Quantum effects on one-dimensional collision dynamics of fermion clusters

TL;DR

This study investigates quantum effects on the collision dynamics of fermion clusters in one-dimensional systems, revealing the limits of quasi-classical approximations under varying interaction strengths.

Contribution

It applies the time-dependent density matrix renormalization group to simulate fermion cluster collisions, providing insights into quantum effects and the validity of classical models.

Findings

Quantum effects significantly alter collision reflectance at strong interactions.

Quasi-classical approximation is valid only in weak interaction regimes.

Simulation results match experimental conditions in cold atomic gases.

Abstract

Recently, many experiments with cold atomic gases have been conducted from interest in the non-equilibrium dynamics of correlated quantum systems. Of these experiments, the mixing dynamics of fermion clusters motivates us to research cluster-cluster collision dynamics in one-dimensional Fermi systems. We adopt the one-dimensional Fermi-Hubbard model and apply the time-dependent density matrix renormalization group method. We simulate collisions between two fermion clusters of spin-up and spin-down, and calculate reflectance of the clusters R changing the particle number in each cluster and the interaction strength between two fermions with up and down spins. We also evaluate the quasi-classical (independent collision) reflectance R^{qc} to compare it with R. The quasi-classical picture is quantitatively valid in the limit of weak interaction, but it is not valid when interaction is strong.