Thermodynamics of magnetized bps baryonic layers and the effects of the isospin chemical potential.
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Date
2026
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Universidad de Concepción
Abstract
Estudiamos la termodinámica de capas bariónicas BPS magnetizadas, las cuales poseen tanto carga bariónica como flujo magnético. El estudio termodinámico de este sistema resulta altamente no trivial debido a que la carga topológica, que aparece naturalmente en el lado derecho de la cota BPS, es una función no lineal de la carga bariónica. Estas capas fueron construidas a través de la ecuación de Hamilton-Jacobi de la mecánica clásica en el modelo sigma no lineal acoplado minimalmente a la teoría de Maxwell, la cual es una de las teorías efectivas más relevantes para la cromodinámica cuántica (QCD) en el régimen fuertemente interactuante del límite de bajas energías que también toma en consideración las interacciones electromagnéticas. Para la construcción de la función de partición grancanónica del sistema (que resulta interesante por su relación con la función zeta de Riemann), utilizamos herramientas del efecto Casimir para derivar una relación analítica entre la carga topológica, la carga bariónica y el flujo magnético. Con base en esto y utilizando física estadística clásica, fue posible derivar cantidades termodinámicas relevantes de estas capas, tales como la energía, la entropía, la capacidad calorífica y la susceptibilidad magnética, logrando identificar el potencial químico bariónico crítico. Los efectos del potencial químico de isospín también pueden ser incluidos: en particular, construimos una cota BPS explícita y las correspondientes configuraciones BPS para el caso en el que el potencial químico de isospín es no nulo. Por otro lado, derivamos de forma analítica, a partir del tensor de energía momento del sistema, la ecuación de estado y la velocidad del sonido tanto para el caso con potencial químico de isospín cero como distinto de cero. Desde el punto de vista técnico, es un resultado bastante notable derivar expresiones explícitas para todas estas cantidades termodinámicas de un sistema magnetizado fuertemente interactuante a densidad bariónica finita. Finalmente, la interpretación física de nuestros resultados analíticos será discutida.
We study the thermodynamics of magnetized BPS baryonic layers, which possess both baryonic charge and magnetic flux. The thermodynamic study of this interacting system is highly non-trivial because the topological charge, which naturally appears on the right-hand side of the BPS bound, is a non-linear function of the baryonic charge. These layers were constructed using the Hamilton-Jacobi equation of classical mechanics in the non-linear sigma model minimally coupled to Maxwell’s theory, which is one of the most relevant effective theories for Quantum Chromodynamics (QCD) in the strongly interacting regime of the low-energy limit, which also takes electromagnetic interactions into account. To construct the grand canonical partition function of the system (which is interestingly related to the Riemann zeta function), we used tools from the Casimir effect to derive an analytical relationship between the topological charge, the baryonic charge, and the magnetic flux. Based on this, and using classical statistical physics, it was possible to derive relevant thermodynamic quantities of these layers, such as energy, entropy, heat capacity, and magnetic susceptibility, successfully identifying the critical baryonic chemical potential. The effects of the isospin chemical potential can also be included: in particular, we constructed an explicit BPS bound and the corresponding BPS configurations for the case in which the isospin chemical potential is non-zero. Furthermore, we analytically derived, from the energymomentum tensor of the system, the equation of state and the speed of sound for both the cases with zero and non-zero isospin chemical potential. From a technical point of view, it is a quite remarkable result to derive explicit expressions for all these thermodynamic quantities of a strongly interacting magnetized system at finite baryonic density. Finally, the physical interpretation of our analytical results will be discussed.
We study the thermodynamics of magnetized BPS baryonic layers, which possess both baryonic charge and magnetic flux. The thermodynamic study of this interacting system is highly non-trivial because the topological charge, which naturally appears on the right-hand side of the BPS bound, is a non-linear function of the baryonic charge. These layers were constructed using the Hamilton-Jacobi equation of classical mechanics in the non-linear sigma model minimally coupled to Maxwell’s theory, which is one of the most relevant effective theories for Quantum Chromodynamics (QCD) in the strongly interacting regime of the low-energy limit, which also takes electromagnetic interactions into account. To construct the grand canonical partition function of the system (which is interestingly related to the Riemann zeta function), we used tools from the Casimir effect to derive an analytical relationship between the topological charge, the baryonic charge, and the magnetic flux. Based on this, and using classical statistical physics, it was possible to derive relevant thermodynamic quantities of these layers, such as energy, entropy, heat capacity, and magnetic susceptibility, successfully identifying the critical baryonic chemical potential. The effects of the isospin chemical potential can also be included: in particular, we constructed an explicit BPS bound and the corresponding BPS configurations for the case in which the isospin chemical potential is non-zero. Furthermore, we analytically derived, from the energymomentum tensor of the system, the equation of state and the speed of sound for both the cases with zero and non-zero isospin chemical potential. From a technical point of view, it is a quite remarkable result to derive explicit expressions for all these thermodynamic quantities of a strongly interacting magnetized system at finite baryonic density. Finally, the physical interpretation of our analytical results will be discussed.
Description
Tesis presentada para optar al grado de Magíster en Ciencias con mención en Física.
Keywords
Thermodynamics, Equation of state, Casimir effect, Isospin