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Mathematics > Spectral Theory

arXiv:1811.09692 (math)
[Submitted on 23 Nov 2018 (v1), last revised 24 Dec 2018 (this version, v2)]

Title:Anderson localization for two interacting quasiperiodic particles

Authors:Jean Bourgain, Ilya Kachkovskiy
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Abstract:We consider a system of two discrete quasiperiodic 1D particles as an operator on $\ell^2(\mathbb Z^2)$ and establish Anderson localization at large disorder, assuming the potential has no cosine-type symmetries. In the presence of symmetries, we show localization outside of a neighborhood of finitely many energies. One can also add a deterministic background potential of low complexity, which includes periodic backgrounds and finite range interaction potentials. Such background potentials can only take finitely many values, and the excluded energies in the symmetric case are associated to those values.
Comments: Some notation has been revised, and the referee's suggestions addressed. The result now covers a larger class of interaction potentials. To appear in Geometric and Functional Analysis
Subjects: Spectral Theory (math.SP); Mathematical Physics (math-ph)
Cite as: arXiv:1811.09692 [math.SP]
  (or arXiv:1811.09692v2 [math.SP] for this version)
  https://doi.org/10.48550/arXiv.1811.09692

Submission history

From: Ilya Kachkovskiy [view email]
[v1] Fri, 23 Nov 2018 21:13:37 UTC (36 KB)
[v2] Mon, 24 Dec 2018 17:59:23 UTC (37 KB)
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