Quantum Breathing Mode of Interacting Particles in a One-dimensional Harmonic Trap

TL;DR

This paper investigates the quantum breathing mode in one-dimensional interacting particles confined in a harmonic trap, analyzing its dependence on interaction strength, particle number, and quantum-classical transition using simulations.

Contribution

It introduces time-dependent Hartree-Fock simulations for 2-20 fermions and compares results with exact methods to validate findings.

Findings

Breathing mode depends on pair interaction strength.

Quantum breathing mode varies with particle number.

Results validated against exact solutions for small systems.

Abstract

Extending our previous work, we explore the breathing mode---the [uniform] radial expansion and contraction of a spatially confined system. We study the breathing mode across the transition from the ideal quantum to the classical regime and confirm that it is not independent of the pair interaction strength (coupling parameter). We present the results of time-dependent Hartree-Fock simulations for 2 to 20 fermions with Coulomb interaction and show how the quantum breathing mode depends on the particle number. We validate the accuracy of our results, comparing them to exact Configuration Interaction results for up to 8 particles.