Universal Scaling Properties of Cold Atom Scattering Dynamics in Confined Low Dimensional Geometries

TL;DR

This paper derives universal scaling laws for scattering dynamics of cold atoms in low-dimensional traps at intermediate energies, revealing non-interacting behavior at transverse energy levels and power-law scaling near these levels.

Contribution

It introduces universal scaling relations for the reflection coefficient in confined low-dimensional cold atom systems at intermediate energies, highlighting non-interacting points and power-law behaviors.

Findings

Reflection coefficient exhibits universal scaling near transverse energy levels.

System becomes non-interacting when energy matches a transverse level.

Power-law behavior characterizes scattering observables at intermediate energies.

Abstract

Intermediate energy scale physics plays a very important role in non-equilibrium dynamics of quasi-low dimensional cold atom systems. In this article we obtain the universal scaling relations for the generalized reflection coefficient, i.e., the fraction of atoms scattered out of the initial state, at intermediate energies scales. These intermediate energies are larger than the trap frequency, but necessarily smaller than the effective range of the inter-atomic potential. For harmonically confined one and two dimensional geometries, whenever the energy of the system is commensurate with a transverse energy level, it is shown that the system becomes non-interacting. For energies close to a transverse energy level, the reflection coefficient and scattering dynamics take on universal scaling forms, only depending on the difference between the energy of the particles and the transverse energy level. In this article, the universal power law behaviors of these scattering observables are obtained.