Coherence properties of bulk matter

We prove a theorem, using the density functional approach and relying on a classical result by Lieb and Simon on Thomas-Fermi model, showing that in the thermodynamic limit bulk matter is at most semiclassical and coherence preserving. The connection between quantum fluid dynamics and density functional theory in the formulation due to Kohn and Sham play a significant role leading to a Vlasov-Poisson system of equations for the Wigner function. Coherence stability is achieved by noting that small oscillations in bulk matter are damped by Landau damping. In some conditions the initial Wigner function could generate an opposite effect and coherence stability can be lost involving higher order quantum effects for a macroscopic body.