arXiv subjects

Chandrodoy Chattopadhyay

Publications and source records attributed to Chandrodoy Chattopadhyay.

At least 19 recordsLinked to original sources

arXiv2026

Critical dynamics of the superfluid phase transition in Model F

We describe numerical simulations of the critical dynamics near the superfluid phase transition. The calculations are based on an implementation of a stochastic hydrodynamic theory known as model F in the classification of Hohenberg and Halperin. This theory is expected to describe dynamic scaling near the lambda transition in liquid $^4$He, Bose-Einstein condensation in ultracold atomic gases, and the superfluid transition in the unitary Fermi gas. Our simulation is based on a Metropolis algorithm previously applied to the critical endpoint of the liquid-gas phase transition in ordinary fluids. In the model E truncation of model F we obtain the expected dynamical exponent $z\simeq 3/2$. We observe the emergence of a propagating second sound mode at the phase transition. The second sound diffusivity $D_s$ is consistent with the scaling relation $D_s\sim ξ^{x_κ}$, where $ξ$ is the correlation length and $x_κ=1/2$.

cond-mat.quant-gas↗

arXiv2025

Transport properties of stochastic fluids

We study heat conduction and momentum transport in the context of stochastic fluid dynamics. We consider a fluid described by model H in the classification of Hohenberg and Halperin. We study both non-critical and critical fluids, and we investigate transport properties in two as well as three dimensions. Our results are based on numerical simulations of model H using a Metropolis algorithm, and we employ Kubo relations to extract transport coefficients. We observe the expected logarithmic divergence of the shear viscosity in a two-dimensional non-critical fluid. At a critical point, we find that the transport coefficients exhibit power-law scaling with the system size $L$. The strongest divergence is seen for the thermal conductivity $κ$ in two dimensions. We find $κ\sim L^{x_κ}$ with $x_κ=1.6\pm 0.1$. The divergence is weaker in three dimensions, $x_κ=1.25 \pm 0.3$, and the scaling exponent for the shear viscosity, $x_η$, is significantly smaller than $x_κ$ in both two and three dimensions.

nucl-th↗

arXiv2025

Simulating stochastic fluid dynamics

We present simulations of the real time dynamics of a fluid in the vicinity of a critical endpoint in the phase diagram. The relevant hydrodynamic theory is known as model H, and it is expected to describe the long-distance dynamics of QCD matter in the vicinity of a possible critical endpoint in the QCD phase diagram.

nucl-th↗

arXiv2025

Critical fluid dynamics in two and three dimensions

We describe a numerical method for simulating stochastic fluid dynamics near a critical point in the Ising universality class. This theory is known as model H, and is expected to govern the non-equilibrium dynamics of Quantum Chromodynamics (QCD) near a possible critical endpoint of the phase transition between a hadron liquid and the quark-gluon plasma. The numerical algorithm is based on a Metropolis scheme, and automatically ensures that the distribution function of the hydrodynamic variables in equilibrium is independent of the transport coefficients and only governed by the microscopic free energy. We verify dynamic scaling near the critical point of a two and three-dimensional fluid and extract the associated critical exponent $z$. We find $z\simeq 3$ in three dimensions, and $z\simeq 2$ for a two-dimensional fluid. In a finite system, we observe a crossover between the mean field value $z=4$ and the true critical exponent $z\simeq 3$ ($z \simeq 2$ in $d=2$). This crossover is governed by the values of the correlation length and the renormalized shear viscosity.

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arXiv2024

Simulations of stochastic fluid dynamics near a critical point in the phase diagram

We present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of Quantum Chromodynamics (QCD). We focus on the interaction of shear modes with a conserved scalar density, which is known as model H. We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid. As the correlation length is increased or the viscosity is decreased we observe a cross-over from the dynamical exponent of critical diffusion, $z\simeq 4$, to the expected scaling exponent of model H, $z\simeq 3$. We use our method to investigate time-dependent correlation function of non-Gaussian moments $M^n(t)$ of the order parameter. We find that the relaxation time depends in non-trivial manner on the power $n$.

nucl-th↗

arXiv2023

Far-off-equilibrium early-stage dynamics in high-energy nuclear collisions

We explore the far-off-equilibrium aspects of the (1+1)-dimensional early-stage evolution of a weakly-coupled quark-gluon plasma using kinetic theory and hydrodynamics. For a large set of far-off-equilibrium initial conditions the system exhibits a peculiar phenomenon where its total equilibrium entropy decreases with time. Using a non-equilibrium definition of entropy based on Boltzmann's H-function, we demonstrate how this apparently anomalous behavior is consistent with the second law of thermodynamics. We also use the H-function to formulate `maximum-entropy' hydrodynamics, a far-off-equilibrium macroscopic theory that can describe both free-streaming and near-equilibrium regimes of quark-gluon plasma in a single framework.

nucl-th↗

arXiv2023

Dynamic scaling of order parameter fluctuations in model B

We describe numerical simulations of the stochastic diffusion equation with a conserved charge. We focus on the dynamics in the vicinity of a critical point in the Ising universality class. The model we consider is expected to describe the critical dynamics near a possible QCD critical point if the coupling of the order parameter to the momentum density of the fluid can be neglected. The simulations are performed on a spatial lattice, and the time evolution is performed using a Metropolis algorithm. We determine the dynamical critical exponent $z\simeq 3.972(2)$, which agrees with predictions of the epsilon expansion. We also study non-equilibrium sweeps of the reduced temperature and observe approximate Kibble-Zurek scaling.

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arXiv2023

Fluid dynamics from the Boltzmann equation using a maximum entropy distribution

Using the recently developed ``Maximum Entropy'' (or ``least biased'') distribution function to truncate the moment hierarchy arising from kinetic theory, we formulate a far-from-equilibrium macroscopic theory that provides the possibility of describing both free-streaming and hydrodynamic regimes of heavy-ion collisions within a single framework. Unlike traditional hydrodynamic theories that include viscous corrections to finite order, the present formulation incorporates contributions to all orders in shear and bulk inverse Reynolds numbers, allowing it to handle large dissipative fluxes. By considering flow profiles relevant for heavy-ion collisions (Bjorken and Gubser flows), we demonstrate that the present approach provides excellent agreement with underlying kinetic theory throughout the fluid's evolution and, especially, in far-off-equilibrium regimes where traditional hydrodynamics breaks down.

hep-ph↗

arXiv2022

Far-off-equilibrium expansion trajectories in the QCD phase diagram

We consider the hydrodynamic evolution of a quark-gluon gas with non-zero quark masses and net baryon number in its phase diagram. For far-off-equilibrium initial conditions the expansion trajectories appear to violate simple rules based on the second law of thermodynamics that were previously established for ideal or weakly dissipative fluids. For Bjorken flow we present a detailed analysis within kinetic theory that provides a full microscopic understanding of these macroscopic phenomena and establishes their thermodynamic consistency. We point out that, for certain far-off-equilibrium initial conditions, the well-known phenomenon of "viscous heating" turns into "viscous cooling" where, driven by dissipative effects, the temperature decreases faster than in adiabatic expansion.

hep-ph↗

arXiv2022

Far-from-equilibrium attractor in non-conformal plasmas

We study the far-off-equilibrium dynamics of a Bjorken expanding non-conformal system within kinetic theory and hydrodynamics. We show that, in contrast to the conformal case, neither shear nor bulk viscous pressure relax quickly to a non-equilibrium attractor. In kinetic theory an early-time, far-from-equilibrium attractor exists for the scaled longitudinal pressure, driven by the rapid longitudinal expansion of the medium. Second-order dissipative hydrodynamics fails to accurately describe this attractor, but a modified anisotropic hydrodynamic formulation reproduces it and provides excellent agreement with kinetic theory.

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arXiv2022

Pre-hydrodynamic evolution and its impact on quark-gluon plasma signatures

State-of-the-art hydrodynamic models of heavy-ion collisions have considerable theoretical model uncertainties in the description of the very early pre-hydrodynamic stage. We add a new computational module, K$_\mathrm{T}$Iso, that describes the pre-hydrodynamic evolution kinetically, based on the relativistic Boltzmann equation with collisions treated in the Isotropization Time Approximation. As a novelty, K$_\mathrm{T}$Iso allows for the inclusion and evolution of initial-state momentum anisotropies. To maintain computational efficiency K$_\mathrm{T}$Iso assumes strict longitudinal boost invariance and allows collisions to isotropize only the transverse momenta. We use it to explore the sensitivity of hadronic observables measured in relativistic heavy-ion collisions to initial-state momentum anisotropies and microscopic scattering during the pre-hydrodynamic stage.

nucl-th↗

arXiv2021

On non-conformal kinetic theory and hydrodynamics for Bjorken flow

Using and comparing kinetic theory and second-order Chapman-Enskog hydrodynamics, we study the non-conformal dynamics of a system undergoing Bjorken expansion. We use the concept of `free-streaming fixed lines' for scaled shear and bulk stresses in non-conformal kinetic theory and hydrodynamics, and show that these `fixed lines' behave as early-time attractors and repellors of the evolution. In the conformal limit, the free-streaming fixed lines reduce to the well-known fixed points of conformal Bjorken dynamics. A new fixed point in the free streaming regime is identified which lies at the intersection of these fixed lines. Contrary to the conformal scenario, both kinetic theory and hydrodynamics predict the absence of attractor behavior in the normalised shear stress channel. In kinetic theory a far-off-equilibrium attractor is found for the normalised effective longitudinal pressure, driven by rapid longitudinal expansion. Second-order viscous hydrodynamics fails to accurately describe this attractor. From a thorough analysis of the free-streaming dynamics in Chapman-Enskog hydrodynamics we conclude that this failure results from an inaccurate approximation of the fixed lines and a related incorrect description of the nature of the fixed point. A modified anisotropic hydrodynamic description is presented that provides excellent agreement with kinetic theory results and reproduces the far-from-equilibrium attractor for the scaled longitudinal pressure.

hep-ph↗

arXiv2021

Non-conformal attractor in boost-invariant plasmas

We study the dissipative evolution of (0+1)-dimensionally expanding media with Bjorken symmetry using the Boltzmann equation for massive particles in relaxation-time approximation. Breaking conformal symmetry by a mass induces a non-zero bulk viscous pressure in the medium. It is shown that even a small mass (in units of the local temperature) drastically modifies the well-known attractor for the shear Reynolds number previously observed in massless systems. For generic nonzero particle mass, neither the shear nor the bulk viscous pressure relax quickly to a non-equilibrium attractor; they approach the hydrodynamic limit only late, at small values of the inverse Reynolds numbers. Only the longitudinal pressure, which is a combination of thermal, shear and bulk viscous pressures, continues to show early approach to a far-off-equilibrium attractor, driven by the rapid longitudinal expansion at early times. Second-order dissipative hydrodynamics based on a gradient expansion around locally isotropic thermal equilibrium fails to reproduce this attractor.

nucl-th↗

arXiv2021

Dynamics of QCD Matter -- current status

In this article, there are 18 sections discussing various current topics in the field of relativistic heavy-ion collisions and related phenomena, which will serve as a snapshot of the current state of the art. Section 1 reviews experimental results of some recent light-flavored particle production data from ALICE collaboration. Other sections are mostly theoretical in nature. Very strong but transient magnetic field created in relativistic heavy-ion collisions could have important observational consequences. This has generated a lot of theoretical activity in the last decade. Sections 2, 7, 9, 10 and 11 deal with the effects of the magnetic field on the properties of the QCD matter. There are several unanswered questions about the QCD phase diagram. Sections 3, 11 and 18 discuss various aspects of the QCD phase diagram and phase transitions. Recent years have witnessed interesting developments in foundational aspects of hydrodynamics and their application to heavy-ion collisions. Sections 12, 15, 16 and 17 of this article probe some aspects of this exciting field. Transport coefficients together with their temperature- and density-dependence, are essential inputs in hydrodynamical calculations. Sections 5, 8 and 14 deal with calculation/estimation of various transport coefficients (shear and bulk viscosity, thermal conductivity, relaxation times, etc.) of quark matter and hadronic matter. Sections 4, 6 and 13 deals with interesting new developments in the field. Section 4 discusses color dipole gluon distribution function at small transverse momentum in the form of a series of Bells polynomials. Section 6 discusses the properties of Higgs boson in the quark gluon plasma using Higgs-quark interaction. Section 13 discusses modification of coalescence model to incorporate viscous corrections and application of this model.

hep-ph↗

arXiv2021

Maximum entropy kinetic matching conditions for heavy-ion collisions

Coupling hadronic kinetic theory models to fluid dynamics in phenomenological studies of heavy ion collisions requires a prescription for ``particlization''. Existing particlization models are based on implicit or explicit assumptions about the microscopic degrees of freedom that go beyond the information provided by the preceding fluid dynamical history. We propose an alternative prescription which uses only macroscopic information provided by the hydrodynamic output. This method follows directly from the connections between information theory and statistical mechanics.

hep-ph↗

arXiv2019

Hydrodynamics from free-streaming to thermalization and back again

We study the evolution of the Knudsen and Reynolds numbers in (0+1)-dimensionally expanding fluids with Bjorken symmetry for systems whose microscopic mean free path rises more quickly with time than usually assumed. This allows us to explore within a simple 1-dimensional model the transition from initially thermalizing to ultimately decoupling dynamics. In all cases studied the dynamics is found to be controlled by hydrodynamic attractors for both the Knudsen and Reynolds numbers whose trajectories undergo characteristic changes as the dynamics changes from thermalizing to decoupling.

nucl-th↗

arXiv2019

Exact solutions and attractors of higher-order viscous fluid dynamics for Bjorken flow

We consider causal higher order theories of relativistic viscous hydrodynamics in the limit of one-dimensional boost-invariant expansion and study the associated dynamical attractor. We obtain evolution equations for the inverse Reynolds number as a function of Knudsen number. The solutions of these equations exhibit attractor behavior which we analyze in terms of Lyapunov exponents using several different techniques. We compare the attractors of the second-order Müller-Israel-Stewart (MIS), transient DNMR, and third-order theories with the exact solution of the Boltzmann equation in the relaxation-time approximation. It is shown that for Bjorken flow the third-order theory provides a better approximation to the exact kinetic theory attractor than both MIS and DNMR theories. For three different choices of the time dependence of the shear relaxation rate we find analytical solutions for the energy density and shear stress and use these to study the attractors analytically. By studying these analytical solutions at both small and large Knudsen numbers we characterize and uniquely determine the attractors and Lyapunov exponents. While for small Knudsen numbers the approach to the attractor is exponential, strong power-law decay of deviations from the attractor and rapid loss of initial state memory is found even for large Knudsen numbers. Implications for the applicability of hydrodynamics in far-off-equilibrium situations are discussed.

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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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