Abstract
We discuss the thermoelectric effect of hot and dense hadron gas within the framework of the hadron resonance gas model. Using the relativistic Boltzmann equation within the relaxation time approximation we estimate the Seebeck coefficient of the hot and dense hadronic medium with a gradient in temperature and baryon chemical potential. The hadronic medium in this calculation is modeled by the hadron resonance gas (HRG) model with hadrons and their resonances up to a mass cutoff $\Lambda\sim 2.6$ GeV. We also extend the formalism of the thermoelectric effect for a nonvanishing magnetic field. The presence of magnetic field also leads to a Hall type thermoelectric coefficient (Nernst coefficient) for the hot and dense hadronic matter apart from a magneto-Seebeck coefficient. We find that generically in the presence of a magnetic field Seebeck coefficient decreases while the Nernst coefficient increases with the magnetic field. At higher temperature and/or baryon chemical potential these coefficients approach to their values at vanishing magnetic field.
Highlights
Transport coefficients are important characteristics of thermodynamic systems that determine the evolution of the system toward equilibrium starting from an initial out of equilibrium state
We would like to mention here that, some of us studied the Seebeck coefficient for the hadronic medium using the formalism originally developed for condensed matter system, here we study the magnetoSeebeck coefficient and Nernst coefficient for the hadronic system using the formalism of thermoelectric effect compatible with relativistic systems
In the expression of thermal conductivity ðε − ðω=nBÞÞ always comes as a square, in the absence of thermoelectric effect, the positivity of thermal conductivity is ensured which can be seen in Eq (21)
Summary
Transport coefficients are important characteristics of thermodynamic systems that determine the evolution of the system toward equilibrium starting from an initial out of equilibrium state. The success of hydrodynamical modeling of the QCD plasma inspires a deeper understanding of hydrodynamical behavior in the presence of a magnetic field In this context, magnetohydrodynamic simulations have been used to study the flow coefficient of the strongly interacting matter produced in heavy-ion collisions [17,18]. Have been used to estimate various transport coefficients for the QCD matter both in the absence and in the presence of magnetic field [37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71] Another transport coefficient which becomes important in the presence of temperature gradient at finite baryon density is the thermal conductivity [72,73]. We summarize our work with an outlook in the conclusion section
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