منابع مشابه
On the Gross-Pitaevskii equation for trapped dipolar quantum gases
We study the time-dependent Gross–Pitaevskii equation describing Bose–Einstein condensation of trapped dipolar quantum gases. Existence and uniqueness as well as the possible blow-up of solutions are studied. Moreover, we discuss the problem of dimension-reduction for this nonlinear and nonlocal Schrödinger equation.
متن کاملRigorous derivation of the Gross-Pitaevskii equation.
The time-dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schrödinger equation with a short-scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short-scale correlation structure in the condensate.
متن کاملStochastic Fluctuations in the Gross-pitaevskii Equation
Abstract. We study from a mathematical point of view a model equation for Bose Einstein condensation, in the case where the trapping potential varies randomly in time. The model is the so called Gross-Pitaevskii equation, with a quadratic potential with white noise fluctuations in time. We prove the existence of solutions in 1D and 2D in the energy space. The blowup phenomenon is also discussed...
متن کاملHaus/Gross-Pitaevskii equation for random lasers
Marco Leonetti, and Claudio Conti, 1 Dep. of Physics, University “Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy 2 CNR-ISC Institute for Complex Systems Dep. of Physics, University “Sapienza”, Piazzale Aldo Moro 2, 00185 Roma, Italy and ∗Corresponding author: [email protected], current address: Photonic Crystal Group, ICMM,C.Sor Juana Ins de la Cruz, 3, Cantoblanco, 28049 Madrid, Spain.
متن کاملVortex helices for the Gross-Pitaevskii equation
We prove the existence of travelling vortex helices to the Gross-Pitaevskii equation in R. These solutions have an infinite energy, are periodic in the direction of the axis of the helix and have a degree one at infinity in the orthogonal direction. Résumé : Nous prouvons l’existence d’ondes progressives à vorticité sur une hélice pour l’équation de GrossPitaevskii dans R. Ces solutions sont d’...
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ژورنال
عنوان ژورنال: SciPost Physics
سال: 2017
ISSN: 2542-4653
DOI: 10.21468/scipostphys.3.1.006