arXiv subjects

Victor E. Ambrus

Publications and source records attributed to Victor E. Ambrus.

At least 37 records · Page 2Linked to original sources

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

Spin waves in spin hydrodynamics

The propagation properties of spin degrees of freedom are analyzed in the framework of relativistic hydrodynamics with spin based on the de Groot--van Leeuwen--van Weert definitions of the energy-momentum and spin tensors. We derive the analytical expression for the spin wave velocity for arbitrary statistics and show that it goes to half the speed of light in the ultra-relativistic limit. We find that only the transverse degrees of freedom propagate, analogously to electromagnetic waves. Finally, we consider the effect of dissipative corrections and calculate the damping coefficients for the case of Maxwell-Jüttner statistics.

hep-ph↗

arXiv2022

Development of transverse flow for small and large systems in conformal kinetic theory

We employ an effective kinetic description to study the space-time dynamics and development of transverse flow of small and large collision systems. By combining analytical insights in the few interactions limit with numerical simulations at higher opacity, we are able to describe the development of transverse flow from very small to very large opacities, realised in small and large collision systems. Surpisingly, we find that deviations between kinetic theory and hydrodynamics persist even in the limit of very large interaction rates, which can be attributed to the presence of the early pre-equilibrium phase.

hep-ph↗

arXiv2022

Vortical Effects for Free Fermions on Anti-De Sitter Space-Time

Here, we study a quantum fermion field in rigid rotation at finite temperature on anti-de Sitter space. We assume that the rotation rate $Ω$ is smaller than the inverse radius of curvature $\ell ^{-1}$, so that there is no speed of light surface and the static (maximally-symmetric) and rotating vacua coincide. This assumption enables us to follow a geometric approach employing a closed-form expression for the vacuum two-point function, which can then be used to compute thermal expectation values (t.e.v.s). In the high temperature regime, we find a perfect analogy with known results on Minkowski space-time, uncovering curvature effects in the form of extra terms involving the Ricci scalar $R$. The axial vortical effect is validated and the axial flux through two-dimensional slices is found to escape to infinity for massless fermions, while for massive fermions, it is completely converted into the pseudoscalar density $-i {\bar ψ} γ^5 ψ$. Finally, we discuss volumetric properties such as the total scalar condensate and the total energy within the space-time and show that they diverge as $[1 - \ell^2 Ω^2]^{-1}$ in the limit $Ω\rightarrow \ell ^{-1}$.

hep-th↗

arXiv2021

Bjorken flow attractors with transverse dynamics

In the context of the longitudinally boost-invariant Bjorken flow with transverse expansion, we use three different numerical methods to analyze the emergence of attractor solutions in an ideal gas of massless particles exhibiting constant shear viscosity to entropy density ratio $η/ s$. The fluid energy density is initialized using a Gaussian profile in the transverse plane, while the ratio $χ= \mathcal{P}_L / \mathcal{P}_T$ between the longitudinal and transverse pressures is set at initial time $τ_0$ to a constant value $χ_0$ throughout the system employing the Romatschke-Strickland distribution. We introduce the hydrodynamization time $δτ_H = (τ_H - τ_0)/ τ_0$ based on the time $τ_H$ when the standard deviation $σ(χ)$ of a family of solutions with different $χ_0$ reaches a minimum value at the point of maximum convergence of the solutions. In the $0+1{\rm D}$ setup, $δτ_H$ exhibits scale invariance, being a function only of $(η/ s) / (τ_0 T_0)$. With transverse expansion, we find a similar $δτ_H$ computed with respect to the local initial temperature, $T_0(r)$. We highlight the transition between the regimes where the longitudinal and transverse expansions dominate. We find that the hydrodynamization time required for the attractor solution to be reached increases with the distance from the origin, as expected based on the properties of the $0+1{\rm D}$ system defined by the local initial conditions. We argue that hydrodynamization is predominantly the effect of the longitudinal expansion, being significantly influenced by the transverse dynamics only for small systems or for large values of $η/ s$.

nucl-th↗

arXiv2021

Development of transverse flow at small and large opacities in conformal kinetic theory

We employ an effective kinetic description, based on the Boltzmann equation in the relaxation time approximation, to study the space-time dynamics and development of transverse flow of small and large collision systems. By combining analytical insights in the small opacity limit with numerical simulations at larger opacities, we are able to describe the development of transverse flow from very small to very large opacities. Suprisingly, we find that deviations between kinetic theory and hydrodynamics persist even in the limit of very large opacities, which can be attributed to the presence of the early pre-equilibrium phase.

hep-ph↗

arXiv2021

Exact solutions in quantum field theory under rotation

We discuss the construction and properties of rigidly-rotating states for free scalar and fermion fields in quantum field theory. On unbounded Minkowski space-time, we explain why such states do not exist for scalars. For the Dirac field, we are able to construct rotating vacuum and thermal states, for which expectation values can be computed exactly in the massless case. We compare these quantum expectation values with the corresponding quantities derived in relativistic kinetic theory.

hep-th↗

arXiv2020

Hyperon--anti-hyperon polarization asymmetry in relativistic heavy-ion collisions as an interplay between chiral and helical vortical effects

We argue that the enhancement in the spin polarization of anti-hyperons compared to the polarization of the hyperons in noncentral relativistic heavy-ion collisions arises as a result of an interplay between the chiral and helical vortical effects. The chiral vortical effect generates the axial current of quarks along the vorticity axis while the recently found helical vortical effect generates the helicity flow -- the projection of the quark's polarization vector onto its momentum -- along the same axis. For massless fermions, the helical charge corresponds to a difference in the contributions of particles and anti-particles to the axial charge. Assuming that the spin of light quarks transfers to the strange quarks via the vector kaon states ("the spin-vector dominance"), we are able to describe the ratio of the (anti)hyperon spin polarizations, obtained by the STAR group, without fitting parameters. We also argue that the helical vortical effect dominates over the chiral vortical effect and the chiral magnetic effect in the generation of the electric current.

hep-ph↗

arXiv2020

Helical massive fermions under rotation

The properties of a massive fermion field undergoing rigid rotation at finite temperature and chemical potential are discussed. The polarisation imbalance is taken into account by considering a helicity chemical potential, which is dual to the helicity charge operator. The advantage of the proposed approach is that, as opposed to the axial current, the helicity charge current remains conserved at finite mass. A computation of thermal expectation values of the vector, helicity and axial charge currents, as well as of the fermion condensate and stress-energy tensor is provided. In all cases, analytic constitutive equations are derived for the non-equilibrium transport terms, as well as for the quantum corrections to the equilibrium terms (which are derived using an effective relativistic kinetic theory model for fermions with helicity imbalance) in the limit of small masses. In the context of the parameters which are relevant to relativistic heavy ion collisions, the expressions derived in the massless limit are shown to remain valid for masses up to the thermal energy, except for the axial charge conductivity in the azimuthal direction, which presents strong variations with the particle mass.

nucl-th↗

arXiv2020

Comparison of the Shakhov and ellipsoidal models for the Boltzmann equation and DSMC for ab initio-based particle interactions

In this paper, we consider the capabilities of the Boltzmann equation with the Shakhov and ellipsoidal models for the collision term to capture the characteristics of rarefied gas flows. The benchmark is performed by comparing the results obtained using these kinetic model equations with direct simulation Monte Carlo (DSMC) results for particles interacting via ab initio potentials. The analysis is restricted to channel flows between parallel plates and we consider three flow problems, namely: the heat transfer between stationary plates, the Couette flow and the heat transfer under shear. The simulations are performed in the non-linear regime for the 3He, 4He, and Ne gases. The reference temperature ranges between 1 K and 3000 K for 3He and 4He and between 20 K and 5000 K for Ne. While good agreement is seen up to the transition regime for the direct phenomena (shear stress, heat flux driven by temperature gradient), the relative errors in the cross phenomena (heat flux perpendicular to the temperature gradient) exceed 10% even in the slip-flow regime. The kinetic model equations are solved using the finite difference lattice Boltzmann algorithm based on half-range Gauss-Hermite quadratures with the third order upwind method used for the implementation of the advection.

physics.comp-ph↗

arXiv2020

Phase diagram of helically imbalanced QCD matter

We discuss the influence of a helicity imbalance on the phase diagram of dense QCD at finite temperature. We argue that the helical chemical potential is a thermodynamically relevant quantity in theories with the mass gap generation. Using the linear sigma model coupled to quarks, we show that the presence of the helical density substantially affects the phase diagram of dense quark matter. A moderate helical density makes the chiral phase transition softer while shifting the critical endpoint towards lower temperatures and higher baryon chemical potentials. As the helical density increases, the segment of the first-order transition disappears, and the chiral transition becomes a soft crossover. At even higher helical chemical potentials, the first-order transition reappears again at the zero-density finite-temperature transition and extends into the interior of the phase diagram. This evolution of the chiral transition reflects the existence of a thermodynamic duality between helical and vector (baryonic) chemical potentials. We also show that the presence of the helicity imbalance of quark matter increases the curvature of the chiral pseudocritical line in QCD.

hep-th↗

arXiv2019

Fermion condensation under rotation on anti-de Sitter space

Due to the local curvature, the fermion condensate (FC) for a free Dirac field on anti-de Sitter (adS) space becomes finite, even in the massless limit. Employing the point splitting method using an exact expression for the Feynman two-point function, an experssion for the local FC is derived. Integrating this expression, we report the total FC in the adS volume and on its boundary.

hep-th↗

arXiv2019

Implicit-Explicit Finite-Difference Lattice Boltzmann Model with Varying Adiabatic Index

The perfect fluid limit can be obtained from the Boltzmann equation in the limit of vanishing Knudsen number. By treating the collision term in an implicit manner, the implicit-explicit (IMEX) time stepping scheme allows this limit to be achieved at finite values of the time step. We consider the 9th order monotonicity-preserving (MP-9) scheme to implement the advection, which is treated explicitly in the IMEX approach. We reduce the computational costs using reduced distribution functions, which also permits the adiabatic index to be varied. We validate the capabilities of our model by considering the propagation of shock waves in one-dimensional and two-dimensional setups.

physics.comp-ph↗

arXiv2019

Comparison between isothermal collision-streaming and finite-difference lattice Boltzmann models

We present here a comparison between collision-streaming and finite-difference lattice Boltzmann (LB) models. This study provides a derivation of useful formulae which help one to properly compare the simulation results obtained with both LB models. We consider three physical problems: the shock wave propagation, the damping of shear waves, and the decay of Taylor-Green vortices, often used as benchmark tests. Despite the different mathematical and computational complexity of the two methods, we show how the physical results can be related to obtain relevant quantities.

physics.comp-ph↗

arXiv2019

Lattice Boltzmann models based on the vielbein formalism for the simulation of flows in curvilinear geometries

In this paper, we consider the Boltzmann equation with respect to orthonormal vielbein fields in conservative form. This formalism allows the use of arbitrary coordinate systems to describe the space geometry, as well as of an adapted coordinate system in the momentum space, which is linked to the physical space through the use of vielbeins. Taking advantage of the conservative form, we derive the macroscopic equations in a covariant tensor notation, and show that the hydrodynamic limit can be obtained via the Chapman-Enskog expansion in the Bhatnaghar-Gross-Krook (BGK) approximation for the collision term. We highlight that in this formalism, the component of the momentum which is perpendicular to some curved boundary can be isolated as a separate momentum coordinate, for which the half-range Gauss-Hermite quadrature can be applied. We illustrate the capabilities of this formalism by considering two applications. The first one is the circular Couette flow between rotating coaxial cylinders, for which benchmarking data is available for all degrees of rarefaction, from the hydrodynamic to the ballistic regime. The second application concerns the flow in a gradually expanding channel. We employ finite-difference lattice Boltzmann models based on half-range Gauss-Hermite quadratures for the implementation of diffuse reflection, together with the fifth order WENO and third-order TVD Runge-Kutta numerical methods for the advection and time-stepping, respectively.

physics.flu-dyn↗

arXiv2019

Lattice Boltzmann approach to rarefied gas flows using half-range Gauss-Hermite quadratures: Comparison to DSMC results based on ab initio potentials

In this paper, we employ the lattice Boltzmann method to solve the Boltzmann equation with the Shakhov model for the collision integral in the context of the 3D planar Couette flow. The half-range Gauss-Hermite quadrature is used to account for the wall-induced discontinuity in the distribution function. The lattice Boltzmann simulation results are compared with direct simulation Monte Carlo (DSMC) results for ${}^3{\rm He}$ and ${}^4{\rm He}$ atoms interacting via ab initio potentials, at various values of the rarefaction parameter $δ$, where the temperature of the plates varies from $1\ {\rm K}$ up to $3000\ {\rm K}$. Good agreement is observed between the results obtained using the Shakhov model and the DSMC data at large values of the rarefaction parameter. The agreement deteriorates as the rarefaction parameter is decreased, however we highlight that the relative errors in the non-diagonal component of the shear stress do not exceed $2.5\%$.

physics.comp-ph↗

arXiv2019

Lattice Boltzmann study of the one-dimensional boost-invariant expansion with anisotropic initial conditions

A numerical algorithm for the implementation of anisotropic distributions in the frame of the relativistic Boltzmann equation is presented. The implementation relies on the expansion of the Romatschke-Strickland distribution with respect to orthogonal polynomials, which is evolved using the lattice Boltzmann algorithm. The validation of our proposed scheme is performed in the context of the one-dimensional boost invariant expansion (Bjorken flow) at various values of the ratio $η/ s$ of the shear viscosity to the entropy density. This study is limited to the case of massless particles obeying Maxwell-Jüttner statistics.

nucl-th↗

arXiv2018

Half-range lattice Boltzmann models for the simulation of Couette flow using the Shakhov collision term

The three-dimensional Couette flow between parallel plates is addressed using mixed lattice Boltzmann models which implement the half-range and the full-range Gauss-Hermite quadratures on the Cartesian axes perpendicular and parallel to the walls, respectively. The ability of our models to simulate rarefied flows are validated through comparison against previously reported results obtained using the linearized Boltzmann-BGK equation for values of the Knudsen number (Kn) up to $100$. We find that recovering the non-linear part of the velocity profile (i.e., its deviation from a linear function) at ${\rm Kn} \gtrsim 1$ requires high quadrature orders. We then employ the Shakhov model for the collision term to obtain macroscopic profiles for Maxwell molecules using the standard $μ\sim T^ω$ law, as well as for monatomic Helium and Argon gases, modeled through ab-initio potentials, where the viscosity is recovered using the Sutherland model. We validate our implementation by comparison with DSMC results and find excellent match for all macroscopic quantities for ${\rm Kn} \lesssim 0.1$. At ${\rm Kn} \gtrsim 0.1$, small deviations can be seen in the profiles of the diagonal components of the pressure tensor, the heat flux parallel to the plates, and the velocity profile, as well as in the values of the velocity gradient at the channel center. We attribute these deviations to the limited applicability of the Shakhov collision model for highly out of equilibrium flows.

physics.flu-dyn↗