arXiv subjects

Dirk H. Rischke

Publications and source records attributed to Dirk H. Rischke.

At least 19 recordsLinked to original sources

arXiv2026

Negative diffusion in the Functional Renormalization Group flow for the Quark-Diquark Model

We investigate the Quark-Diquark Model (QDM) with the Functional Renormalization Group (FRG) in the Local Potential Approximation. In a recent work [arXiv:2510.01066 [hep-ph]], problems were reported in applying this method at low temperatures and large quark chemical potentials, which were attributed to numerical artifacts. In this work, we trace the origin of these problems to the occurrence of a negative diffusion coefficient during the FRG flow of the derivative of the effective potential, leading to strong oscillations of the latter quantity. We show that negative diffusion is a model feature and not a numerical artifact. We propose a regularization scheme which introduces a hyperdiffusion term to remove these oscillations and demonstrate its effectiveness for studies of the phase diagram of the QDM. Regularizing the negative diffusion in the FRG flow is particularly important to reliably study phenomena such as color superconductivity and inhomogeneous phases, which might emerge in the high-density, low-temperature region of the QCD phase diagram.

hep-ph↗

arXiv2026

The $(2+1)$-dimensional Gross-Neveu-Yukawa model at finite temperature, density, and magnetic field within the Functional Renormalization Group

We investigate the phase diagram of the (2+1)-dimensional Gross-Neveu-Yukawa (GNY) model at finite temperature, density, and magnetic field beyond mean-field, using the Functional Renormalization Group (FRG) in the local potential approximation. Large magnetic fields result in magnetic catalysis, a dimensional reduction of the system, and enhancement of chiral symmetry breaking. We employ a hydrodynamical algorithm to solve the FRG flow equation for the effective potential, which allows for go further into the infrared region than with previously used methods. We find that the chiral condensate exhibits non-trivial behavior in various regions of the phase diagram: several first-order phase transitions and de Haas -- van Alphen oscillations at small magnetic field and large chemical potential, as well as a critical endpoint which shifts to higher temperature with increasing magnetic field.

hep-ph↗

arXiv2026

Near-Light-Cone Nonhydrodynamic Structure from Boosted Hydrodynamics

Hydrodynamics provides a universal description of many-body systems at long wavelengths. Its long-lived collective excitations, known as hydrodynamic modes, admit long-wavelength expansions whose convergence is encoded in the analytic structure of retarded correlators of conserved quantities in thermal equilibrium. We show that a boost can change which nonhydrodynamic singularity limits such an expansion. In the large-boost limit, the relevant singularity originates in the large-momentum, near-light-cone region of the rest-frame spectrum. After factoring out the Lorentz-factor growth, the rescaled convergence scale is controlled by the microscopic spectral structure of the theory. We explicitly demonstrate this in two examples: relaxation-time kinetic theory and holography.

hep-th↗

arXiv2026

Vector-Meson Spin Alignment from Anisotropic Quark or Hadron Coalescence

The distribution of particles is highly anisotropic in the initial stage of a heavy-ion collision. In this paper we demonstrate that this anisotropy induces a sizable effect on the spin alignment of vector mesons. We study two different production mechanisms for $ϕ$ and $K^{*0}$ mesons, on one hand the coalescence of quarks and on the other that of pseudoscalar mesons. In the quark-coalescence picture where $ϕ$ and $K^{*0}$ are produced via a bare vector coupling to quarks, a negative $δρ_{00}^y$ of order $10^{-3}$ is observed. In contrast, when $ϕ$ and $K^{*0}$ are produced via quark coalescence with a vertex with spin-orbit coupling, or when they are produced via pseudoscalar-meson coalescence, a positive $δρ_{00}^y$ emerges. In all cases, the magnitude of the spin alignment is directly proportional to the degree of anisotropy. The sign difference between the cases provides a possibility to clarify the production mechanism for vector mesons.

hep-ph↗

arXiv2026

Analysis of regulator and cutoff artifacts in the phase diagram of the quark-meson model

We study regulator and cutoff artifacts in the quark-meson model at finite temperature and quark chemical potential within the functional renormalization-group approach using the local potential approximation. To this end, we discuss the concept of renormalization-group consistency in effective models, which necessitates a nontrivial parameter-fixing procedure to enable a meaningful comparison of results obtained with different regulators and cutoffs. We employ a standard range of cutoff values used in phenomenological studies and regulators that differ significantly in their analytic properties as well as in their classification according to the principle of strongest singularity. We find that regulator and cutoff dependences are small at low temperatures and quark chemical potentials. At high temperatures and low quark chemical potentials, significant cutoff artifacts arise, whereas the properties of the regulator affect the dynamics in the regime governed by a chiral phase transition of first order at low temperatures and high quark chemical potentials.

hep-ph↗

arXiv2025

Hyperon spin correlation in high-energy heavy-ion collisions

Recent experimental data show an unexpectedly large spin alignment of $ϕ$ mesons in high-energy heavy-ion collisions, which can be explained by short-distance fluctuations of strong-force fields (vector $ϕ$ fields) within the constituent-quark model. We calculate the hyperon spin correlations within the same model, taking into account hydrodynamic effects and a $ϕ$ field fluctuating in space-time according to a Gaussian distribution. The $Λ\barΛ$ spin correlation induced by the $ϕ$ field is shown to be negative as opposed to that of $ΛΛ$ or $\barΛ\barΛ$. We thus propose a new net spin-correlation observable as a sensitive probe to separate strong-force effects from hydrodynamic ones. With the strength of the field fluctuations extracted from the observed $ϕ$ spin alignment, we predict the collision-energy dependence of the hyperon spin correlations and also investigate the dependence of the net spin correlation on azimuthal-angle and rapidity difference.

hep-ph↗

arXiv2025

Magnetization by Rotation: Spin and Chiral Condensates in the NJL Model

The role of spin degrees of freedom in the quark-gluon plasma (QGP) has attracted significant interest in recent years. Spin hydrodynamics extends conventional hydrodynamics by incorporating spin via the spin tensor. In the mean-field limit of the Nambu-Jona-Lasinio (NJL) model under rigid rotation, spin degrees of freedom manifest naturally as axial-vector, or spin, condensate. We investigate the interplay between chiral and spin condensates in this framework. While rotation typically suppresses the formation of a chiral condensate, the presence of a spin condensate may counteract this effect, enhancing the chiral condensate. Moreover, it can alter the nature of the chiral transition from second to first order.

nucl-th↗

arXiv2025

Gradient corrections to the local-equilibrium energy-momentum tensor in the Zubarev approach

We compute the expectation value of the energy-momentum tensor of a real scalar field in an approximation which accounts for spacetime gradients of the hydrodynamical variables in local thermodynamical equilibrium. We show that the energy-momentum tensor receives corrections with respect to the standard local-equilibrium result. Notably, the relation between the energy density and pressure, i.e., the equation of state, is modified with respect to the one in global equilibrium. The obtained corrections might be relevant for systems created in relativistic hadron and heavy-ion collisions.

hep-ph↗

arXiv2025

Comparison between Causal and Acausal Diffusion: a Schwinger-Keldysh Effective Field Theory Perspective

In Fick's time-honored theory of diffusion, the system responds instantaneously to external perturbations, resulting in acausal behavior. Maxwell-Cattaneo theory addresses this issue by introducing a relaxation time, rendering the diffusion process causal. We focus on systems where this relaxation time is comparable to the diffusion time and significantly larger than the relaxation times of all other non-conserved operators. In such systems, late-time diffusion is influenced by this relaxation process, leading to a theory of quasi-diffusion. Using the Schwinger-Keldysh Effective Field Theory (SK-EFT) framework, we compare the theories of diffusion and quasi-diffusion by analyzing the real-time dynamics of correlation functions both in linear response and at one-loop order. In particular, we show that the one-loop corrections in the causal (quasi-diffusion) theory, in both the underdamped and the overdamped cases, are governed by two universal functions. In the overdamped case, the behavior mirrors that of the acausal (diffusion) theory, which has recently been applied for precision tests of SK-EFT in diffusive systems. We suggest that our results in the underdamped limit can also be used for precision tests in quasi-diffusive systems.

hep-th↗

arXiv2025

Three-point functions from a Schwinger-Keldysh effective action, resummed in derivatives

The search for the conjectured QCD critical point in heavy-ion collisions requires to account for far-from equilibrium effects as well as fluctuations, and in particular non-Gaussian fluctuations, in the modeling of the dynamics of the hot and dense matter created in such collisions. In order to study far-from equilibrium effects as well as fluctuations, in this work we construct a Schwinger-Keldysh effective field theory (EFT) for the diffusion of the density to all orders in derivatives. The dissipation in the free part of our EFT follows the Boltzmann equation in the relaxation-time approximation (RTA). The interaction part of the EFT is constructed based on the self-interaction of the density field. We analytically find the quadratic and cubic parts of the KMS-invariant EFT in closed form, resummed in derivatives. We then explicitly compute the symmetrized three-point function at tree level, and investigate its analytical structure in detail. We also analytically calculate the branch-point singularity that appears in the structure of the two-point response function due to loop effects. Our results are important for future studies of the real-time dynamics of the correlation functions and the possible relation to thermalization when the system is far from equilibrium.

hep-th↗

arXiv2025

Divergence and resummation of the moment expansion for an ultrarelativistic gas in Bjorken flow

In this letter, we demonstrate for the first time that the moment expansion for an ultrarelativistic gas undergoing Bjorken flow diverges. We then show how this series can be resummed using the Borel-Padé method and use this to determine the single-particle distribution function of the gas. Finally, we compare the exact resummed solution of the single-particle distribution function with solutions of the Boltzmann equation in the hydrodynamic limit and verify that the system displays considerable deviations from local equilibrium.

nucl-th↗

arXiv2025

Damping of spin waves

We show that, in ideal-spin hydrodynamics, the components of the spin tensor follow damped wave equations. The damping rate is related to nonlocal collisions of the particles in the fluid, which enter at first order in $\hbar$ in a semi-classical expansion. This rate provides an estimate for the timescale of spin equilibration and is computed by considering a system of spin-1/2 fermions interacting via a quartic self-interaction as well as via (screened) one-gluon exchange. It is found that the relaxation times of the components of the spin tensor can become very large compared to the usual dissipative timescales of the system. Our results suggest that the spin degrees of freedom in a heavy-ion collision may not be in equilibrium by the time of freeze-out, and thus should be treated dynamically.

nucl-th↗

arXiv2025

Higher-order dissipative anisotropic magnetohydrodynamics from the Boltzmann-Vlasov equation

We apply the method of moments to the relativistic Boltzmann-Vlasov equation and derive the equations of motion for the irreducible moments of arbitrary tensor-rank of the invariant single-particle distribution function. We study two cases, in the first of which the moments are taken to be irreducible with respect to the little group associated with the time-like fluid four-velocity, while in the second case they are assumed to be also irreducible with respect to a space-like four-vector orthogonal to the fluid four-velocity, which breaks the spatial isotropy to a rotational symmetry in the plane transverse to this vector. A systematic truncation and closure of the general moment equations leads, in the first case, to a theory of relativistic higher-order dissipative resistive magnetohydrodynamics. In the second case, we obtain a novel theory of dissipative resistive anisotropic magnetohydrodynamics, where the momentum anisotropy is in principle independent from that introduced by the external magnetic field.

physics.plasm-ph↗

arXiv2024

BHAC-QGP: three-dimensional MHD simulations of relativistic heavy-ion collisions, I. Methods and tests

We present BHAC-QGP, a new numerical code to simulate the evolution of matter created in heavy-ion collisions in the presence of electromagnetic fields. It is derived from the Black Hole Accretion Code (BHAC), which has been designed to model astrophysical processes in a general-relativistic magnetohydrodynamical description. As the original Black Hole Accretion Code, BHAC-QGP benefits from the use of Adaptive Mesh Refinement (AMR), which allows us to dynamically adjust the resolution where necessary, and makes use of time-dependent Milne coordinates and the ultrarelativistic equation of state, $P = e/3$. We demonstrate that BHAC-QGP accurately passes a number of systematic and rigorous tests.

hep-ph↗

arXiv2024

BHAC-QGP: three-dimensional MHD simulations of relativistic heavy-ion collisions, II. Application to Au-Au collisions

We present BHAC-QGP, a new numerical code to simulate the evolution of matter created in heavy-ion collisions. BHAC-QGP is based on the Black Hole Accretion Code (BHAC), which has been designed to model astrophysical processes through the solution of the equations of general-relativistic magnetohydrodynamics. Like the mother code, BHAC-QGP uses Adaptive Mesh Refinement (AMR), which allows for a dynamic adjustment of the resolution in regions of the computational domain where a particularly high accuracy is needed. We here discuss a number of applications of BHAC-QGP to Au-Au collisions at Relativistic Heavy-Ion Collider (RHIC) energies and show that the code is able to reproduce results of other simulations of these scenarios, but with much higher accuracy.

hep-ph↗

arXiv2024

Functional Renormalization Group analysis of the quark-condensation pattern on the Fermi surface: A simple effective-model approach

A simple effective model for the intermediate-density regime is constructed from the high-density effective theory of quantum chromodynamics (QCD). In the effective model, under a renormalization-group (RG) scaling towards low momenta, the original QCD interactions lead to four-quark contact interactions for the relevant quark and hole modes around the Fermi surface. The contact interaction in the scalar channel can be traced back to zero-sound-type collinear quark scattering near the Fermi surface in an instanton background. The quark and hole states in opposite directions of a given Fermi velocity form the collective scalar bosonic mode $σ$. The magnitude of $σ$ is investigated via the non-perturbative Functional Renormalization Group (FRG) evolution of the effective average action from the ultraviolet (UV) to the infrared (IR). In the mean background-field approximation for $σ$, nontrivial minima ($\barσ \neq 0$) are found in the IR limit of the effective average action. A nonvanishing $\barσ$ corresponds to condensation of quark and hole states in opposite directions of a given Fermi velocity, in a thin shell-like structure in momentum space around the Fermi surface. This looks similar to the shell-like baryon distribution in momentum space assumed in the quarkyonic-matter concept. However, when including a dynamic bosonic $σ$-mode in the RG flow, we find that its diffusive nature destroys the quark-hole condensate, i.e., the IR potential does not show any minima beyond the trivial one.

nucl-th↗

arXiv2024

Relativistic second-order dissipative and anisotropic fluid dynamics in the relaxation-time approximation for an ideal gas of massive particles

In this paper, we study all transport coefficients of second-order dissipative fluid dynamics derived by V. E. Ambrus et al. [Phys. Rev. D 106, 076005 (2022)] from the relativistic Boltzmann equation in the relaxation-time approximation for the collision integral. These transport coefficients are computed for a classical ideal gas of massive particles, with and without taking into account the conservation of intrinsic quantum numbers. Through rigorous comparison between kinetic theory, second-order dissipative fluid dynamics, and leading-order anisotropic fluid dynamics for a (0+1)--dimensional boost-invariant flow scenario, we show that both fluid-dynamical theories describe the early far-from-equilibrium stage of the expansion reasonably well.

nucl-th↗

arXiv2024

Linear stability analysis in inhomogeneous equilibrium configurations

We propose a novel method to find local plane-wave solutions of the linearized equations of motion of relativistic hydrodynamics in inhomogeneous equilibrium configurations, i.e., when a fluid in equilibrium is rigidly moving with nonzero thermal vorticity. Our method is based on extending the conserved currents to the tangent bundle, using a type of Wigner transformation. The Wigner-transformed conserved currents can then be Fourier-transformed into the cotangent bundle to obtain the dispersion relations for the space-time dependent eigenfrequencies. We show that the connection between the stability of hydrodynamics and the evolution of plane waves is not as straightforward as in the homogeneous case, namely, it is restricted to the equilibrium-preserving directions in the cotangent bundle. We apply this method to Mueller-Israel-Stewart (MIS) theory and show that the interplay between the bulk viscous pressure and the shear-stress tensor with acceleration and rotation leads to novel modes, as well as modifications of the already known ones. We conclude that, within the domain of applicability, i.e., when boundary effects are negligible and the vorticity is not too large, MIS theory is stable and causal, with the same stability and causality conditions as for homogeneous equilibrium configurations.

physics.flu-dyn↗