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Localization studies for ground states of the Gross‐Pitaevskii equation
Author(s) -
Altmann Robert,
Peterseim Daniel,
Varga Dora
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800343
Subject(s) - gross–pitaevskii equation , amplitude , nonlinear system , operator (biology) , physics , nonlinear schrödinger equation , exponential growth , mathematics , classical mechanics , quantum mechanics , mathematical physics , chemistry , biochemistry , repressor , transcription factor , gene
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.