arXiv subjects

Eduardo Grossi

Publications and source records attributed to Eduardo Grossi.

30 records · Page 2Linked to original sources

arXiv2022

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 $O(N)$-model in the large $N$ 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.

hep-th↗

arXiv2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. I. The $O(N)$ model

The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this approach relies on the derivation of so-called flow equations, which describe the change of the quantum effective action under the variation of a coarse-graining parameter. In the present work, we discuss in detail a novel approach to solve such flow equations. This approach relies on the fact that RG equations can be rewritten such that they exhibit similarities with the conservation laws of fluid dynamics. This observation can be exploited in different ways. First of all, we show that this allows to employ powerful numerical techniques developed in the context of fluid dynamics to solve RG equations. In particular, it allows us to reliably treat the emergence of nonanalytic behavior in the RG flow of the effective action as it is expected to occur in studies of, e.g., spontaneous symmetry breaking. Second, the analogy between RG equations and fluid dynamics offers the opportunity to gain novel insights into RG flows and their interpretation in general, including the irreversibility of RG flows. We work out this connection in practice by applying it to zero-dimensional quantum-field theoretical models. The generalization to higher-dimensional models is also discussed. Our findings are expected to help improving future FRG studies of quantum field theories in higher dimensions both on a qualitative and quantitative level.

cond-mat.stat-mech↗

arXiv2022

Numerical fluid dynamics for FRG flow equations: Zero-dimensional QFTs as numerical test cases. II. Entropy production and irreversibility of RG flows

We demonstrate that the reformulation of renormalization group (RG) flow equations as non-linear heat equations has severe implications on the understanding of RG flows in general. We demonstrate by explicitly constructing an entropy function for a zero-dimensional $\mathbb{Z}_2$-symmetric model that the dissipative character of generic non-linear diffusion equations is also hard-coded in the functional RG equation. This renders RG flows manifestly irreversible, revealing the semi-group property of RG transformations on the level of the flow equation itself. Additionally, we argue that the dissipative character of RG flows, its irreversibility and the entropy production during the RG flow may be linked to the existence of a so-called $\mathcal{C}$-/$\mathcal{A}$-function. In total, this introduces an asymmetry in the so-called RG time -- in complete analogy to the thermodynamic arrow of time -- and allows for an interpretation of infrared actions as equilibrium solutions of dissipative RG flows equations. The impossibility of resolving microphysics from macrophysics is evident in this framework. Furthermore, we directly link the irreversibility and the entropy production in RG flows to an explicit numerical entropy production, which is manifest in diffusive and non-linear partial differential equations (PDEs) and a standard mathematical tool for the analysis of PDEs. Using exactly solvable zero-dimensional $\mathbb{Z}_2$-symmetric models, we explicitly compute the (numerical) entropy production related to the total variation non-increasing property of the PDE during RG flows toward the infrared limit. Finally, we discuss generalizations of our findings and relations to the $\mathcal{C}$-/$\mathcal{A}$-theorem as well as how our work may help to construct truncations of RG flow equations in the future, including numerically stable schemes for solving the corresponding PDEs.

cond-mat.stat-mech↗

arXiv2022

Conserved and non-conserved Noether currents from the quantum effective action

The quantum effective action yields equations of motion and correlation functions including all quantum corrections. We discuss here how it encodes also Noether currents at the full quantum level. Interestingly, the construction can be generalized beyond the standard symmetry transformations that leave the action invariant. We also discuss an extended set of transformations, which change the action by a term that is locally known on the level of the quantum effective action. Associated to such extended gauge transformations are currents for which we obtain a divergence-type equation of motion, but they are not conserved. We call them non-conserved Noether currents. We discuss in particular symmetries and extended transformations associated to space-time geometry for relativistic quantum field theories. These encompass local dilatations or Weyl gauge transformation, local Lorentz transformations and local shear transformations. Together they constitute the symmetry group of the frame bundle GL$(d)$. The corresponding non-conserved Noether currents are the dilatation or Weyl current, the spin current and the shear current. In particular for the latter we obtain a new divergence-type equations of motion.

hep-th↗

arXiv2021

Dynamics of the $O(4)$ critical point in QCD

We perform a real-time simulation of the $O(4)$ critical point of QCD, which lies in the dynamic universality class of Model G. The axial charge and the order parameter $ϕ_a =(σ, \vecπ)$ exhibit a rich dynamical interplay, which reflects the qualitative differences in the hydrodynamic effective theories above and below $T_c$. From the axial charge correlators on the critical line we extract a dynamical critical exponent of $ζ=1.47 \pm 0.01 ({\rm stat})$, which is compatible with the theoretical expectation of $ζ= d/2$ (with $d=3$) when systematic errors are taken into account. At low temperatures, we quantitatively match the $O(4)$ simulations to the superfluid effective theory of soft pions.

hep-lat↗

arXiv2021

Shocks and quark-meson scatterings at large density

We discuss the phase structure of the two-flavour quark-meson model including quantum, thermal, density and critical fluctuations with the functional renormalisation group. This study combines two technical advances in the literature, that are also chiefly important for the quantitative access of the phase boundary of QCD at large density or baryon chemical potential. Specifically we allow for the formation and propagation of shocks as well as a fully self-consistent computation of the order parameter potential for chiral symmetry breaking.

hep-ph↗

arXiv2021

Soft pions and transport near the chiral critical point

During the expansion of a heavy ion collision, the system passes close to the $O(4)$ critical point of QCD, and thus the fluctuations of the order parameter $(σ, \vecπ)$ are expected to be enhanced. Our goal is to compute how these enhanced fluctuations modify the transport coefficients of QCD near the pseudo-critical point. We also make a phenomenological estimate for how chiral fluctuations could effect the momentum spectrum of soft pions. We first formulate the appropriate stochastic hydrodynamic equations close to the $O(4)$ critical point. Then, working in mean field, we determine the correlation functions of the stress tensor and the currents which result from this stochastic real time theory, and use these correlation functions to determine the scaling behavior of the transport coefficients. The hydrodynamic theory also describes the propagation of pion waves, fixing the scaling behavior of the dispersion curve of soft pions. We present scaling functions for the shear viscosity and the charge conductivities near the pseudo-critical point, and estimate the absolute magnitude of the critical fluctuations to these parameters and the bulk viscosity. Using the calculated pion dispersion curve, we estimate the expected critical enhancement of soft pion yields, and this estimate provides a plausible explanation for the excess seen in experiment relative to ordinary hydrodynamic computations. Our results motivate further phenomenological and numerical work on the implications of chiral symmetry on real time properties of thermal QCD near the pseudo-critical point.

nucl-th↗

arXiv2020

Model comparison for initial density fluctuations in high energy heavy ion collisions

Four models for the initial conditions of a fluid dynamic description of high energy heavy ion collisions are analysed and compared. We study expectation values and event-by-event fluctuations in the initial transverse energy density profiles from Pb-Pb collisions. Specifically, introducing a Fourier-Bessel mode expansion for fluctuations, we determine expectation values and two-mode correlation functions of the expansion coefficients. The analytically solveable independent point-sources model is compared to an initial state model based on Glauber theory and two models based on the Color Glass Condensate framework. We find that the large wavelength modes of all investigated models show universal properties for central collisions and also discuss to which extent general properties of initial conditions can be understood analytically.

hep-ph↗

arXiv2020

Transport and hydrodynamics in the chiral limit

We analyze the evolution of hydrodynamic fluctuations for QCD matter below $T_c$ in the chiral limit, where the pions (the Goldstone modes) must be treated as additional non-abelian superfluid degrees of freedom, reflecting the broken $SU_L(2) \times SU_R(2)$ symmetry of the theory. In the presence of a finite pion mass $m_π$, the hydrodynamic theory is ordinary hydrodynamics at long distances, and superfluid-like at short distances. The presence of the superfluid degrees of freedom then gives specific contributions to the bulk viscosity, the shear viscosity, and diffusion coefficients of the ordinary theory at long distances which we compute. This determines, in some cases, the leading dependence of the transport parameters of QCD on the pion mass. We analyze the predictions of this computation, as the system approaches the $O(4)$ critical point.

hep-th↗

arXiv2019

Fast resonance decays in nuclear collisions

In the context of ultra-relativistic nuclear collisions, we present a fast method for calculating the final particle spectra after the direct decay of resonances from a Cooper-Frye integral over the freeze-out surface. The method is based on identifying components of the final particle spectrum that transform in an irreducible way under rotations in the fluid-restframe. Corresponding distribution functions can be pre-computed including all resonance decays. Just a few of easily tabulated scalar functions then determine the Lorentz invariant decay spectrum from each space-time point, and simple integrals of these scalar functions over the freeze-out surface determine the final decay products. This by-passes numerically costly event-by-event calculations of the intermediate resonances. The method is of considerable practical use for making realistic data to model comparisons of the identified particle yields and flow harmonics, and for studying the viscous corrections to the freeze-out distribution function.

nucl-th↗

arXiv2018

Fluid dynamics of heavy ion collisions with Mode expansion (FluiduM)

The fluid dynamics of a relativistic fireball with longitudinal and transverse expansion is described using a background-fluctuation splitting. Symmetry representations of azimuthal rotations and longitudinal boosts are used for a classification of initial state configurations and their fluid dynamic propagation in terms of a mode expansion. We develop an accurate and efficient numerical scheme based on the pseudo-spectral method to solve the resulting hyperbolic partial differential equations. Comparison to the analytically known Gubser solution underlines the high accuracy of this technique. We also present first applications of FluiduM to central heavy ion collisions at the LHC energies featuring a realistic thermodynamic equations of state as well as shear and bulk viscous dissipation.

nucl-th↗

arXiv2018

Causality of fluid dynamics for high-energy nuclear collisions

Dissipative relativistic fluid dynamics is not always causal and can favor superluminal signal propagation under certain circumstances. On the other hand, high-energy nuclear collisions have a microscopic description in terms of QCD and are expected to follow the causality principle of special relativity. We discuss under which conditions the fluid evolutions for a radial expansion are hyperbolic and how the properties of the solutions are encoded in the associated characteristic curves. The expansion dynamics is causal in relativistic sense if the characteristic velocities are smaller than the speed of light. We obtain a concrete inequality from this constraint and discuss how it can be violated for certain initial conditions. We argue that causality poses a bound to the applicability of relativistic fluid dynamics. }

nucl-th↗