing ultracold alkali atoms. We then introduce the concept of the effective action, which generalizes the classical action principle to full quantum status and provides an intuitive and versatile tool for practical calculations. This framework is applied to weakly interacting degenerate bosons and fermions in the spatial continuum. In particular, we discuss the related BEC and BCS quantum condensation mechanisms. We then turn to the BCS-BEC crossover, which interpolates between both phenomena, and which is realized experimentally in the vicinity of a Feshbach resonance. For its description, we introduce the Functional Renormalization Group approach. After a general discussion of the method in the cold atoms context, we present a detailed and pedagogical application to the crossover problem. This not only provides the physical mechanism underlying this phenomenon. More generally, it also reveals how the renormalization group can be used as a tool to capture physics at all scales, from few-body scattering on microscopic scales, through the finite temperature phase diagram governed by many-body length scales, up to critical phenomena dictating long distance physics at the phase transition. The presentation aims to equip students at the beginning PhD level with knowledge on key physical phenomena and flexible tools for their description, and should enable to embark upon practical calculations in this field.
We analyze chiral symmetry breaking in quark matter in an external magnetic field at zero and finite temperature and quark chemical potential. We first give a brief overview of analytic results within the mean-field approximation. There the critical temperature for chiral restoration is increased by the magnetic field effect. Then we investigate the effects of matter and quantum fluctuations on the Magnetic Catalysis. More specifically, we compute the critical coupling as a function of the magnetic field and the temperature for zero and finite quark chemical potential in the presence of quantum fluctuations. As soon as a non-zero temperature and/or density is turned on, long-range correlations are screened and the critical coupling is no longer vanishing. We extend our dynamical results beyond the leading-order bubble resummation which results in a non-local four-Fermi coupling. This includes in-medium meson effects on the more quantitative level.
We evaluate the phase diagram of quantum gravity within a fully diffeomorphism-invariant renormalisation group approach. The construction is based on the geometrical or Vilkovisky-DeWitt effective action. We also resolve the difference between the fluctuation metric and the background metric. This allows for fully background-independent flows in gravity. The results provide further evidence for the ultraviolet fixed point scenario in quantum gravity with quantitative changes for the fixed point physics. We also find a stable infrared fixed point related to classical Einstein gravity. Implications and possible extensions are discussed.
The deconfinement phase transition of pure Yang-Mills theory at finite temperature is reflected in the behavior of gauge-fixed gluonic correlation functions. This is one of many examples of how physical information can be extracted from gauge-dependent correlations which is not always obvious. Here, we study the behavior of the Landau-gauge gluon propagator of pure SU(2) across the phase transition in 2+1 and 3+1 dimensions in order to assess to what extend the corresponding critical behavior is reflected in these correlations. We discuss why it should emerge from a continuum perspective and test our expectations in lattice simulations. A comparison with SU(3) furthermore reveals quite clear indications for a sensitivity of the gluon propagator to the order of the transition.
We study the behaviour of Yang-Mills theory under the inclusion of gravity. In the weak- gravity limit, the running gauge coupling receives no contribution from the gravitational sector, if all symmetries are preserved. This holds true with and without cosmological constant. We also show that asymptotic freedom persists in general field-theory-based gravity scenarios including gravitational shielding as well as asymptotically safe gravity.
We study the effect of quantum and thermal fluctuations as well as the mass dependence of the phase structure of QCD at finite temperature and density within a dynamical Polyakov-loop--extended quark-meson model. The glue dynamics is simulated by the Polyakov-loop potential, also including the back-coupling of the matter sector to the glue dynamics. In the chiral limit, the chiral phase transition at large chemical potential and low temperature splits into two transition branches. For non-vanishing pion masses the chiral transition at small chemical potential changes from a phase transition to a crossover. We close with a discussion of a systematical improvement of the current model towards full QCD.
We compute ghost and gluon propagators of Yang-Mills theory in the Landau gauge at non-vanishing temperature within a functional renormalisation group setting. We construct purely thermal flows, that project onto thermal fluctuations only. For temperatures and momenta above the confinement-deconfinement temperature Tc the electric propagator shows a thermal suppression due to Debye screening. The magnetic gluon propagator shows a thermal scaling and tends towards the three-dimensional one. In this region both propagators match the lattice propagators. The thermal scaling is also reflected in the infrared suppression of the ghost-gluon vertex. For temperatures below Tc the electric propagator shows an enhancement which is in qualitative agreement with the lattice behaviour.