# Equations of state in a strongly interacting relativistic system

#### Abstract

It has long been understood that the ground state of a superdense quark system, a Fermi liquid of weakly interacting quarks, is unstable with respect to the formation of diquark condensates. This nonperturbative phenomenon is essentially equivalent to the Cooper in-stability of conventional BCS superconductivity. As the quark pairs have nonzero color charge, this kind of superconductivity breaks the SU(3) color gauge symmetry, thus the phe-nomenon is called color superconductivity. However, not much is known about the behavior of quark systems at moderate densities between the formation of baryons and asymptotic freedom. Strong theoretical and experimental evidence suggests that there will be a smooth crossover between the two, during which the color superconducting properties of the quark system will undergo a shift between dynamics of a Bose-Einstein condensate (BEC) and weakly bound diquark pairs governed by BCS theory. Chromomagnetic instabilities exist for the densities in question and it is unclear what phase will resolve them. Therefore, there are many different proposed models accounting for several possible phases in need of thorough investigation. The analysis of two simple models that exhibit the crossover between a BCS state and a Bose-Einstein Condensate (BEC), as well as the evolution of the corresponding equation of state through the crossover, are the topics of this thesis.^

#### Subject Area

Physics, Quantum|Physics, Theory

#### Recommended Citation

Keith, Jason P, "Equations of state in a strongly interacting relativistic system" (2014). *ETD Collection for University of Texas, El Paso*. AAI1564680.

https://digitalcommons.utep.edu/dissertations/AAI1564680