Results 61 to 70 of about 15,069 (140)

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, V. V. Konotop, Valeriy A. Brazhnyi, Vladimir V. Konotop, Víctor M. Pérez-García   +4 more
core   +1 more source

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, Yanghong Huang, Zeng Liu, Vitaly Moroz   +3 more
wiley   +1 more source

Derivation of the Gross-Pitaevskii dynamics through renormalized excitation number operators

Forum of Mathematics, Sigma
We 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

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, Danchin, Raphael, Smets, Didier   +2 more
core   +6 more sources

Optical Soliton Structure Solutions, Sensitivity, and Modulation Stability Analysis in the Chiral Nonlinear Schrödinger Equation With Bohm Potential

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, Shah Muhammad, Muhammad Shakeel, Baboucarr Ceesay, Ivan Giorgio   +4 more
wiley   +1 more source

Quantum field effects in coupled atomic and molecular Bose-Einstein condensates

, 2001
This paper examines the parameter regimes in which coupled atomic and molecular Bose-Einstein condensates do not obey the Gross-Pitaevskii equation. Stochastic field equations for coupled atomic and molecular condensates are derived using the functional ...
B. Levi, D. J. Heinzen, D. Walls, E. A. Burt, E. P. Gross, J. J. Hope, J. J. Hope, J. J. Hope, J. Javanainen, J. Javanainen, K. Góral, L. P. Pitaevskii, M. H. Anderson, M. Holland, M. J. Steel, M. K. Olsen, M. K. Olsen, M. K. Olsen, M. K. Olsen, M. K. Olsen, M. Mackie, P. D. Drummond, P. D. Drummond, P. D. Drummond, P. S. Julienne, R. Graham, R. Graham, R. J. Ballagh, R. Onofrio, R. Wynar, U. V. Poulsen   +30 more
core   +2 more sources

Exploring Solitons and Modulation Instability in the Nonlinear Fractional Coupled Painlevé–Burgers Model

Journal of Mathematics, Volume 2025, Issue 1, 2025.
This work reveals the novel types of exact solitons for the coupled (2 + 1)‐dimensional Painlevé’s–Burgers model in the sense of novel fractional derivative. To gain the different kinds of exact solitons, we utilized the modified extended direct algebraic technique.
Waseem Razzaq, Asim Zafar, Naif Almusallam, Fawaz Khaled Alarfaj, Pramita Mishra   +4 more
wiley   +1 more source

Coupling Dynamics and Linear Polarization Phenomena in Codirectional Polariton Waveguide Couplers

Advanced Optical Materials, Volume 12, Issue 33, November 25, 2024.
Rozas and co‐workers examine integrated devices utilizing polariton waveguides, forming codirectional couplers. With appropriate parameters, the transfer of polariton condensates between the arms is triggered and tunable Josephson‐type oscillations arise.
Elena Rozas, Alexey Yulin, Sebastian Klembt, Sven Höfling, María Dolores Martín, Luis Viña   +5 more
wiley   +1 more source

Using Artificial Neural Networks to Solve the Gross–Pitaevskii Equation

Axioms
The current work proposes the incorporation of an artificial neural network to solve the Gross–Pitaevskii equation (GPE) efficiently, using a few realistic external potentials.
Ioannis G. Tsoulos, Vasileios N. Stavrou, Dimitrios Tsalikakis   +2 more
doaj   +1 more source

Berry phases for the nonlocal Gross-Pitaevskii equation with a quadratic potential

, 2005
A countable set of asymptotic space -- localized solutions is constructed by the complex germ method in the adiabatic approximation for the nonstationary Gross -- Pitaevskii equation with nonlocal nonlinearity and a quadratic potential.
A V Shapovalov, A Yu Trifonov, Bang O Krolikowski W Wyller J Rasmussen J J, Belov V V, Belov V V, Belov V V, Berry M V, Berry M V, Biswas S N, Chen Z-D Liang J-Q Shen S-Q Xie W F, Deconinck B Kutz J N, Dodonov V V, F N Litvinets, Ginibre J, Gross E P, Hannay J H, Hartree D R, Hartree D R, Hartree D R, Hayashi N, Kivshar Y S, Klyshko D N, Landau L D, Lisok A L, Lisok A L, Maslov V P, Maslov V P, Messia A, Pitaevskii L P, Pitaevskii L P, Pitaevskii L P, Shchesnovich V S, Trifonov A Yu, Vinitskii S I, Yakubovich V A, Zakharov V E, Zakharov V E   +36 more
core   +1 more source