Phase space signatures of the Anderson transition

Abstract

We use the inverse participation ratio based on the Husimi function to perform a phase space analysis of the Anderson model in one, two, and three dimensions. Important features of the quantum states remain observable in phase space in the large system size limit, while they would be lost in a real or momentum space description. From perturbative approaches in the limits of weak and strong disorder, we find that the appearance of a delocalization-localization transition is connected to the coupling, by a weak potential, of momentum eigenstates which are far apart in momentum space. This is consistent with recent results obtained for the Aubry-Andre model and provides a novel view on the metal-insulator transition.

arXiv comment10 pages, 7 figures, RevTeX4

References in corpus (4)

• Statistics of energy levels and eigenfunctions in disordered systems
• Entropy and Wigner Functions
• Second moment of the Husimi distribution as a measure of complexity of quantum states
• Delocalization and Heisenberg's uncertainty relation

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• Robust quantum metrology with random Majorana constellations
• Ordered and periodic chaos of the bounded one dimensinal multibarrier potential