Abstract
The compressibility of magnetized quark matter is investigated in the SU(2) NJL model. The increases of the chemical potential and the temperature can reduce the compressibility, and lead to the much stiffer equation of state. The variation of the compressibility with the magnetic field will depend on the phase region. Due to the anisotropic structure, the compressibility is different in the directions parallel and perpendicular to the field. The discontinuity of longitudinal compressibility with the chemical potential and the temperature captures the signature of a first-order chiral phase transition and the crossover at high temperature. Moreover, the magnetic-field-and-temperature running coupling would have an important effect on the position of the phase transition. Under the lowest landau level approximation at zero temperature, the longitudinal compressibility has a direct inverse proportional relation to the magnetic field strength and the chemical potential square as ${\ensuremath{\kappa}}_{\mathrm{LLL},\ensuremath{\chi}}^{\ensuremath{\parallel}}\ensuremath{\propto}1/(eB{\ensuremath{\mu}}^{2})$.
Highlights
The properties of the quark matter are of most importance in understanding many physical aspects of nature, such as the quark gluon plasma in the big bang of the early universe, the possible structure in the core of compact objects, and the hadronic quark phase transition in experiments, where the high temperature and high densities characterize the extreme conditions
The discontinuity of longitudinal compressibility with the chemical potential and the temperature captures the signature of a first-order chiral phase transition and the crossover at high temperature
It can be predicted that the magnetic field would lead to much stiffer equation of state in neutron stars compared to zero magnetic field condition
Summary
The properties of the quark matter are of most importance in understanding many physical aspects of nature, such as the quark gluon plasma in the big bang of the early universe, the possible structure in the core of compact objects, and the hadronic quark phase transition in experiments, where the high temperature and high densities characterize the extreme conditions. It is widely accepted that the strong magnetic fields could exist in the early universe, in the core of neutron stars, and in the noncentral heavy ion collision experiments, such as the Relativistic Heavy Ion Collider or the Large Hadron Collider (LHC) [5].
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