Spin turbulence with small spin magnitude in spin-1 spinor Bose-Einstein condensates

TL;DR

This paper investigates spin turbulence with small spin magnitude in spin-1 Bose-Einstein condensates, revealing characteristic -1 and -7/3 power laws in the energy spectrum through theoretical analysis and numerical simulations.

Contribution

It introduces the first detailed analysis of spin turbulence with small spin magnitude, deriving and confirming specific power laws in the energy spectrum.

Findings

-7/3 power law appears in high-wave-number region for antiferromagnetic interaction

Both -1 and -7/3 power laws are observed in ferromagnetic interaction case

Numerical simulations confirm the theoretical power laws in a 2D uniform system

Abstract

We theoretically and numerically study spin turbulence (ST) with small spin magnitude in spin-1 spinor Bose-Einstein condensates by using the spin-1 spinor Gross-Pitaevskii (GP)equations. This kind of ST is realized in two cases: (i) with antiferromagnetic interaction and (ii) with ferromagnetic interaction under a static magnetic field. The ST with small spin magnitude can exhibit two characteristic power laws in the spectrum of the spin-dependent interaction energy: -1 and -7/3 power laws in the low- and high-wave-number regions, respectively. These power laws are derived from a Kolmogorov-type dimensional scaling analysis for the equations of motion of the spin vector and nematic tensor. To confirm these power laws, we perform a numerical calculation of the spin-1 spinor GP equations in a two-dimensional uniform system. In case (i), the -7/3 power law appears in the high-wave-number region, but the spectrum in the low-wave-number region deviates from the -1 power law. In contrast, both -1 and -7/3 power laws are found to clearly appear in case (ii).