Results 101 to 110 of about 32,263 (260)
Defect modes of a Bose-Einstein condensate in an optical lattice with a localized impurity
, 2006 We study defect modes of a Bose-Einstein condensate in an optical lattice with a localized defect within the framework of the one-dimensional Gross-Pitaevskii equation.
A. I. Anselm +4 more
core +1 more source
Symmetry, 2020 We propose an approach to constructing semiclassical solutions for the generalized multidimensional Gross–Pitaevskii equation with a nonlocal interaction term. The key property of the solutions is that they are concentrated on a one-dimensional manifold (
A. V. Shapovalov +2 more
semanticscholar +1 more source
Domain Walls in the Coupled Gross–Pitaevskii Equations [PDF]
Archive for Rational Mechanics and Analysis, 2014 A thorough study of domain wall solutions in coupled Gross-Pitaevskii equations on the real line is carried out including existence of these solutions; their spectral and nonlinear stability; their persistence and stability under a small localized potential. The proof of existence is variational and is presented in a general framework: we show that the
Alama, Stan +3 more
openaire +2 more sources
Numerical solution to the time-independent gross-Pitaevskii Equation
Journal of Applied Science and Engineering A, 2021 We solve the time-independent Gross-Pitaevskii equation modeling the Bose-Einstein condensate trapped in an anistropic harmonic potential using a pseudospectral method. Numerically obtained values for an energy and a chemical potential for the condensate with positive and negative scattering length have been compared with those from the literature. The
Tsednee, Tsogbayar +2 more
openaire +3 more sources
A New Thermodynamic Approach to Multimode Fiber Self‐cleaning and Soliton Condensation
Laser &Photonics Reviews, Volume 19, Issue 6, March 18, 2025.A new thermodynamic theory for optical multimode systems is presented, based on a weighted Bose–Einstein law (wBE) and including a state equation, fundamental equation for the entropy and an accuracy metric. An experimental comparison of two propagation regimes of a multimode optical fiber is carried out in terms of wBE, namely the self‐cleaning in the
Mario Zitelli
wiley +1 more source
On the linear wave regime of the Gross-Pitaevskii equation
, 2008 We study a long wave-length asymptotics for the Gross-Pitaevskii equation corresponding to perturbation of a constant state of modulus one. We exhibit lower bounds on the first occurence of possible zeros (vortices) and compare the solutions with the ...
Bethuel, Fabrice +2 more
core +6 more sources
Ground states of a non‐local variational problem and Thomas–Fermi limit for the Choquard equation
Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract We study non‐negative optimisers of a Gagliardo–Nirenberg‐type inequality ∫∫RN×RN|u(x)|p|u(y)|p|x−y|N−αdxdy⩽C∫RN|u|2dxpθ∫RN|u|qdx2p(1−θ)/q,$$\begin{align*} & \iint\nolimits _{\mathbb {R}^N \times \mathbb {R}^N} \frac{|u(x)|^p\,|u(y)|^p}{|x - y|^{N-\alpha }} dx\, dy\\ &\quad \leqslant C{\left(\int _{{\mathbb {R}}^N}|u|^2 dx\right)}^{p\theta } {\
Damiano Greco +3 more
wiley +1 more source
The stochastic Gross-Pitaevskii equation and some applications [PDF]
Laser Physics, 2009 14 pages, 9 figures.
Cockburn SP, Proukakis NP
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Advances in Mathematical Physics, Volume 2025, Issue 1, 2025.This study examines the optical soliton structure solutions, sensitivity, and modulation stability analysis of the chiral nonlinear Schrödinger equation (NLSE) with Bohm potential, a basic model in nonlinear optics and quantum mechanics. The equation represents wave group dynamics in numerous physical systems, involving quantum Hall and nonlinear ...
Ishrat Bibi +4 more
wiley +1 more source
Derivation of the Gross-Pitaevskii dynamics through renormalized excitation number operators
Forum of Mathematics, SigmaWe revisit the time evolution of initially trapped Bose-Einstein condensates in the Gross-Pitaevskii regime. We show that the system continues to exhibit BEC once the trap has been released and that the dynamics of the condensate is described by the time-
Christian Brennecke, Wilhelm Kroschinsky
doaj +1 more source