Magneto-Thomson and transverse Thomson effects in an interacting hadron gas in the presence of an external magnetic field

TL;DR

This work addresses higher-order thermoelectric transport in a hot, dense hadron gas under external magnetic fields, focusing on magneto-Thomson ($Th_B$) and transverse Thomson ($Th_N$) effects. It employs the relativistic Boltzmann transport equation in relaxation-time approximation to compute leading- and higher-order thermoelectric coefficients within four hadron-resonance gas models (IHRG, EVHRG, RMFHRG, VDWHRG), incorporating Landau quantization and both static and time-varying magnetic fields. A key contribution is the first comprehensive estimation of $Th_B$ and $Th_N$ in hadronic matter, revealing strong sensitivity to magnetic-field strength and dynamics, baryon chemical potential, and inter-hadron interactions. The results illuminate how magnetic-field evolution shapes heat generation and anisotropic thermoelectric responses in heavy-ion collisions, with potential links to spin-caloritronic phenomena in QCD matter and implications for transport in the late-stage hadronic medium.

Abstract

The universality of electric charge as a quantum number allows thermoelectric properties to manifest across diverse systems, starting from a hot quantum chromodynamic matter in heavy-ion collisions at a high energy scale to semiconductors in condensed matter systems at a low energy scale. In this work, we explore the emergence of magneto-transport phenomena, specifically the magneto-Thomson and transverse Thomson effects, in a hot and dense hadronic medium produced in relativistic heavy-ion collisions at the Relativistic Heavy Ion Collider and Large Hadron Collider energies. These phenomena arise due to the combined influence of temperature gradients and non-zero baryon chemical potential, particularly in the presence of an external magnetic field. Using the relativistic Boltzmann transport equation within the relaxation time approximation, we analyze the behavior of the hadronic medium considering different frameworks of hadron resonance gas models. The presence of external magnetic fields breaks the isotropy of the thermoelectric transport coefficient matrix, giving rise to new components of the Thomson coefficient, namely, magneto-Thomson and transverse Thomson coefficients. For the first time, we estimate the magneto-Thomson and transverse Thomson coefficients, which originate from the temperature dependence of the magneto-Seebeck coefficient and Nernst coefficient, respectively, in hadron gas under the influence of a static and time-varying magnetic field. Our findings provide a novel perspective on the higher-order thermoelectric properties of the hot and dense hadronic medium in the context of heavy-ion collisions.

Figures (5)

• Figure 1: Thomson coefficient ($Th$) obtained in different hadronic models as a function of temperature at $\mu_{B}$ = 0.10 GeV (left panel), 0.30 GeV (middle panel), and 0.40 GeV (right panel).
• Figure 2: Magneto-Thomson coefficient ($Th_{B}$) as a function of temperature at magnetic field $eB$ = 0.1 $m_{\pi}^2$ (upper panel) and $eB$ = 1.0 $m_{\pi}^2$ (lower panel) for baryon chemical potential at $\mu_{B}$ = 0.10 GeV (left), 0.30 GeV (middle), and 0.40 GeV (right).
• Figure 3: Transverse Thomson coefficient ($Th_N$) as a function of temperature at magnetic field $eB$ = 0.1 $m_{\pi}^2$ (upper panel) and $eB$ = 1.0 $m_{\pi}^2$ (lower panel) for baryon chemical potential at $\mu_{B}$ = 0.10 GeV (left), 0.30 GeV (middle), and 0.40 GeV (right).
• Figure 4: Upper panel: left figure shows scaled electrical conductivity ($\sigma_{el}/T$) and right figure shows scaled Hall-like component of electrical conductivity ($\sigma_{H}/T$), bottom panel: left figure shows scaled integral ($\mathcal{I}_{31}/T^2$) and right figure shows scaled integral ($\mathcal{I}_{42}/T^2$) at $\mu_{B}$ = 0.30 GeV with three different scenario of magnetic field $eB$ = 0.0, $eB$ = 0.1 $m_{\pi}^2$, and $eB_0$ = 1.0 $m_{\pi}^2$ with decay parameter $\tau_B$ = 6 fm.
• Figure 5: Left panel: Magneto-Thomson coefficient ($Th_{B}$), and right panel: transverse Thomson coefficient ($Th_{N}$) as a function of temperature for baryon chemical potential at $\mu_{B}$ = 0.30 GeV with three different scenario of magnetic field $eB$ = 0.0, $eB$ = 0.1 $m_{\pi}^2$, and $eB_0$ = 1.0 $m_{\pi}^2$ with decay parameter $\tau_B$ = 6 fm.