Quasi-long-range order in trapped systems

TL;DR

This paper studies how trapping potentials affect the quasi-long-range order in 2D particle systems with U(1) symmetry, combining scaling theory and Monte Carlo simulations to reveal universal trap-size effects.

Contribution

It introduces a scaling framework for understanding trap-size dependence in 2D systems with U(1) symmetry, supported by numerical simulations.

Findings

Universal trap-size scaling behavior identified

Monte Carlo simulations confirm theoretical predictions

Implications for quantum atomic gases in traps

Abstract

We investigate the effects of a trapping space-dependent potential on the low-temperature quasi-long-range order phase of two-dimensional particle systems with a relevant U(1) symmetry, such as quantum atomic gases. We characterize the universal features of the trap-size dependence using scaling arguments. The resulting scenario is supported by numerical Monte Carlo simulations of a classical two-dimensional XY model with a space-dependent hopping parameter whose inhomogeneity is analogous to that arising from the trapping potential in experiments of atomic gases.