# Dynamics of spin and density fluctuations in strongly interacting few-body systems

## TL;DR

This paper investigates how spin and density fluctuations evolve over time in small, strongly interacting fermionic systems, revealing distinct signatures and the impact of SU(N) symmetry on spin excitations.

## Contribution

It provides new insights into spin-density dynamics in few-body quantum systems and explores the effects of SU(N) symmetry on spin excitations.

## Key findings

- Spin and density dynamics show separate signatures even in few-body systems.
- SU(N) symmetry leads to the vanishing of spin excitations in balanced systems.
- Distinct excitation spectra characterize spin and density fluctuations.

## Abstract

The decoupling of spin and density dynamics is a remarkable feature of quantum one-dimensional many-body systems. In a few-body regime, however, little is known about this phenomenon. To address this problem, we study the time evolution of a small system of strongly interacting fermions after a sudden change in the trapping geometry. We show that, even at the few-body level, the excitation spectrum of this system presents separate signatures of spin and density dynamics. Moreover, we describe the effect of considering additional internal states with SU(N) symmetry, which ultimately leads to the vanishing of spin excitations in a completely balanced system.