New Submission1-D Quark Gas For SU(3) Color System.

The thermodynamics of quarks moving classically in a spatial 1-D with SU(2) and SU(3) color

system has previously been studied. Previous work was for zero baryon density. In this work, we

focus on quarks with finite baryon density. Our objective is to get an exact solution for the whole

transition between two asymptotic limits,the baryon gas at low density and the quark gas at high

density. To achieve this, we solve a complex differential equation governing SU(3) quarks both

numerically and analytically in the asymptotic limits.This complex differential equation arises from

diagonalizing the transfer matrix of the 1-D system. Additionally, we numerically solve the differen-

tial equation for the SU(3) zero baryon density system and validate our results by comparing them

with existing analytical solutions. The equation of state is derived from the maximum eigenvalues at

different pressure values, clearly confirming the transition between baryonic and quark-gas behavior.

These findings provide deeper insight into the behavior of SU(3) color systems in the finite density

case that is difficult to probe in lattice QCD.