Localization studies for ground states of the Gross‐Pitaevskii equation. Issue 1 (17th December 2018)

• Record Type: Journal Article
• Authors: Altmann, Robert; Peterseim, Daniel; Varga, Dora
• Other Names: Müller G. guestEditor.; Ulbrich M. guestEditor.
• Is Part Of: Proceedings in applied mathematics and mechanics. Volume 18:Issue 1(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-12-17
• Subjects: Applied mathematics -- Periodicals; Engineering mathematics -- Periodicals; Mathematical physics -- Periodicals; 519
• DOI: 10.1002/pamm.201800343
• Languages: English
• ISSNs: 1617-7061

Abstract

Abstract: For oscillatory high‐amplitude potentials it is known that the linear Schrödinger operator leads to exponentially localized ground states. This localization result can be quantified explicitly in terms of geometric parameters and the degree of disorder within the potential. In the present paper we study the influence of the amplitude and the importance of the periodicity in the nonlinear setting of the Gross‐Pitaevskii equation which models ultracold bosonic gases.