When the interactions are scale invariant, the quantum dynamics of a quantum gas are strongly constrained by a resultant conformal symmetry. In this Letter we study the expansion dynamics of strongly interacting quantum systems in a shallow harmonic trap in one and three spatial dimensions while interparticle interactions break the scale symmetry explicitly. Our main finding is that in one dimension the dynamics can be strongly constrained by an emergent infrared conformal dynamics (EIRCD) which significantly reduces entropy production, as opposed to three dimensions where there is no EIRCD in the strong coupling limit. We investigate the possibility and signatures of EIRCD in terms of the damping rate of the large amplitude oscillations of the gas, as well as the work done following a two-quench protocol. We find that the damping and the work done are constrained by the EIRCD, and become vanishingly small in the infrared limit when the final harmonic trap frequency is small. Our analysis is based on a close connection between the renormalization group equation flow and expansion dynamics in real space, and as such can be readily applied to a wide range of strongly interacting systems, like one-dimensional (1D) quantum gases and the three-dimensional (3D) unitary Fermi gas.

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• Bose gases
• Cold atoms & matter waves
• Fermi gases
• Atomic gases
• Trapped atoms
• Nonperturbative methods