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Soret and Dufour effects in hot and dense QCD matter

Kamaljeet Singh, Kangkan Goswami, Raghunath Sahoo

TL;DR

This work presents the first-principles study of the Soret and Dufour thermo-diffusion effects in hot and dense QCD matter using the relativistic Boltzmann equation in the relaxation time approximation, incorporating gradients of temperature $T$ and baryon chemical potential $\mu_B$. By employing a quasiparticle model for the QGP and an ideal hadron resonance gas for the hadronic phase, the authors derive explicit kinetic-theory expressions for the diffusion coefficient $D$, the Soret coefficient $S_T$, the Dufour coefficient $D_F$, and the thermal conductivity $\kappa$, capturing the coupled transport of heat and baryon current. The results reveal strong $\mu_B$-driven enhancements of $D$ and $D_F$ in baryon-rich environments, while $S_T$ remains dominated by light mesons and shows weaker sensitivity to $\mu_B$, with implications for heavy-ion phenomenology and hydrodynamic modeling across the QCD phase diagram. The study provides a framework to embed thermo-diffusion into QCD matter simulations, potentially affecting observables like net-baryon fluctuations and cooling dynamics in both heavy-ion collisions and astrophysical settings.

Abstract

The gradients act as invisible engines of transport, converting microscopic imbalances into macroscopic flows, and thus providing deep insights into the dynamics of physical systems. Thermal gradients do not merely drive the flow of heat, but they also set the microscopic constituents of the system into motion. In such scenarios, the constituents of the system not only transport energy but also diffuse collectively under the influence of these gradients. For the very first time, we present a first-principles investigation of the Soret and Dufour effects in hot and dense quantum chromodynamics (QCD) matter. We use the relativistic Boltzmann transport equation under the relaxation time approximation. By incorporating chemical potential and temperature gradients into the kinetic theory framework, we derive explicit expressions for the Dufour coefficient, which quantifies the heat flow due to concentration gradients, and the Soret coefficient, which describes the particle diffusion induced by thermal gradients. These coupled-transport phenomena are traditionally studied in multi-component classical systems at low energy scales. In this study, we follow quasiparticle models for the deconfined phase and the hadron resonance gas model for the confined hadronic phase in the context of heavy-ion collisions. This study provides novel insights into the thermo-diffusion and diffusion-thermo phenomena and opens avenues for incorporating such effects in hydrodynamic modeling and transport simulations of QCD matter.

Soret and Dufour effects in hot and dense QCD matter

TL;DR

This work presents the first-principles study of the Soret and Dufour thermo-diffusion effects in hot and dense QCD matter using the relativistic Boltzmann equation in the relaxation time approximation, incorporating gradients of temperature and baryon chemical potential . By employing a quasiparticle model for the QGP and an ideal hadron resonance gas for the hadronic phase, the authors derive explicit kinetic-theory expressions for the diffusion coefficient , the Soret coefficient , the Dufour coefficient , and the thermal conductivity , capturing the coupled transport of heat and baryon current. The results reveal strong -driven enhancements of and in baryon-rich environments, while remains dominated by light mesons and shows weaker sensitivity to , with implications for heavy-ion phenomenology and hydrodynamic modeling across the QCD phase diagram. The study provides a framework to embed thermo-diffusion into QCD matter simulations, potentially affecting observables like net-baryon fluctuations and cooling dynamics in both heavy-ion collisions and astrophysical settings.

Abstract

The gradients act as invisible engines of transport, converting microscopic imbalances into macroscopic flows, and thus providing deep insights into the dynamics of physical systems. Thermal gradients do not merely drive the flow of heat, but they also set the microscopic constituents of the system into motion. In such scenarios, the constituents of the system not only transport energy but also diffuse collectively under the influence of these gradients. For the very first time, we present a first-principles investigation of the Soret and Dufour effects in hot and dense quantum chromodynamics (QCD) matter. We use the relativistic Boltzmann transport equation under the relaxation time approximation. By incorporating chemical potential and temperature gradients into the kinetic theory framework, we derive explicit expressions for the Dufour coefficient, which quantifies the heat flow due to concentration gradients, and the Soret coefficient, which describes the particle diffusion induced by thermal gradients. These coupled-transport phenomena are traditionally studied in multi-component classical systems at low energy scales. In this study, we follow quasiparticle models for the deconfined phase and the hadron resonance gas model for the confined hadronic phase in the context of heavy-ion collisions. This study provides novel insights into the thermo-diffusion and diffusion-thermo phenomena and opens avenues for incorporating such effects in hydrodynamic modeling and transport simulations of QCD matter.

Paper Structure

This paper contains 7 sections, 21 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Framework for the QCD Equation of State
  3. Quasiparticle Model
  4. Ideal Hadron Resonance Gas Model
  5. coupled-transport coefficients in QCD Matter
  6. Results and Discussion
  7. Summary

Figures (1)

  • Figure 1: Temperature dependence of scaled coefficients of coupled-transport in the hadron resonance gas (HRG) and quark-gluon plasma (QGP) phases at different values of baryon chemical potential $\mu_{B}$. Shown are scaled (top left) diffusion coefficient ($D/T$), (top right) Soret coefficient ($S_{T}/T$), (bottom left) Dufour coefficient ($D_{F}/T^{2}$), and (bottom right) thermal conductivity ($\kappa/T^{2}$). HRG results are plotted with solid lines and QGP results with dashed lines. Each colour corresponds to a fixed $\mu_{B}$ value.