Stationary states of a nonlinear Schrödinger lattice with a harmonic trap

Effects of finite curvature on soliton dynamics in nonlinear Schrödinger models

For a curved chain of nonlinear oscillators it is shown that the interplay of curvature and nonlinearity may lead to symmetry breaking when an asymmetric stationary state becomes energetically more favorable than a symmetric stationary state. This phenomenon is studied analytically for a minimal model which effectively takes into account both mechanisms of localization: linear and nonlinear one...

Stability of Stationary Solutions of the Schrödinger-langevin Equation

The stability properties of a class of dissipative quantum mechanical systems are investigated. The nonlinear stability and asymptotic stability of stationary states (with zero and nonzero dissipation respectively) is investigated by Liapunov’s direct method. The results are demonstrated by numerical calculations on the example of the damped harmonic oscillator.

Generation and detection of matter-wave gap vortices in optical lattices

We analyze numerically the process of dynamical generation of spatially localized vortices in Bose-Einstein condensates BEC’s with repulsive atomic interactions confined by two-dimensional optical lattices. Akin to bright solitons in a repulsive condensate, these nonlinear localized states exist only within the gaps of the matter-wave band-gap spectrum imposed by the periodicity of the lattice ...

Stationary states of the two-dimensional nonlinear Schrödinger model with disorder

Numerical Solutions of the Schrödinger Equation

for the energy eigenvalues En and the associated energy eigenfunctions (stationary states) Ψn. There are a number of important cases for which the stationary Schrödinger equation can be solved analytically, e.g., the harmonic oscillator (in any number of dimensions) and the hydrogen atom. However, in most cases of practical interest (in, e.g., atomic, molecular, and solid-state physics) exact o...