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

• URL: http://arxiv.org/abs/2202.10741v4
• Date: Tue, 31 Jan 2023 07:58:34 GMT
• Title: Random walk and non-Gaussianity of the 3D second-quantized Schr\"odinger-Newton nonlocal soliton
• Authors: Claudio Conti
• Abstract summary: We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schroedinger-Newton equation. numerical results unveil the onset of non-Gaussian statistics of the soliton.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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