arXiv subjects

Dirk H. Rischke

Publications and source records attributed to Dirk H. Rischke.

At least 37 records · Page 2Linked to original sources

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↗

arXiv2024

Phenomenology of isospin-symmetry breaking with vector mesons

We study the effect of isospin-symmetry breaking in the framework of the extended Linear Sigma Model (eLSM) in vacuum. In this model, several particles mix with each other at tree level, due to the three non-zero scalar condensates (non-strange, strange, isospin). We resolve these mixings with the help of various field transformations. We compute all possible meson mixings and decay widths at tree level and perform a $χ^2$ fit to PDG data. A very good fit is found if we exclude the (very small $\sim 130$~keV) $ω\to ππ$ decay. We also investigate the violation of Dashen's theorem.

hep-ph↗

arXiv2023

Theories of Relativistic Dissipative Fluid Dynamics

Relativistic dissipative fluid dynamics finds widespread applications in high-energy nuclear physics and astrophysics. However, formulating a causal and stable theory of relativistic dissipative fluid dynamics is far from trivial; efforts to accomplish this reach back more than 50 years. In this review, we give an overview of the field and attempt a comparative assessment of (at least most of) the theories for relativistic dissipative fluid dynamics proposed until today and used in applications.

nucl-th↗

arXiv2023

Reanalysis of critical exponents for the O(N) model via a hydrodynamic approach to the Functional Renormalization Group

We compute the critical exponents of the O(N) model within the Functional Renormalization Group (FRG) approach. We use recent advances which are based on the observation that the FRG flow equation can be put into the form of an advection-diffusion equation. This allows to employ well-tested hydrodynamical algorithms for its solution. In this study we work in the local potential approximation (LPA) for the effective average action and put special emphasis on estimating the various sources of errors. Our results complement previous results for the critical exponents obtained within the FRG approach in LPA. Despite the limitations imposed by restricting the discussion to the LPA, the results compare favorably with those obtained via other methods.

hep-th↗

arXiv2023

General-relativistic hydrodynamics of non-perfect fluids: 3+1 conservative formulation and application to viscous black-hole accretion

We consider the relativistic hydrodynamics of non-perfect fluids with the goal of determining a formulation that is suited for numerical integration in special-relativistic and general-relativistic scenarios. To this end, we review the various formulations of relativistic second-order dissipative hydrodynamics proposed so far and present in detail a particular formulation that is fully general, causal, and can be cast into a 3+1 flux-conservative form, as the one employed in modern numerical-relativity codes. As an example, we employ a variant of this formulation restricted to a relaxation-type equation for the bulk viscosity in the general-relativistic magnetohydrodynamics code $\texttt{BHAC}$. After adopting the formulation for a series of standard and non-standard tests in 1+1-dimensional special-relativistic hydrodynamics, we consider a novel general-relativistic scenario, namely, the stationary, spherically symmetric, viscous accretion onto a black hole. The newly developed solution $-$ which can exhibit even considerable deviations from the inviscid counterpart $-$ can be used as a testbed for numerical codes simulating non-perfect fluids on curved backgrounds.

gr-qc↗

arXiv2023

Charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics

We study charge diffusion in relativistic resistive second-order dissipative magnetohydrodynamics. In this theory, charge diffusion is not simply given by the standard Navier-Stokes form of Ohm's law, but by an evolution equation which ensures causality and stability. This, in turn, leads to transient effects in the charge diffusion current, the nature of which depends on the particular values of the electrical conductivity and the charge-diffusion relaxation time. The ensuing equations of motion are of so-called stiff character, which requires special care when solving them numerically. To this end, we specifically develop an implicit-explicit Runge-Kutta method for solving relativistic resistive second-order dissipative magnetohydrodynamics and subject it to various tests. We then study the system's evolution in a simplified 1+1-dimensional scenario for a heavy-ion collision, where matter and electromagnetic fields are assumed to be transversely homogeneous, and investigate the cases of an initially non-expanding fluid and a fluid initially expanding according to a Bjorken scaling flow. In the latter case, the scale invariance is broken by the ensuing self-consistent dynamics of matter and electromagnetic fields. However, the breaking becomes quantitatively important only if the electromagnetic fields are sufficiently strong. The breaking of scale invariance is larger for smaller values of the conductivity. Aspects of entropy production from charge diffusion currents and stability are also discussed.

nucl-th↗

arXiv2023

Linear stability analysis of Israel-Stewart theory in the case of a nonzero background charge

Linear stability of Israel-Stewart theory in the presence of net-charge diffusion was investigated in [Phys.~Rev.~D 102 (2020) 116009] for the case of a massless, classical gas of noninteracting particles. However, in that work only a vanishing net-charge background was considered. In this work, we extend that study to the case of a nonvanishing background charge. We find that this effectively results in a change of the numeric value of the charge-diffusion coefficient, in a way that when the background charge goes to infinity, this coefficient can become at most four times its value at zero background charge. We also extend the analysis of [Phys.~Rev.~D 102 (2020) 116009] by performing a systematic parameter study in the plane of charge-diffusion coefficient vs.\ the coupling term between shear-stress and net-charge diffusion. In this plane, we identify regions where the solutions remain stable and causal and where they become acausal and/or unstable.

hep-th↗

arXiv2023

Particle Interferometry in a Moat Regime

Dense strongly interacting matter can exhibit regimes with spatial modulations, akin to crystalline phases. In this case particles can have a moat spectrum with minimal energy at nonzero momentum. We show that particle interferometry is a sensitive probe of such a regime in heavy-ion collisions. To this end, we develop a field-theoretical formalism that relates particle spectra to in-medium real-time correlation functions of quantum fields on curved hypersurfaces of spacetime. This is then applied to the study of Bose-Einstein correlations in a moat regime in heavy-ion collisions. The resulting two-particle spectra exhibit peaks at nonzero average pair momentum, in contrast to the two-particle spectra in a normal phase, which peak at zero momentum. These peaks lead to non-trivial structures in the ratio of two-particle correlation functions, which should be experimentally measurable if the resolution in the direction of average pair momentum is sufficiently large. We propose these structures in the correlation-function ratios as clear signature of a moat regime and spatially modulated phases in quantum chromodynamics (QCD).

hep-ph↗

arXiv2022

Lorentz-covariant kinetic theory for massive spin-1/2 particles

We construct a matrix-valued spin-dependent distribution function (MVSD) for massive spin-1/2 fermions and study its properties under Lorentz transformations. Such transformations result in a Wigner rotation in spin space and in a nontrivial matrix-valued shift in space-time, which corresponds to the side jump in the massless case. We express the vector and axial-vector components of the Wigner function in terms of the MVSD and show that they transform in a Lorentz-covariant manner. We then construct a manifestly Lorentz-covariant Boltzmann equation which contains a nonlocal collision term encoding spin-orbit coupling. Finally, we obtain the spin-dependent distribution function in local equilibrium by demanding detailed balance.

nucl-th↗

arXiv2022

Relativistic dissipative spin hydrodynamics from kinetic theory with a nonlocal collision term

We derive relativistic dissipative spin hydrodynamics from kinetic theory featuring a nonlocal collision term using the method of moments. In this framework, the components of the spin tensor are dynamical variables which obey relaxation-type equations. We find that the corresponding relaxation times are determined by the local part of the collision term, while the nonlocal part contributes to the Navier-Stokes terms in these equations of motion. The spin relaxation time scales are comparable to those of the usual dissipative currents. Finally, the Navier-Stokes limit of the Pauli-Lubanski vector receives contributions proportional to the shear tensor of the fluid, which implies that the polarization of hadrons observed in heavy-ion collisions is influenced by dissipative effects.

nucl-th↗

arXiv2022

Lorentz-covariant nonlocal collision term for spin-1/2 particles

We revisit the derivation of the nonlocal collision term in the Boltzmann equation for spin-1/2 particles, using both the Wigner-function approach by de Groot, van Leeuwen, and van Weert, and the Kadanoff-Baym equation in $T$-matrix approximation. Contrary to previous calculations, our results maintain full Lorentz covariance of the nonlocal collision term.

nucl-th↗

arXiv2022

Transport coefficients of second-order relativistic fluid dynamics in the relaxation-time approximation

We derive the transport coefficients of second-order fluid dynamics with $14$ dynamical moments using the method of moments and the Chapman-Enskog method in the relaxation-time approximation for the collision integral of the relativistic Boltzmann equation. Contrary to results previously reported in the literature, we find that the second-order transport coefficients derived using the two methods are in perfect agreement. Furthermore, we show that, unlike in the case of binary hard-sphere interactions, the diffusion-shear coupling coefficients $\ell_{Vπ}$, $λ_{Vπ}$, and $τ_{Vπ}$ actually diverge in some approximations when the expansion order $N_\ell \rightarrow \infty$. Here we show how to circumvent such a problem in multiple ways, recovering the correct transport coefficients of second-order fluid dynamics with $14$ dynamical moments. We also validate our results for the diffusion-shear coupling by comparison to a numerical solution of the Boltzmann equation for the propagation of sound waves in an ultrarelativistic ideal gas.

nucl-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

Multicomponent relativistic dissipative fluid dynamics from the Boltzmann equation

We derive multicomponent relativistic second-order dissipative fluid dynamics from the Boltzmann equations for a reactive mixture of $N_{\text{spec}}$ particle species with $N_q$ intrinsic quantum numbers (e.g. electric charge, baryon number, and strangeness) using the method of moments. We obtain the continuity equations for multiple conserved charges as well as the conservation equations for the total energy and momentum in the single-fluid approximation. These $4+N_q$ conservation laws are closed by deriving the second-order equations of motion for the dissipative quantities in the $(10+4N_q)$-moment approximation. The resulting fluid-dynamical equations are formally similar to those of a single-component system, but feature different thermodynamic relations and transport coefficients. We derive general relations for all transport coefficients and compute them explicitly in the ultrarelativistic limit.

nucl-th↗

arXiv2022

Relativistic second-order dissipative hydrodynamics from Zubarev's non-equilibrium statistical operator

We present a new derivation of relativistic second-order dissipative hydrodynamics for quantum systems using Zubarev's non-equilibrium statistical-operator formalism. This is achieved by a systematic expansion of the energy-momentum tensor and the charge current to second order in deviations from equilibrium. As a concrete example, we obtain the relaxation equations for the shear-stress tensor, the bulk-viscous pressure, and the charge-diffusion currents required to close the set of equations of motion for relativistic second-order dissipative hydrodynamics. We also identify new transport coefficients which describe the relaxation of dissipative processes to second order and express them in terms of equilibrium correlation functions, thus establishing new Kubo-type formulas for second-order transport coefficients.

nucl-th↗

arXiv2021

Spectral representation of the shear viscosity for local scalar QFTs at finite temperature

In local scalar quantum field theories (QFTs) at finite temperature correlation functions are known to satisfy certain non-perturbative constraints, which for two-point functions in particular implies the existence of a generalisation of the standard Källén-Lehmann representation. In this work, we use these constraints in order to derive a spectral representation for the shear viscosity arising from the thermal asymptotic states, $η_{0}$. As an example, we calculate $η_{0}$ in $ϕ^{4}$ theory, establishing its leading behaviour in the small and large coupling regimes.

hep-th↗

arXiv2021

Derivation of the nonlocal collision term in the relativistic Boltzmann equation for massive spin-1/2 particles from quantum field theory

We derive the Boltzmann equation and the collision kernel for massive spin-1/2 particles, using the Wigner-function formalism and employing an expansion in powers of $\hbar$. The phase space is enlarged to include a variable related to the spin degrees of freedom. This allows to reduce the transport equations of the independent components of the Wigner function to one scalar equation. To next-to-leading order in $\hbar$, we find that the collision kernel contains both local and nonlocal terms. We show that off-shell contributions cancel in the Boltzmann equation. Our framework can be used to study spin-polarization phenomena induced by vorticity as recently observed in heavy-ion collisions and in condensed-matter systems.

nucl-th↗

arXiv2021

Generating spin polarization from vorticity through nonlocal collisions

We derive the collision term in the Boltzmann equation using the equation of motion for the Wigner function of massive spin-1/2 particles. To next-to-lowest order in $\hbar$ it contains a nonlocal contribution, which is responsible for the conversion of orbital into spin angular momentum. In a proper choice of pseudo-gauge the antisymmetric part of the energy-momentum tensor arises solely from this nonlocal contribution. We show that the collision term vanishes only in global equilibrium and that the spin potential is then equal to the thermal vorticity. In the nonrelativistic limit, the equations of motion for the energy-momentum and spin tensors reduce to the well-known form for hydrodynamics for micropolar fluids.

hep-ph↗