Extended relaxation time approximation and relativistic dissipative hydrodynamics

Dash, D.; Bhadury, Samapan; Jaiswal, Sunil; Jaiswal, Amaresh

doi:10.1016/j.physletb.2022.137202

Cited by 20 publications

(9 citation statements)

References 94 publications

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“…The integrals 𝐽 ± 𝑛,𝑞 appearing in the above expressions, and 𝐾 ± 𝑛,𝑞 , 𝑦 ± 𝑛,𝑞 appearing in the expression of coefficients (9) below, can be found in Ref. [4].…”

Section: Dipika Dashmentioning

confidence: 99%

“…The expressions of dimensionless variables C 1 , C 2 and C 3 can be found in Ref. [4]. The coefficients C 1 , C 2 and C 3 vanishes when the relaxation time is particle energy independent, which in turn leads to vanishing of 𝛿𝑢 𝜇 , 𝛿𝑇, and 𝛿𝜇, and the first order viscous correction 𝛿 𝑓 (1) reduces to what is obtained from RTA approximation.…”

Section: Hydrodynamic Frame and Matching Conditionsmentioning

confidence: 99%

“…However, the time scale of collision for any realistic system depends on the microscopic interactions [2,3]. In this proceedings, we extend the Anderson-Witting relaxation-time approximation which allows for particle energydependent relaxation time, and introduce a framework for consistent derivation of relativistic hydrodynamics from the resulting Boltzmann equation [4]. Within this extended RTA framework, we derive the first-order hydrodynamic equations and demonstrate that the modified transport coefficients depends, in some cases rather dramatically, on the energy-dependence of the relaxation time.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Relativistic dissipative hydrodynamics within extended relaxation time approximation

Dash¹,

Bhadury²,

Jaiswal³

et al. 2023

Proceedings of the Tenth Annual Conference on Large Hadron Collider Physics — PoS(LHCP2022)

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The derivation of hydrodynamics from Boltzmann equation in the Anderson-Witting relaxation time approximation assumes the relaxation time to be independent of particle energy, and one is restricted to work in the Landau frame to ensure macroscopic conservation laws. However, the collision time scale typically depends on the microscopic interactions for any realistic system. We present a framework for consistent derivation of relativistic dissipative hydrodynamics from the Boltzmann equation with a particle energy dependent relaxation time by extending the Anderson-Witting relaxation-time approximation, and derive first-order hydrodynamic equations. We show that the obtained transport coefficients have corrections due to the energy dependence of relaxationtime compared to what one obtains from the Anderson-Witting approximation of the collision term, and discuss several interesting scaling features for the ratio of these transport coefficients.

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Section: Dipika Dashmentioning

confidence: 99%

Section: Hydrodynamic Frame and Matching Conditionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Relativistic dissipative hydrodynamics within extended relaxation time approximation

Dash¹,

Bhadury²,

Jaiswal³

et al. 2023

Proceedings of the Tenth Annual Conference on Large Hadron Collider Physics — PoS(LHCP2022)

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show abstract

“…( 1) with (f, q) ↔ ( f , −q) and the collision term under the RTA as C[f, f ]=− k µ uµ τc δ f . 4 The collision term within RTA is constrained by the Landau matching conditions required to satisfy the net-particle four-current and energy-momentum conservations [44,54,56]. These conditions are given by…”

Section: Boltzmann-vlasov Equationmentioning

confidence: 99%

Effects of magnetic field on the evolution of energy density fluctuations

Dave¹,

Pal²

2023

Preprint

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We study the effects of a static and uniform magnetic field on the evolution of energy density fluctuations present in a medium. By numerically solving the relativistic Boltzmann-Vlasov equation within the relaxation time approximation, we explicitly show that magnetic field can affect the characteristics of energy density fluctuations at the timescale the system achieves local thermodynamic equilibrium. A detailed momentum mode analysis of fluctuations reveals that magnetic field increases the damping of mode oscillations, especially for the low momentum modes. This leads to a reduction in the ultraviolet (high momentum) cutoff of fluctuations and also slows down the dissipation of relatively low momentum fluctuation modes. We discuss the phenomenological implications of our study on various sources of fluctuations in relativistic heavy-ion collisions.

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“…Of course, this is not the only possible linear approximation to the collision term, just one of the best known, together with Marle’s [ 81 ]. Over time, other proposals have been advanced, with the goal of allowing for a momentum dependence of the relaxation time [ 45 , 46 , 73 , 82 ] and/or to account for both elastic and inelastic collisions [ 83 ].…”

Section: From Stochastic Kinetic Theory To Stochastic Hydrodynamicsmentioning

confidence: 99%

Field Theory Approaches to Relativistic Hydrodynamics

Mirón-Granese

Kandus

Calzetta

2022

Entropy

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Just as non-relativistic fluids, oftentimes we find relativistic fluids in situations where random fluctuations cannot be ignored, with thermal and turbulent fluctuations being the most relevant examples. Because of the theory’s inherent nonlinearity, fluctuations induce deep and complex changes in the dynamics of the system. The Martin–Siggia–Rose technique is a powerful tool that allows us to translate the original hydrodynamic problem into a quantum field theory one, thus taking advantage of the progress in the treatment of quantum fields out of equilibrium. To demonstrate this technique, we shall consider the thermal fluctuations of the spin two modes of a relativistic fluid, in a theory where hydrodynamics is derived by taking moments of the Boltzmann equation under the relaxation time approximation.

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Extended relaxation time approximation and relativistic dissipative hydrodynamics

Cited by 20 publications

References 94 publications

Relativistic dissipative hydrodynamics within extended relaxation time approximation

Relativistic dissipative hydrodynamics within extended relaxation time approximation

Effects of magnetic field on the evolution of energy density fluctuations

Field Theory Approaches to Relativistic Hydrodynamics

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