arXiv subjects

Farid Taghinavaz

Publications and source records attributed to Farid Taghinavaz.

9 recordsLinked to original sources

arXiv2025

Kinetic Theory of Quasiparticles, Retarded Correlators and Hydrodynamics

Within the relaxation time approximation under a constant mass profile, we investigate the collective dynamics of a system of massive relativistic particles described by the Maxwell-Boltzmann equilibrium distribution. We analytically derive the two-point retarded correlation functions for both charge and energy-momentum tensor components at arbitrary momentum and frequency. We expand our results in the limits of very small and very large mass-to-temperature ratios ($m/T$). Similar to the massless case, we identify a critical threshold in ($k \tau$) below which the correlators permit physical solutions. This behavior arises from a logarithmic branch cut in the spectral function. At higher momenta, solutions emerge significantly below this cut, corresponding to non-hydrodynamic modes. Our analysis demonstrates that hydrodynamic poles dominate in the strong coupling regime, while the weak coupling regime features a logarithmic branch cut extending along $\omega = k$ and $\omega = -k$. Notably, in the sound channel, finite mass modifies the standard propagating sound mode, converting it into a purely imaginary mode. In contrast, the shear channel exhibits modes that asymptotically converge to their massless counterparts. Additionally, we compute the transport coefficients for shear and bulk viscosity, along with higher-order gradient corrections up to third order, expressed as perturbative expansions in both the small and large ($m/T$) regimes.

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arXiv2024

Linearized fluctuating hydrodynamics via random polynomials

We argue that an ensemble of backgrounds best understands hydrodynamic dispersion relations in a medium with few degrees of freedom and is therefore subject to strong thermal fluctuations. In the linearized regime, dispersion relations become describeable by polynomials with random coefficients. We give a short review of this theory and perform a numerical study of the distribution of the roots of polynomials whose coefficients are of the order of a Knudsen series but fluctuate in accordance with canonical fluctuations of temperature. We find that, remarkably, the analytic structure of the poles of fluctuating dispersion relations is very different from deterministic ones, particularly regarding the distribution of imaginary parts with respect to real components. We argue that this provides evidence that hydrodynamic behavior persists, and is enhanced, by non-perturbative background fluctuations.

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arXiv2024

Stability and causality of rest frame modes in second-order spin hydrodynamics

We analyze the low- and high-momentum rest frame modes in the second-order spin hydrodynamics and check the asymptotic causality of the theory. A truncation scheme of the Israel-Stewart formalism derived in our earlier work is proposed that extends the minimal causal formulation. It consists of altogether 40 interconnected relaxation-type dynamical equations -- 16 (24) of them correspond to the independent components of the energy-momentum (spin) tensor. Similarly to previous studies, we find that the stability of the perturbations and asymptotic causality require using the spin equation of state that satisfies the generalized Frenkel condition demanding that the ``electric'' and ``magnetic'' components of the spin density tensor have opposite signs. For low-momentum modes this behavior is similar to that found earlier for the first-order (Navier-Stokes) spin hydrodynamics.

hep-ph↗

arXiv2024

Local univalence versus stability and causality in hydrodynamic models

Our main objective is to compare the analytic properties of hydrodynamic series with the stability and causality conditions applied to hydrodynamic modes. Analyticity, in this context, implies that the hydrodynamic series behaves as a univalent or single-valued function. Stability and causality adhere to physical constraints where hydrodynamic modes neither exhibit exponential growth nor travel faster than the speed of light. Through an examination of various hydrodynamic models, such as the Muller-Israel-Stewart (MIS) and the first-order hydro models like the BDNK (Bemfica-Disconzi-Noronha-Kovtun) model, we observe no new restrictions stemming from the analyticity limits in the shear channel of these models. However, local univalence is maintained in the sound channel of these models despite the global divergence of the hydrodynamic series. Notably, differences in the sound equations between the MIS and BDNK models lead to distinct analyticity limits. The MIS model's sound mode remains univalent at high momenta within a specific transport range. Conversely, in the BDNK model, the univalence of the sound mode extends to intermediate momenta across all stable and causal regions. Generally, the convergence radius is independent of univalence and the given dispersion relation predominantly influences their correlation. For second-order frequency dispersions, the relationship is precise, i.e. within the convergence radius, the hydro series demonstrates univalence. However, with higher-order dispersions, the hydro series is locally univalent within certain transport regions, which may fall within or outside the stable and causal zones.

hep-ph↗

arXiv2021

Critical behaviour of hydrodynamic series

We investigate the time-dependent perturbations of strongly coupled $\mathcal{N} = 4$ SYM theory at finite temperature and finite chemical potential with a second order phase transition. This theory is modelled by a top-down Einstein-Maxwell-dilaton description which is a consistent truncation of the dimensional reduction of type IIB string theory on AdS$_5\times$S$^5$. We focus on spin-1 and spin-2 sectors of perturbations and compute the linearized hydrodynamic transport coefficients up to the third order in gradient expansion. We also determine the radius of convergence of the hydrodynamic mode in spin-1 sector and the lowest non-hydrodynamic modes in spin-2 sector. Analytically, we find that all the hydrodynamic quantities have the same critical exponent near the critical point $θ= 1/2$. Moreover, we establish a relation between symmetry enhancement of the underlying theory and vanishing the only third order hydrodynamic transport coefficient $θ_1$, which appears in the shear dispersion relation of a conformal theory on a flat background.

hep-th↗

arXiv2020

Causality and Stability Conditions of a Conformal Charged Fluid

In this paper, I study the conditions imposed on a normal charged fluid so that the causality and stability criteria hold for this fluid. I adopt the newly developed General Frame (GF) notion in the relativistic hydrodynamics framework which states that hydrodynamic frames have to be fixed after applying the stability and causality conditions. To my purpose, I take a charged conformal matter in the flat and $3+1$ dimension to analyze better these conditions. The causality condition is applied by looking to the asymptotic velocity of sound hydro modes at the large wave number limit and stability conditions are imposed by looking to the imaginary parts of hydro modes as well as the Routh-Hurwitz criteria. By fixing some of the transports, the suitable spaces for other ones are derived. I have observed that in a dense medium with finite $U(1)$ charged chemical potential $μ_0$, negative values for transports appear and the second law of thermodynamics has not ruled out the existence of such values. Sign of scalar transports are not limited by any constraints and just a combination of vector transports is limited by the second law of thermodynamic. Also numerically it is proved that the most favorable region for transports $\tildeγ_{1, 2}$, coefficients of the dissipative terms of the current, is of negative values.

hep-th↗

arXiv2019

Magneto-Transport in a Chiral Fluid from Kinetic Theory

We argue that in order to study the magneto-transport in a relativistic Weyl fluid, it is needed to take into account the associated quantum corrections, namely the side-jump effect, at least to second order. To this end, we impose Lorentz invariance to a system of free Weyl fermions in the presence of the magnetic field and find the second order correction to the energy dispersion. By developing a scheme to compute the integrals in the phase space, we show that the mentioned correction has non-trivial effects on the thermodynamics of the system. Specifically, we predict the form of the negative magnetoresistance in the system from the enthalpy density in equilibrium. Then in analogy with Weyl semimetal, in the framework of the chiral kinetic theory and under the relaxation time approximation, we explicitly compute the magneto-conductivities, at low temperature limit ($T\ll μ$). We show that the conductivities obey the set of Ward identities which follow from the generating functional including the Chern-Simons part.

hep-th↗

arXiv2019

Magneto-transport in an anomalous fluid with weakly broken symmetries, in weak and strong regime

We consider a general system with weakly broken time and translation symmetries. We assume the system also possesses a $U(1)$ symmetry which is not only weakly broken, but is anomalous. We use the second order chiral quasi-hydrodynamics to compute the magneto-conductivities in the system in the presence of a weak magnetic field. Analogous to electrical and thermoelectric conductivities, it turns out that the thermal conductivity is identified with a coefficient which depends on the mixed gauge-gravitational anomaly. By applying our general formulas to a free system of Weyl fermions at low temperature limit $T\ll μ$, we find that our system is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit $T\gg μ$, we consider a strongly coupled $SU(N_c)$ gauge theory with $N_c\gg1$ in the hydrodynamic limit. Its gravity dual is a magnetized charged brane to which, we apply our formulas and compute the conductivities. On the way, we show that analogous to the weak regime, an energy cut-off emerges to regulate the thermodynamic quantities. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of the Son-Surowka.

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arXiv2017

Hydrodynamic Excitations from Chiral Kinetic Theory and the Hydrodynamic Frames

In the framework of chiral kinetic theory (CKT), we consider a system of right- and left-handed Weyl fermions out of thermal equilibrium in a homogeneous weak magnetic field. We show that the Lorentz invariance implies a modification in the definition of the momentum current in the phase space, compared to the case in which the system is in global equilibrium. Using this modified momentum current, we derive the linearized conservation equations from the kinetic equation up to second order in the derivative expansion. It turns out that the eigenmodes of these equations, namely the hydrodynamic modes, differ from those obtained from the hydrodynamic in the Landau-Lifshitz (LL) frame at the same order. We show that the modes of the former case may be transformed to the corresponding modes in the latter case by a global boost. The velocity of the boost is proportional to the magnetic field as well as the difference between the right- and left-handed charges susceptibility. We then compute the chiral transport coefficients in a system of non-Abelian chiral fermions in the no-drag frame and by making the above boost, obtain the well-known transport coeffiecients of the system in the LL frame. Finally by using the idea of boost, we reproduce the AdS/CFT result for the chiral drag force exerted on a quark at rest in the rest frame of the fluid, without performing any holographic computations.

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