Anderson Localization in Quantum Chaos: Scaling and Universality

• Authors: A. García-García , J. Wang
• Languages of publication: EN

Abstracts

EN

The one-parameter scaling theory is a powerful tool to investigate Anderson localization effects in disordered systems. In this paper we show that this theory can be adapted to the context of quantum chaos provided that the classical phase space is homogeneous, not mixed. The localization problem in this case is defined in momentum, not in real space. We then employ the one-parameter scaling theory to: (a) propose a precise characterization of the type of classical dynamics related to the Wigner-Dyson and Poisson statistics which also predicts in which situations Anderson localization corrections invalidate the relation between classical chaos and random matrix theory encoded in the Bohigas-Giannoni-Schmit conjecture, (b) to identify the universality class associated with the metal-insulator transition in quantum chaos. In low dimensions it is characterized by classical superdiffusion, in higher dimensions it has in general a quantum origin as in the case of disordered systems. We illustrate these two cases by studying 1d kicked rotors with non-analytical potentials and a 3d kicked rotor with a smooth potential.

Keywords

EN

72.15.Rn; 71.30.+h; 05.45.Df; 05.40.-a

Discipline

• 05.45.Df: Fractals(see also 47.53.+n Fractals in fluid dynamics; 61.43.Hv Fractals; macroscopic aggregates in structure of solids)
• 71.30.+h: Metal-insulator transitions and other electronic transitions
• 72.15.Rn: Localization effects (Anderson or weak localization)
• 05.40.-a: Fluctuation phenomena, random processes, noise, and Brownian motion(for fluctuations in superconductivity, see 74.40.-n; for statistical theory and fluctuations in nuclear reactions, see 24.60.-k; for fluctuations in plasma, see 52.25.Gj; for nonlinear dynamics and chaos, see 05.45.-a)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2007
• Volume: 112
• Issue: 4
• Pages: 635-653

Dates

published

2007-10

received

2007-05-25

Contributors

author

A. García-García

• Physics Department, Princeton University, Princeton, New Jersey 08544, USA
• The Abdus Salam International Centre for Theoretical Physics, P.O.B. 586, 34100 Trieste, Italy

author

J. Wang

• Temasek Laboratories, National University of Singapore, 117542 Singapore
• Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Systems, National University of Singapore, 117542 Singapore

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Identifiers

DOI

10.12693/APhysPolA.112.635