Stationary States for Nonlinear Schrodinger Equations with Periodic Potentials

被引：8

作者：

Fukuizumi, Reika ^{[1
]}

Sacchetti, Andrea ^{[2
]}

机构：

[1] Tohoku Univ, Grad Sch Informat Sci, Sendai, Miyagi 9808579, Japan

[2] Univ Modena & Reggio Emilia, Dept Phys Comp Sci & Math, Modena, Italy

来源：

JOURNAL OF STATISTICAL PHYSICS | 2014年 / 156卷 / 04期

关键词：

Nonlinear Schrodinger and Discrete Nonlinear Schrodinger equations; Semiclassical approximation; Bose-Einstein condensates in periodic lattices; DISCRETE SOLITONS; LOCALIZED MODES;

D O I：

10.1007/s10955-014-1023-x

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

In this paper we consider a one-dimensional non-linear Schrodinger equation with a periodic potential. In the semiclassical limit we prove the existence of stationary solutions by means of the reduction of the non-linear Schrodinger equation to a discrete non-linear Schrodinger equation. In particular, in the limit of large nonlinearity strength the stationary solutions turn out to be localized on a single lattice site of the periodic potential. A connection of these results with the Mott insulator phase for Bose-Einstein condensates in a one-dimensional periodic lattice is also discussed.

引用

页码：707 / 738

页数：32

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