Multidimensional self-trapping in linear and nonlinear potentials

Malomed, Boris A.

doi:10.48550/arxiv.2111.00547

Cited by 3 publications

(3 citation statements)

References 109 publications

(143 reference statements)

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“…Three-dimensional (3D) self-localized nonlinear waves enter various fields of research [1,2], but their quantum properties are unexplored. Classical 3D solitary waves (in short, 3D solitons) need to be stabilized against catastrophic collapse.…”

Section: Introductionmentioning

confidence: 99%

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Conti

2023

New J. Phys.

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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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Section: Introductionmentioning

confidence: 99%

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Conti

2023

New J. Phys.

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“…Solitons are solitary waves and self-trapped and localized objects, existing in a great variety of physical media due to the interplay of dispersion and non-linearity, which represents the self-attraction of matter [27]. In one-dimensional settings, solitons come in different forms-bright, dark, grey, kink, and antikink-but in two-and three-dimensional settings, the question on stability impedes their progress with time [28].…”

Section: Introductionmentioning

confidence: 99%

Quantum Droplet in Lower Dimensions

Khan

Debnath

2022

Front. Phys.

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The study of Bose–Einstein condensation (BEC) in lower dimensions plays an important role in understanding the fundamentals of many-body physics as they can be treated theoretically with relative ease and can be verified experimentally. Recently, observation of a liquid-like state in a BEC mixture has been reported along with a theoretical prescription for its observation in the lower dimension. This observation is unique and has serious ramifications in our prevailing conception of the liquid state, which has a deep influence on the van der Waals theory. In explaining the self-bound nature of this state, quantum fluctuation and its fine balance with mean-field (MF) interaction turn out to be playing a key role. Though the experiments are performed predominantly in three dimensions, theoretical studies extend to the lower dimensions. In this brief review, we plan to summarize the recent theoretical advances in droplet research in the lower dimension and elaborate on the description of our contributions. We will mainly focus on analytical results related to this self-bound state in a one-dimension and quasi one-dimension environment. We aim to cover a few results from the family of cnoidal solutions to droplet solutions with smooth transitions between each other, finishing it by carrying a modest discussion on the supersolid phase.

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“…Three-dimensional (3D) self-localized nonlinear waves enter various fields of research [1,2], but their quantum properties are unexplored. Classical three-dimensional solitary waves (in short, 3D solitons) need to be stabilized against catastrophic collapse.…”

mentioning

confidence: 99%

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger-Newton nonlocal soliton

Conti¹

2022

Preprint

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Nonlocal quantum fluids emerge as dark-matter models and tools for quantum simulations and technologies. However, strongly nonlinear regimes, like those involving multi-dimensional selflocalized solitary waves (nonlocal solitons), are marginally explored for what concerns quantum features. We study the dynamics of 3D+1 solitons in the second-quantized nonlocal nonlinear Schrödinger 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 of the quantum diffusion of the soliton parameters and the stable invariant propagation. The fluctuations and the non-Gaussianity are universal effects expected for any nonlocality and dimensionality.

show abstract

Multidimensional self-trapping in linear and nonlinear potentials

Cited by 3 publications

References 109 publications

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger–Newton nonlocal soliton

Quantum Droplet in Lower Dimensions

Random walk and non-Gaussianity of the 3D second-quantized Schrödinger-Newton nonlocal soliton

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