In this paper, we propose some efficient and robust numerical methods to
compute the ground states and dynamics of Fractional Schr\"{o}dinger Equation
(FSE) with a rotation term and nonlocal nonlinear interactions. In particular,
a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal
interaction evaluation \cite{EMZ2015}. To compute the ground states, we
integrate the preconditioned Krylov subspace pseudo-spectral method \cite{AD1}
and the GauSum solver. For the dynamics simulation, using the rotating
Lagrangian coordinates transform \cite{BMTZ2013}, we first reformulate the FSE
into a new equation without rotation. Then, a time-splitting pseudo-spectral
scheme incorporated with the GauSum solver is proposed to simulate the new FSE

Antoine, Xavier

Tang, Qinglin

Zhang, Yong

English

arXiv

International audienceIn this paper, we propose some efficient and robust numerical methods to compute the ground states anddynamics of Fractional Schrödinger Equation (FSE) with a rotation term and nonlocal nonlinear interactions.In particular, a newly developed Gaussian-sum (GauSum) solver is used for the nonlocal interactionevaluation [33]. To compute the ground states, we integrate the preconditioned Krylov subspace pseudospectralmethod [5] and the GauSum solver. For the dynamics simulation, using the rotating Lagrangiancoordinates transform [16], we first reformulate the FSE into a new equation without rotation. Then, atime-splitting pseudo-spectral scheme incorporated with the GauSum solver is proposed to simulate the newFSE. In parallel to the numerical schemes, we also prove some existence and nonexistence results for theground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentumand the center of mass, are stated. The ground states properties with respect to the fractional orderand/or rotating frequencies, dynamics involving decoherence and turbulence together with some interestingphenomena are reported

HAL-Rennes 1

On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions

INRIA a CCSD electronic archive server

HAL - Normandie Université