Breathing Modes as a Probe of Energy Fluctuations in a Unitary Fermi Gas

TL;DR

This paper demonstrates that in scale-invariant quantum gases with SO(2,1) symmetry, the amplitude of breathing modes directly measures energy fluctuations, providing a universal, symmetry-based method to probe nonequilibrium energy statistics.

Contribution

It establishes an exact, universal relation between breathing mode amplitude and energy fluctuations, independent of microscopic details, using symmetry principles.

Findings

Breathing mode amplitude is directly proportional to energy fluctuations.

The relation is fixed solely by the Bargmann index, a symmetry parameter.

Breathing-state excitation follows a universal statistical distribution.

Abstract

Directly accessing energy fluctuations in interacting quantum many-body systems remains a long-standing challenge, especially far from equilibrium. Here we show that in scale-invariant quantum gases with SO$(2,1)$ dynamical symmetry, the amplitude of the breathing mode provides a direct and quantitative probe of energy fluctuations. We establish an exact and universal relation between the oscillation amplitude and the energy fluctuation, with a dimensionless ratio fixed solely by the Bargmann index $k$, which labels the irreducible representation of the underlying SU$(1,1)$ algebra and thereby determines the structure of the many-body spectrum and dynamics. As a consequence, this relation is fully dictated by symmetry and remains independent of microscopic details and excitation protocols. Furthermore, we show that the excitation of breathing-mode states follows a universal statistical distribution governed by a single parameter, independent of the specific driving protocol. Our findings demonstrate that energy fluctuations, typically encoded in the many-body spectrum, can be directly accessed through collective dynamics, offering a symmetry-based route to probe nonequilibrium energy statistics in strongly interacting quantum systems.