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

Stationary States for Nonlinear Schrödinger Equations with Periodic Potentials / R., Fukuizumi; Sacchetti, Andrea. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 156:(2014), pp. 707-738. [ 10.1007/s10955-014-1023-x]

Stationary States for Nonlinear Schrödinger Equations with Periodic Potentials

SACCHETTI, Andrea
2014

Abstract

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
2014
156
707
738
Stationary States for Nonlinear Schrödinger Equations with Periodic Potentials / R., Fukuizumi; Sacchetti, Andrea. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - STAMPA. - 156:(2014), pp. 707-738. [ 10.1007/s10955-014-1023-x]
R., Fukuizumi; Sacchetti, Andrea
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/1046714
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