TY - JOUR
T1 - Stationary States for Nonlinear Schrödinger Equations with Periodic Potentials
AU - Fukuizumi, Reika
AU - Sacchetti, Andrea
N1 - Funding Information:
Acknowledgments The authors thank the referee for reading carefully the manuscript and giving many helpful comments to improve the demonstration. One of us (A.S.) is grateful for the hospitality of the Tohoku University where part of this paper was written. This work is supported by JSPS KAKENHI Grant Number 24740079. A.S. is partially supported by GNFM-INdAM.
PY - 2014/7
Y1 - 2014/7
N2 - In this paper we consider a one-dimensional non-linear Schrödinger 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 Schrödinger equation to a discrete non-linear Schrödinger 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.
AB - In this paper we consider a one-dimensional non-linear Schrödinger 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 Schrödinger equation to a discrete non-linear Schrödinger 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.
KW - Bose-Einstein condensates in periodic lattices
KW - Nonlinear Schrödinger and Discrete Nonlinear Schrödinger equations
KW - Semiclassical approximation
UR - http://www.scopus.com/inward/record.url?scp=84903701159&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84903701159&partnerID=8YFLogxK
U2 - 10.1007/s10955-014-1023-x
DO - 10.1007/s10955-014-1023-x
M3 - Article
AN - SCOPUS:84903701159
VL - 156
SP - 707
EP - 738
JO - Journal of Statistical Physics
JF - Journal of Statistical Physics
SN - 0022-4715
IS - 4
ER -