# Dynamical symmetry and breathers in a two-dimensional Bose gas

## TL;DR

This study explores the dynamical symmetry and breather phenomena in a two-dimensional Bose gas, demonstrating how scale invariance influences its evolution and revealing novel periodic breather states.

## Contribution

The paper experimentally investigates the dynamical symmetry in a 2D Bose gas and introduces a new type of breather solution in the Gross--Pitaevskii equation.

## Key findings

- Scale invariance relates different evolutions via a scaling transform.
- Certain initial shapes lead to periodic breather states.
- Experimental validation of Lorentz group symmetry in 2D Bose gases.

## Abstract

A fluid is said to be \emph{scale-invariant} when its interaction and kinetic energies have the same scaling in a dilation operation. In association with the more general conformal invariance, scale invariance provides a dynamical symmetry which has profound consequences both on the equilibrium properties of the fluid and its time evolution. Here we investigate experimentally the far-from-equilibrium dynamics of a cold two-dimensional rubidium Bose gas. We operate in the regime where the gas is accurately described by a classical field obeying the Gross--Pitaevskii equation, and thus possesses a dynamical symmetry described by the Lorentz group SO(2,1). With the further simplification provided by superfluid hydrodynamics, we show how to relate the evolutions observed for different initial sizes, atom numbers, trap frequencies and interaction parameters by a scaling transform. Finally we show that some specific initial shapes - uniformly-filled triangles or disks - may lead to a periodic evolution, corresponding to a novel type of breather for the two-dimensional Gross--Pitaevskii equation.