Periodic-Orbit Theory of Anderson Localization on Graphs

1999/09/30 by Holger Schanz, Uzy Smilansky · 4 citations
Physics and Astronomy · #Quantum chaos and dynamical systems #Quantum many-body systems #Theoretical and Computational Physics #chao-dyn #nlin.CD

paper · pdf · doi:10.1103/physrevlett.84.1427

published as Phys. Rev. Lett. 84 (2000) 1427-1430 · 4 pages, 3 figures, RevTeX

arxiv created 1999/12/15 · openalex publication_date 2000/02/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We present the first quantum system where Anderson localization is completely described within periodic-orbit theory. The model is a quantum graph analogous to an aperiodic Kronig-Penney model in one dimension. The exact expression for the probability to return to an initially localized state is computed in terms of classical trajectories. It saturates to a finite value due to localization, while the diagonal approximation decays diffusively. Our theory is based on the identification of families of isometric orbits. The coherent periodic-orbit sums within these families, and the summation over all families, are performed analytically using advanced combinatorial methods.

Citations

• The theory of impurity conduction
• Semiclassical theory of spectral rigidity

Cited by

• Topologically induced spectral behavior: the example of quantum graphs
• Phase measurement of quantum walks: application to structure theorem of the positive support of the Grover walk
• Semiclassical spectral correlator in quasi one-dimensional systems
• Degeneracies in the length spectra of metric graphs

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