Generalized Dynamical Duality of Quantum Particles in One Dimension

TL;DR

This paper proves a generalized dynamical duality in 1D quantum systems, showing that different particles with various statistics evolve to the same momentum distribution determined by initial rapidities, observable in ultracold gases.

Contribution

It establishes a universal long-time behavior for 1D quantum particles with arbitrary statistics, linking initial states to asymptotic momentum distributions.

Findings

Different 1D particles approach the same momentum distribution after expansion.

The asymptotic distribution is determined by initial rapidities.

Results are applicable to ultracold gases with tunable interactions.

Abstract

We prove a generalized dynamical duality for identical particles in one dimension (1D). Namely, 1D systems with arbitrary statistics -- including bosons, fermions and anyons -- approach the same momentum distribution after long-time expansion from a trap, provided they share the same scattering length for short-range interactions. This momentum distribution is uniquely given by the rapidities, or quasi-momenta, of the initial trapped state. Our results can be readily detected in quasi-1D ultracold gases with tunable s- and p-wave interactions.