On the problem of the classical limit for statistical characteristics of a quantum Coulomb plasma

Abstract

The general structure of the perturbation theory series for the thermodynamic potential of a system of electrons and point ions is discussed. In the classical limit, when Planck’s constant ℏ → 0, the particular terms of the perturbation theory series diverge due to the impossibility of maintaining of stability of a purely classical system of the opposite sign charges attracted to each other. At the same time, it is known that in a certain range of parameters, a thermodynamic potential that does not contain Planck’s constant is a good approximation. Such thermodynamic functions describes the experimental data well and corresponds to the molecular dynamics calculations of model quasi-Coulomb systems. It is shown that the transition to a purely classical description, which implies the limit ℏ → 0, is impossible, but the terms of the series containing ℏ are small for certain plasma parameters and can be discarded. This is the rationale explanation of using classical models and approximations to describe plasma in certain parameter ranges. On this basis, a hypothesis is formulated about the absence of a classical limit for all measurable physical properties (including kinetic characteristics) of the Coulomb model of plasma, in which point particles interact according to the Coulomb law and, therefore, there are no adjustable parameters.