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On Tight‐Binding Approximations in Optical Lattices
Author(s) -
Ablowitz Mark J.,
Curtis Christopher W.,
Zhu Yi
Publication year - 2012
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2012.00558.x
Subject(s) - tight binding , nonlinear system , lattice (music) , simple (philosophy) , work (physics) , physics , mathematics , statistical physics , quantum mechanics , electronic structure , philosophy , epistemology , acoustics
The validity of using the tight‐binding approximation for the nonlinear Schrödinger equations with a two‐dimensional optical lattice is considered. This work provides a rigorous foundation for a technique based on “orbital” functions that is central to solid‐state physics and nonlinear optics. Simple and honeycomb lattices are addressed, and it is therefore shown that the use of tight‐binding approximations is justified in complicated situations.