کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1895867 | 1044396 | 2012 | 10 صفحه PDF | دانلود رایگان |
We consider the stationary solutions for a class of Schrödinger equations with a NN-well potential and a nonlinear perturbation. By means of semiclassical techniques we prove that the dominant term of the ground state solutions is described by a NN-dimensional Hamiltonian system, where the coupling term among the coordinates is a tridiagonal Toeplitz matrix. In particular, in the limit of large focusing nonlinearity we prove that the ground state stationary solutions consist of NN wavefunctions localized on a single well. Furthermore, we consider in detail the case of N=4N=4 wells, where we show the occurrence of spontaneous symmetry-breaking bifurcation effect.
► Semiclassical analysis of quantum systems, like BECs, in a finite lattice.
► Reduction to finite-dimensional dynamical systems by semiclassical methods.
► Explicit solution of stationary ground states obtained for four cells lattices.
► Analysis of the spontaneous symmetry bifurcation effect.
► Localization effect on a single cell lattice for large focusing nonlinearities.
Journal: Physica D: Nonlinear Phenomena - Volume 241, Issue 21, 1 November 2012, Pages 1815–1824