Bose-Einstein condensation: Twenty years after

Bagnato, V. S.; Frantzeskakis, D. J.; Kevrekidis, P. G.; Malomed, B. A.; Mihalache, D.

doi:10.48550/arxiv.1502.06328

Cited by 7 publications

(10 citation statements)

References 243 publications

(332 reference statements)

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“…These constants are prescribed whereas the parameters λ 1 and λ 2 are unknown and will appear as Lagrange multipliers. The system comes from mean field models for binary mixtures of Bose-Einstein condensates or for binary gases of fermion atoms in degenerate quantum states (Bose-Fermi mixtures, Fermi-Fermi mixtures); see [1,5,14,25] and the references therein. The most famous case is the one of coupled Gross-Pitaevskii equations in dimension N ≤ 3 where p 1 = p 2 = 4, r 1 = r 2 = 2 modeling Bose-Einstein condensation.…”

Section: Introductionmentioning

confidence: 99%

Normalized solutions for nonlinear Schrödinger systems

Bartsch¹,

Jeanjean

2017

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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We consider the existence of normalized solutions in H 1 (R N ) × H 1 (R N ) for systems of nonlinear Schrödinger equations which appear in models for binary mixtures of ultracold quantum gases. Making a solitary wave ansatz one is led to coupled systems of elliptic equations of the formand we are looking for solutions satisfyingwhere a 1 > 0 and a 2 > 0 are prescribed. In the system λ 1 and λ 2 are unknown and will appear as Lagrange multipliers. We treat the case of homogeneous nonlinearities, i.e.

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Section: Introductionmentioning

confidence: 99%

Normalized solutions for nonlinear Schrödinger systems

Bartsch¹,

Jeanjean

2017

Proceedings of the Royal Society of Edinburgh: Section A Mathem

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“…We describe BEC [15] by the stochastic Gross-Pitaevskii equation (sGPE) [16,17], which can be written in dimensionless form as follows:…”

Section: Modelmentioning

confidence: 99%

Stochastic phase slips in toroidal Bose-Einstein condensates

et al. 2016

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Motivated by recent experiments we study the influence of thermal noise on the phase slips in toroidal Bose-Einstein condensates with a rotating weak link. We derive a generalized Arrheniuslike expression for the rate of stochastic phase slips. We develop a method to estimate the energy barrier separating different superflow states. The parameters at which the energy barrier disappears agree with the critical parameters for deterministic phase slips obtained from dynamics simulations, which confirms the validity of our energetic analysis. We reveal that adding thermal noise lowers the phase-slip threshold. However, the quantitative impact of the stochastic phase slips turns out to be too small to explain the significant discrepancy between theoretical and the experimental results.

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“…The evolution of light propagation through periodic optical waveguides is similar, under certain conditions, to the evolution of ultracold atoms in periodic traps (see a BEC review [28] and for a study of system relaxation from nonequilibrium states [29]). A brief discussion of the conditions for similarity follows.…”

Section: Introductionmentioning

confidence: 98%

Universal correlations after thermalization in periodic nonlinear systems

Levy

Yang

Matzliah

et al. 2018

J. Phys. B: At. Mol. Opt. Phys.

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The evolution of random fields with known statistical properties is relatively straightforward to analyze in the linear regime, but becomes considerably more involved when nonlinearity, or interactions, are dominant. Previous works have shown that statistical physics techniques can be applied to predict the evolution of such systems. Here we study the evolution of random fields in a one-dimensional lattice of optical waveguides in the presence of strong nonlinearities, using the discrete nonlinear Schrödinger equation. Extending the 2009 work by Silberberg et al (Phys. Rev. Lett. 102 233904), we assume input fields with random amplitudes and phases. We derive analytic expressions for the system's statistical properties at thermodynamic equilibrium. Specifically, expressions for the probability density functions of field intensities, of fields' phase differences, and an expression for the field correlations. We express these properties in terms of the moments of the assumed statistical excitations, and verify the results with simulations. Most interestingly, we find that at thermodynamic equilibrium, correlations are formed through the interaction between sites. These exponentially decaying fields' correlations take a universal form that is essentially independent of excitation amplitudes but visibly shrink with increased spread of the exciting amplitudes. Our results are valid not only to nonlinear discrete optical systems, but extend also to the evolution of bosonic atoms in optical lattices in the high-occupancy limit that are governed by the equivalent Gross-Pitaevskii equation.

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Bose-Einstein condensation: Twenty years after

Cited by 7 publications

References 243 publications

Normalized solutions for nonlinear Schrödinger systems

Normalized solutions for nonlinear Schrödinger systems

Stochastic phase slips in toroidal Bose-Einstein condensates

Universal correlations after thermalization in periodic nonlinear systems

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