Stability of stationary states in the cubic nonlinear Schrödinger equation: Applications to the Bose-Einstein condensate
نویسندگان
چکیده
منابع مشابه
Approximate Solutions of the Nonlinear Schrödinger Equation for Ground and Excited States of Bose-Einstein Condensates
I present simple analytical methods for computing the properties of ground and excited states of Bose-Einstein condensates, and compare their results to extensive numerical simulations. I consider the effect of vortices in the condensate for both positive and negative scattering lengths, a, and find an analytical expression for the large-N0 limit of the vortex critical frequency for a > 0, by a...
متن کاملDynamics and Stability of Bose-Einstein Condensates: The Nonlinear Schrödinger Equation with Periodic Potential
The cubic nonlinear Schrödinger equation with a lattice potential is used to model a periodic dilute gas Bose-Einstein condensate. Both twoand three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact...
متن کاملStationary states of a rotating Bose-Einstein condensate: routes to vortex nucleation.
Using a focused laser beam we stir a 87Rb Bose-Einstein condensate confined in a magnetic trap. We observe that the steady states of the condensate correspond to an elliptic cloud, stationary in the rotating frame. These steady states depend nonlinearly on the stirring parameters (amplitude and frequency), and various solutions can be reached experimentally depending on the path followed in thi...
متن کاملSolitons for nearly integrable bright spinor Bose-Einstein condensate
Using the explicit forms of eigenstates for linearized operator related to a matrix version of Nonlinear Schrödinger equation, soliton perturbation theory is developed for the $F=1$ bright spinor Bose-Einstein condensates. A small disturbance of the integrability condition can be considered as a small correction to the integrable equation. By choosing appropriate perturbation, the soli...
متن کاملInstabilities in the two-dimensional cubic nonlinear Schrödinger equation.
The two-dimensional cubic nonlinear Schrödinger equation (NLS) can be used as a model of phenomena in physical systems ranging from waves on deep water to pulses in optical fibers. In this paper, we establish that every one-dimensional traveling wave solution of NLS with linear phase is unstable with respect to some infinitesimal perturbation with two-dimensional structure. If the coefficients ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Physical Review E
سال: 2001
ISSN: 1063-651X,1095-3787
DOI: 10.1103/physreve.63.066604