Dynamics and thermodynamics of quantum crystals near the instability point in the self-consistent phonon theory

Formally one can distinguish between the thermodynamic stability conditions and the dynamical ones. These last consists are easily formulated in the self-consistent phonon theory (SCPT) base don the thermodynamic double-time Green's function method. According to it the dynamic instability temperature Ts for a simple Bravais lattice defines the temperature at which the bound crystalline state of atoms vanishes that really means that the phonon frequencies become complex at sufficiently high temperatures T