ORDER INDEXES AND ORDERING IN MACROSCOPIC SYSTEMS

In A. J. Coleman and V. I. Yukalov: Mod. Phys. Lett. B, 5, 1679 (1991) and Nuovo Cimento B, 107, 535 (1992) we introduced order indices of r educed density matrices as a tool to connect macroscopic and microscop ic properties of physical systems. In the present paper, we give a def inition of order indices which is independent of the representation of the density matrices and is valid for both fermion and boson systems and for all types of order: short, mid and long range. Time-dependent indices are introduced to permit discussion of non-equilibrium process es. Special attention is devoted to the study of mid-range order and t he corresponding stability conditions. Mid-range order is examined bot h in a system at rest and in a system with two-velocity motion.