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Rossignolo, Marco (2017) Localization transitions in coupled Aubry-André chains. [Magistrali biennali]

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Abstract

The Aubry–André model admits a localization transition from delocalized to localized states in one dimension. A way to characterize the critical transition is through the fractal dimension. We show that this quantity depends on the energy of the system for the existence of almost localized states near the band edges. Starting from the study of the effects of the next-nearest-neighbor (NNN) hopping in the Aubry-André chain, that presents a mobility edge in the energy, we consider two weakly coupled chains with three different geometries, i.e. square, square with shift and triangular lattice. Using the inverse participation ratio (IPR) as an indicator of the degree of localization, we determine numerically at which critical strength of the potential parameter the localization transition occurs. Whereas the square geometry can be mapped into two identical standard Aubry-André chains, for square with shift and triangular lattices we show that there is a regime of parameters in the spectrum where extended and localized states coexist. The numerical analysis are supported by analytical calculations using in particular Frohlich transformation.

Item Type:Magistrali biennali
Uncontrolled Keywords:Quasi-disordered, Aubry-André, mobility edge, weak coupling, localization transition
Subjects:Area 02 - Scienze fisiche > FIS/03 Fisica della materia
Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Codice ID:57006
Relatore:Dell'Anna, Luca
Data della tesi:September 2017
Biblioteca:Polo di Scienze > Dip. Fisica e Astronomia "Galileo Galilei" - Biblioteca
Tipo di fruizione per il documento:on-line per i full-text
Tesi sperimentale (Si) o compilativa (No)?:Yes

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