"Almost classical" many-body systems: The quantum-mechanical corrections to the moments of a general spectrum

Abstract

The Wigner method in quantum statistical mechanics, which allows the derivation of the quantum-mechanical behavior of the properties of an "almost classical" system, has been applied to the determination of series expansions with respect to $h$ for a general correlation function and the moments related to its spectrum. Explicit expressions of the terms up to the order $h^4$ are given for the zeroth, second, and fourth moment in the case of a many-body system with a Hamiltonian $\mathit{H}=\frac{{\mathit{P}}^2}{2m}+\Phi \left(\mathit{R}\right)$ and for variables which are functions only either of $\left\{\mathit{P}\right\}$ or $\left\{\mathit{R}\right\}$ coordinates. From these expressions the corrections to the classical behavior can be calculated via the classical molecular-dynamics simulation technique.