We report on our results about spontaneous chiral symmetry breaking for quark matter in the background of static and homogeneous parallel electric field, E, and magnetic field, B. A Nambu-Jona-Lasinio model is used to compute the dependence of the chiral condensate at finite temperature, E and B. We study the effect of this background on inverse catalysis of chiral symmetry breaking for E and B of the same order of magnitude. We also consider the effect of equilibration of chiral density, n(5), produced by axial anomaly on the critical temperature. The equilibration of n(5) allows for the introduction of the chiral chemical potential, mu(5), which is computed self-consistently as a function of temperature and field strength. We find that even if the chiral medium is produced by the fields the thermodynamics, with particular reference to the inverse catalysis induced by the external fields, it is not very affected by n(5) at least if the average mu(5), at equilibrium is not too large.
; CONSTANT ELECTROMAGNETIC-FIELD
; GROSS-NEVEU MODEL
; 3-DIMENSIONAL GROSS
; NONZERO TEMPERATURE
; DYNAMICAL MODEL