Random walk and non-Gaussianity of the 3D second-quantized Schr\"odinger-Newton nonlocal soliton

TL;DR

This paper investigates the quantum dynamics of 3D nonlocal solitons in a Schrödinger-Newton framework, revealing non-Gaussian behavior that could indicate quantum-gravitational effects and potential for quantum computing.

Contribution

It provides the first detailed analysis of quantum diffusion and non-Gaussianity in 3D+1 nonlocal solitons within the second-quantized Schrödinger-Newton model, supported by numerical simulations.

Findings

Quantum diffusion of soliton parameters is characterized and varies with interaction length.

Numerical simulations confirm the emergence of non-Gaussian statistics in the soliton dynamics.

Non-Gaussianity and fluctuations are universal effects in nonlocal, multi-dimensional quantum fluids.

Abstract

Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional self-localized solitary waves, are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger-Newton equation. We theoretically investigate the quantum diffusion of the soliton center of mass and other parameters, varying the interaction length. 3D+1 simulations of the Ito partial differential equations arising from the positive P-representation of the density matrix validate the theoretical analysis. The numerical results unveil the onset of non-Gaussian statistics of the soliton, which may signal quantum-gravitational effects and be a resource for quantum computing. The non-Gaussianity arises from the interplay between the soliton parameter quantum diffusion and stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality.