Low-Temperature Quasi-Equilibrium States in the Hydrogen Atom

TL;DR

This paper investigates the approach to equilibrium in hydrogen atoms at low temperatures, revealing a quasi-equilibrium state with aging properties and providing an analytic model that aligns with numerical simulations.

Contribution

It introduces the concept of a low-temperature quasi-equilibrium state in hydrogen atoms and develops an analytic approach to describe it, supported by numerical Monte Carlo results.

Findings

Quasi-equilibrium states exhibit aging behavior with duration increasing exponentially at lower temperatures.

Analytic models fit numerical data well for low temperatures and energies up to 6% of ionization energy.

The approach remains valid for temperatures up to 10^4 K.

Abstract

The dynamics of the approach to equilibrium of the hydrogen atom is investigated numerically through a Monte Carlo procedure. We show that, before approaching ionization, the hydrogen atom may live in a quasi-equilibrium state, characterized by aging, whose duration increases exponentially as the temperatures decreases. By analyzing the quasi-equilibrium state, we compute averages of physical quantities for the hydrogen atom. We have introduced an analytic approach that fits satisfactorily the numerical estimates for low temperatures. Although the present analysis is expected to hold for energies typically up to 6% of the ionization energy, it works well for temperatures as high as 10^{4} K.