Time-dependent driven anharmonic oscillator and the adiabaticity

TL;DR

This paper investigates the non-equilibrium quantum dynamics of a time-dependent driven anharmonic oscillator using the LvN approach, revealing minimal adiabaticity breaking and a Kepler-like equation of motion.

Contribution

It introduces a novel application of the LvN method to analyze adiabaticity and dynamics in a driven anharmonic oscillator, highlighting coherence preservation and angular momentum conservation.

Findings

Adiabaticity is minimally broken, with wave-packets evolving into coherent states.

The dynamics follow a Kepler-like equation of motion with conserved angular momentum.

Coherence factor is proportional to the coupling strength.

Abstract

We use the Liouville-von Neumann (LvN) approach to study the dynamics and the adiabaticity of a time-dependent driven anharmonic oscillator as an eample of non-equilibrium quantum dynamics. We show that the adiabaticity is minimally broken in the sense that a gaussian wave-packet at the past infinity evolves to coherent states, however slowly the potential changes, its coherence factor is order of the coupling. We also show that the dynamics are governed by an equation of motion similar to the Kepler motion which satisfies the angular momentum conservation.