Paper Info
Title
On the ground states and dynamics of space fractional nonlinear Schrödinger/Gross-Pitaevskii equations with rotation term and nonlocal nonlinear interactions.
Abstract
In this paper, we propose some efficient and robust numerical methods to compute the ground states and dynamics 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 interaction evaluation 31. To compute the ground states, we integrate the preconditioned Krylov subspace pseudo-spectral method 4 and the GauSum solver. For the dynamics simulation, using the rotating Lagrangian coordinates transform 14, 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. In parallel to the numerical schemes, we also prove some existence and nonexistence results for the ground states. Dynamical laws of some standard quantities, including the mass, energy, angular momentum and the center of mass, are stated. The ground states properties with respect to the fractional order and/or rotating frequencies, dynamics involving decoherence and turbulence together with some interesting phenomena are reported.
Year
DOI
Venue
2016
10.1016/j.jcp.2016.08.009
J. Comput. Physics
Keywords
Field
DocType
Fractional Schrödinger equation,Rotation,Nonlocal nonlinear interaction,Rotating Lagrangian coordinates,Gaussian-sum solver,Ground state,Dynamics
Krylov subspace,Angular momentum,Mathematical optimization,Nonlinear system,Lagrangian and Eulerian specification of the flow field,Mathematical analysis,Schrödinger equation,Solver,Numerical analysis,Center of mass,Classical mechanics,Mathematics
Journal
Volume
Issue
ISSN
325
C
0021-9991
Citations 
PageRank 
References 
7
0.50
22
Authors
3
Name
Order
Citations
PageRank
Xavier Antoine125132.52
Qinglin Tang2537.29
Yong Zhang3294.56