Quantum dynamics of a nucleon in the Fermi accelerator

Abstract

Highlights: • In nuclear physics, the Fermi accelerator is a coherent open quantum system. • There is not a true equilibrium for a nucleon‘s mean-energy in the Fermi accelerator. • Occupation of higher energy eigen-states remains even after the mean-energy plateaus. • This work paves the way for work on quantum tunnelling in the Fermi accelerator. The quantum dynamics of a particle in a one-dimensional box with an oscillating wall (the Fermi accelerator) is investigated. The model is applied to the motion of a single nucleon in the mean-field potential of a heavy atomic nucleus whose surface vibrates. By directly solving the time-dependent Schrödinger equation, both the state of the particle and its mean-energy are studied. The effects of the frequency of the wall oscillation on the nucleon’s energy are addressed. Its energy oscillates in phase with the moving wall for all frequencies, showing no chaotic behaviour. There is a large initial peak of the nucleon’s energy as the particle adjusts to the sudden change in the size of the box and a varying relaxation time as it plateaus towards lower energy and a partial equilibrium. Small oscillations in energy continue, since there cannot be a true equilibrium while the wall is moving. The quantum coherence between the different parts of the nucleon’s wave-function in real space is very much preserved. This research lays the foundation for future investigations into quantum tunnelling in the Fermi accelerator.