Faraday patterns in Bose-Einstein condensates. Amplitude equation for rolls in the parametrically driven, damped Gross-Pitaevskii equation

TL;DR

This paper derives an amplitude equation describing the formation of spatially modulated roll patterns in Bose-Einstein condensates modeled by a parametrically driven, damped Gross-Pitaevskii equation, highlighting pattern formation mechanisms.

Contribution

It introduces a novel Landau equation with broken phase symmetry that governs the dynamics of pattern formation in modulated Bose-Einstein condensates.

Findings

Supports spatially modulated roll states

Derives a Landau amplitude equation for pattern dynamics

Provides insights into pattern formation in BECs

Abstract

The parametrically driven, damped Gross-Pitaevskii equation, which models Bose-Einstein condensates in which the interatomic s-wave scattering length is modulated in time, is shown to support spatially modulated states in the form of rolls. A Landau equation with broken phase symmetry is derived, which governs the dynamics of the roll amplitude.