arXiv subjects

Subrata Pal

Publications and source records attributed to Subrata Pal.

At least 37 records · Page 2Linked to original sources

arXiv2018

Analytical solutions of causal relativistic hydrodynamic equations for Bjorken and Gubser flows

We obtain general analytical solutions of third-order viscous hydrodynamic equations for Bjorken and Gubser flows in systems with vanishing bulk viscosity and chemical potential, and having a constant shear relaxation time. We also analytically characterize and determine the hydrodynamic attractors for such systems by studying the universal behavior of these solutions at both early and late times. Finally we study the properties of these hydrodynamic attractors for transport coefficients obtained from relativistic kinetic theory in the relaxation-time approximation.

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arXiv2018

Thermalization & hydrodynamics in Bjorken & Gubser flows

The dynamical scaling behavior of hydrodynamic and non-hydrodynamic moments of the distribution function is studied using third-order Chapman-Enskog hydrodynamics and anisotropic hydrodynamics for systems undergoing Bjorken and Gubser expansions, where exact solutions of the Boltzmann equation in Relaxation Time Approximation (RTA) are available for comparison. While dimensionless quantities like normalized shear, pressure anisotropy and normalized entropy show at late times universal scaling relations with small (large) Knudsen number for Bjorken (Gubser) flows, dimensionful quantities like the entropy per unit rapidity do not. Although the two hydrodynamic approximation schemes describe the exact attractors for normalized shear with high accuracy, their description for the normalized entropy is less precise. We attribute this to non-negligible couplings to non-hydrodynamic modes in the entropy evolution.

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arXiv2018

Thermal noise in non-boost-invariant dissipative hydrodynamics

We study the effects of hydrodynamic fluctuations in non-boost-invariant longitudinal expansion of matter formed in relativistic heavy ion collisions. We formulate the theory of thermal noise within second-order viscous hydrodynamics treating noise as a perturbation on top of the non-boost-invariant flow. We develop a numerical simulation model to treat the (1+1)-dimension hydrodynamic evolution. The code is tested to reproduce the analytic results for the Riemann solver for expansion of matter in vacuum. For viscous hydrodynamic expansion, the initial energy density distribution are obtained by reproducing the measured charged hadron rapidity distribution at the RHIC energies. We show that the longitudinal rapidity correlations arising from space-time dependent thermal noise and from an induced thermal perturbation have distinct structures. In general, the rapidity correlations are found to be dominated by temperature fluctuations at small rapidity separation and velocity fluctuations at large rapidities. We demonstrate that thermal noise produce ridge-like two-particle rapidity correlations which persist at moderately large rapidities. The magnitude and pattern of the correlations are quite sensitive to various second-order dissipative formalisms and to the underlying equations of state, especially at large rapidities. The short-range part of the rapidity correlation is found to be somewhat enhanced as compared to that in boost-invariant flow of matter.

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arXiv2018

Effects of initial-state dynamics on collective flow within a coupled transport and viscous hydrodynamic approach

We evaluate the effects of preequilibrium dynamics on observables in ultrarelativistic heavy-ion collisions. We simulate the initial nonequilibrium phase within A MultiPhase Transport (AMPT) model, while the subsequent near-equilibrium evolution is modeled using (2+1)-dimensional relativistic viscous hydrodynamics. We match the two stages of evolution carefully by calculating the full energy-momentum tensor from AMPT and using it as input for the hydrodynamic evolution. We find that when the preequilibrium evolution is taken into account, final-state observables are insensitive to the switching time from AMPT to hydrodynamics. Unlike some earlier treatments of preequilibrium dynamics, we do not find the initial shear viscous tensor to be large. With a shear viscosity to entropy density ratio of $0.12$, our model describes quantitatively a large set of experimental data on Pb+Pb collisions at the Large Hadron Collider(LHC) over a wide range of centrality: differential anisotropic flow $v_n(p_T) ~(n=2-6)$, event-plane correlations, correlation between $v_2$ and $v_3$, and cumulant ratio $v_2\{4\}/v_2\{2\}$.

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arXiv2018

On higher order and anisotropic hydrodynamics for Bjorken and Gubser flows

We study the evolution of hydrodynamic and non-hydrodynamic moments of the distribution function using anisotropic and third-order Chapman-Enskog hydrodynamics for systems undergoing Bjorken and Gubser flows. The hydrodynamic results are compared with the exact solution of the Boltzmann equation with a collision term in relaxation time approximation. While the evolution of the hydrodynamic moments of the distribution function (i.e. of the energy momentum tensor) can be described with high accuracy by both hydrodynamic approximation schemes, their description of the evolution of the entropy of the system is much less precise. We attribute this to large contributions from non-hydrodynamic modes coupling into the entropy evolution which are not well captured by the hydrodynamic approximations. The differences between the exact solution and the hydrodynamic approximations are larger for the third-order Chapman-Enskog hydrodynamics than for anisotropic hydrodynamics, which effectively resums some of the dissipative effects from anisotropic expansion to all orders in the anisotropy, and are larger for Gubser flow than for Bjorken flow. Overall, anisotropic hydrodynamics provides the most precise macroscopic description for these highly anisotropically expanding systems.

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arXiv2018

Radiative heavy quark energy loss in an expanding viscous QCD plasma

We study viscous effects on heavy quark radiative energy loss in a dynamically screened medium with boost-invariant longitudinal expansion. We calculate, to first order in opacity, the energy loss by incorporating viscous corrections in the single-particle phase-space distribution function within relativistic dissipative hydrodynamics. We consider the Grad's 14-moment and the Chapman-Enskog-like methods for the nonequilibrium distribution functions. Our numerical results for the charm quark radiative energy loss show that, as compared to static fluid, an expanding ideal (nonviscous) fluid causes a much smaller energy loss. Viscosity in the evolution lead to somewhat enhanced energy loss which is insensitive to the underlying viscous hydrodynamic models used. Further inclusion of viscous correction induces larger energy loss, the magnitude and pattern of this enhancement crucially depend on the form of viscous corrections used.

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arXiv2017

Thermal noise in a boost-invariant matter expansion in relativistic heavy-ion collisions

We formulate a general theory of thermal fluctuations within causal second-order viscous hydrodynamic evolution of matter formed in relativistic heavy-ion collisions. The fluctuation is treated perturbatively on top of a boost-invariant longitudinal expansion. Numerical simulation of thermal noise is performed for a lattice QCD equation of state and for various second-order dissipative evolution equations. Phenomenological effects of thermal fluctuations on the two-particle rapidity correlations are studied.

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arXiv2016

Nonlinear hydrodynamic response confronts LHC data

Higher order harmonic flow $v_n$ (with $n\ge4$) in heavy-ion collisions can be measured either with respect to their own plane, or with respect to a plane constructed using lower-order harmonics. By assuming that higher flow harmonics are the superposition of medium nonlinear and linear responses to initial anisotropies, we propose a set of nonlinear response coefficients $χ_n$'s, which are independent of initial state by construction. In experiments, $χ_n$'s can be extracted as the ratio between higher order harmonic flow measured in the plane constructed by $v_2$ and $v_3$, and moments of lower order harmonic flow. Simulations with single-shot hydrodynamics and AMPT model lead to results of these nonlinear response coefficients in good agreement with the experimental data at the LHC energy. Predictions for $v_7$ and $v_8$ measured with respect to plane of lower order harmonics are given accordingly.

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arXiv2015

Collective flow in event-by-event partonic transport plus hydrodynamics hybrid approach

Complete evolution of the strongly interacting matter formed in ultrarelativistic heavy-ion collisions is studied within a coupled Boltzmann and relativistic viscous hydrodynamics approach. For the initial nonequilibrium evolution phase, we employ the AMPT model that explicitly includes event-by-event fluctuations in the number and positions of the participating nucleons as well as of the produced partons with subsequent parton transport. The ensuing near-equilibrium evolution of quark-gluon and hadronic matter is modeled within the (2+1)-dimensional viscous hydrodynamics. We probe the role of parton dynamics in generating and maintaining the spatial anisotropy in the preequilibrium phase. Substantial eccentricities epsilon_n are found to be generated in the event-by-event fluctuations in parton production from initial nucleon-nucleon collisions. For ultracentral heavy-ion collisions, the model is able to explain qualitatively the unexpected hierarchy of the harmonic flow coefficients v_n(p_T)(n=2-6) observed at LHC. We find that the results for v_n(p_T) are rather insensitive to the variation (within a range) of the time of switchover from AMPT parton transport to hydrodynamic evolution. The usual Grad and the recently proposed Chapman-Enskog-like (nonequilibrium) single-particle distribution functions are found to give very similar results for v_n(n=2-4). The model describes well both the RHIC and LHC data for v_n(p_T) at various centralities, with a constant shear viscosity to entropy density ratio of 0.08 and 0.12, respectively. The event-by-event distributions of v_{2,3} are in good agreement with the LHC data for midcentral collisions. The linear response relation v_n = k_n epsilon_n is found to be true for n=2,3, except at large values of epsilon_n, where a larger value of k_n is required, suggesting a small admixture of positive nonlinear response even for n=2,3.

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arXiv2015

Principal component analysis of event-by-event fluctuations

We apply principal component analysis to the study of event-by-event fluctuations in relativistic heavy-ion collisions. This method brings out all the information contained in two-particle correlations in a physically transparent way. We present a guide to the method, and apply it to multiplicity fluctuations and anisotropic flow, using ALICE data and simulated events. In particular, we study elliptic and triangular flow fluctuations as a function of transverse momentum and rapidity. This method reveals previously unknown subleading modes in both rapidity and transverse momentum for the momentum distribution as well as elliptic and triangular flows.

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arXiv2015

Relativistic third-order viscous corrections to the entropy four-current from kinetic theory

By employing a Chapman-Enskog like iterative solution of the Boltzmann equation in relaxation-time approximation, we derive a new expression for the entropy four-current up to third order in gradient expansion. We show that unlike second-order and third-order entropy four-current obtained using Grad's method, there is a non-vanishing entropy flux in the present third-order expression. We further quantify the effect of the higher-order entropy density in the case of boost-invariant one-dimensional longitudinal expansion of a system. We demonstrate that the results obtained using third-order evolution equation for shear stress tensor, derived by employing the method of Chapman-Enskog expansion, show better agreement with the exact solution of the Boltzmann equation as well as with the parton cascade BAMPS, as compared to those obtained using the third-order equations from the method of Grad's 14-moment approximation.

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arXiv2015

Characterizing flow fluctuations with moments

We present a complete set of multiparticle correlation observables for ultrarelativistic heavy-ion collisions. These include moments of the distribution of the anisotropic flow in a single harmonic, and also mixed moments, which contain the information on correlations between event planes of different harmonics. We explain how all these moments can be measured using just two symmetric subevents separated by a rapidity gap. This presents a multi-pronged probe of the physics of flow fluctuations. For instance, it allows to test the hypothesis that event-plane correlations are generated by non-linear hydrodynamic response. We illustrate the method with simulations of events in A MultiPhase Transport (AMPT) model.

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arXiv2014

Relativistic viscous hydrodynamics for heavy-ion collisions: A comparison between the Chapman-Enskog and Grad methods

Derivations of relativistic second-order dissipative hydrodynamic equations have relied almost exclusively on the use of Grad's 14-moment approximation to write $f(x,p)$, the nonequilibrium distribution function in the phase space. Here we consider an alternative Chapman-Enskog-like method, which, unlike Grad's, involves a small expansion parameter. We derive an expression for $f(x,p)$ to second order in this parameter. We show analytically that while Grad's method leads to the violation of the experimentally observed $1/\sqrt{m_T}$ scaling of the longitudinal femtoscopic radii, the alternative method does not exhibit such an unphysical behavior. We compare numerical results for hadron transverse-momentum spectra and femtoscopic radii obtained in these two methods, within the one-dimensional scaling expansion scenario. Moreover, we demonstrate a rapid convergence of the Chapman-Enskog-like expansion up to second order. This leads to an expression for $δf(x,p)$ which provides a better alternative to Grad's approximation for hydrodynamic modeling of relativistic heavy-ion collisions.

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arXiv2013

Particle production in relativistic heavy-ion collisions: A consistent hydrodynamic approach

We derive relativistic viscous hydrodynamic equations invoking the generalized second law of thermodynamics for two different forms of the non-equilibrium single-particle distribution function. We find that the relaxation times in these two derivations are identical for shear viscosity but different for bulk viscosity. These equations are used to study thermal dilepton and hadron spectra within longitudinal scaling expansion of the matter formed in relativistic heavy-ion collisions. For consistency, the same non-equilibrium distribution function is used in the particle production prescription as in the derivation of the viscous evolution equations. Appreciable differences are found in the particle production rates corresponding to the two non-equilibrium distribution functions. We emphasize that an inconsistent treatment of the non-equilibrium effects influences the particle production significantly, which may affect the extraction of transport properties of quark-gluon plasma.

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arXiv2013

Event-plane correlators

Correlators between event planes of different harmonics in relativistic heavy-ion collisions have the potential to provide crucial information on the initial state of the matter formed in these collisions. We present a new procedure for analyzing such correlators, which is less demanding in terms of detector acceptance than the one used recently by the ATLAS collaboration to measure various two-plane and three-plane correlators in Pb-Pb collisions at LHC. It can also be used unambiguously for quantitative comparison between theory and data. We use this procedure to carry out realistic simulations within the transport model AMPT. Our theoretical results are in excellent agreement with the ATLAS data, in contrast with previous hydrodynamic calculations which only achieved qualitative agreement. We present predictions for new correlators, in particular four-plane correlators, which can easily be analyzed with our new method.

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arXiv2013

Relativistic hydrodynamics from Boltzmann equation with modified collision term

Generalizing the collision term in the relativistic Boltzmann equation to include nonlocal effects, and using Grad's 14-moment approximation for the single-particle distribution function, we derive evolution equations for the relativistic dissipative fluid dynamics and compare them with the corresponding equations obtained in the standard Israel-Stewart and related approaches. Significance of this generalization on hydrodynamic evolution is demonstrated in the framework of one-dimensional scaling expansion.

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arXiv2013

New relativistic dissipative fluid dynamics from kinetic theory

Starting with the relativistic Boltzmann equation where the collision term is generalized to include nonlocal effects via gradients of the phase-space distribution function, and using Grad's 14-moment approximation for the distribution function, we derive equations for the relativistic dissipative fluid dynamics. We compare them with the corresponding equations obtained in the standard Israel-Stewart and related approaches. Our method generates all the second-order terms that are allowed by symmetry, some of which have been missed by the traditional approaches based on the 14-moment approximation, and the coefficients of other terms are altered. The first-order or Navier-Stokes equations too get modified. Significance of these findings is demonstrated in the framework of one-dimensional scaling expansion of the matter formed in relativistic heavy-ion collisions.

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arXiv2013

Complete relativistic second-order dissipative hydrodynamics from the entropy principle

We present a new derivation of relativistic dissipative hydrodynamic equations, which invokes the second law of thermodynamics for the entropy four-current expressed in terms of the single-particle phase-space distribution function obtained from Grad's 14-moment approximation. This derivation is complete in the sense that all the second-order transport coefficients are uniquely determined within a single theoretical framework. In particular, this removes the long-standing ambiguity in the relaxation time for bulk viscosity thereby eliminating one of the uncertainties in the extraction of the shear viscosity to entropy density ratio from confrontation with the anisotropic flow data in relativistic heavy-ion collisions. We find that in the one-dimensional scaling expansion, these transport coefficients prevent the occurrence of cavitation even for rather large values of the bulk viscosity estimated in lattice QCD.

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