On relation between renormalized frequency and heat capacity for particles in an anharmonic potential

TL;DR

This paper explores how weak anharmonicity affects the natural frequency and heat capacity of particles in a potential, revealing fundamental differences between orbital and thermal motions.

Contribution

It demonstrates that the anharmonic parameters influence orbital and thermal motions differently, challenging the idea that statistical laws emerge solely from deterministic many-body limits.

Findings

Renormalized frequency depends on anharmonic parameters.

Heat capacity correction is influenced by anharmonicity.

Orbital and thermal motions are affected differently by anharmonicity.

Abstract

For free particles in a simple harmonic potential plus a weak anharmonicity, characterized by a set of anharmonic parameters, Newtonian mechanics asserts that there is a renormalization of the natural frequency of the periodic motion; and statistical mechanics claims that the anharmonicity causes a correction to the heat capacity of an ideal gas in the anharmonic potential. The orbital motion and thermal motion depend on the same anharmonic parameters, but in different combinations. These two manners of combinations are fundamentally different, demonstrating that statistical law can not emerge from the many-body limit of deterministic law for one-body.