Multifractality of quantum wave functions in the presence of perturbations

Abstract

We present a comprehensive study of the destruction of quantum multifractality in the presence of perturbations. We study diverse representative models displaying multifractality, including a pseudointegrable system, the Anderson model and a random matrix model. We apply several types of natural perturbations which can be relevant for experimental implementations. We construct an analytical theory for certain cases, and perform extensive large-scale numerical simulations in other cases. The data are analyzed through refined methods including double scaling analysis. Our results confirm the recent conjecture that multifractality breaks down following two scenarios. In the first one, multifractality is preserved unchanged below a certain characteristic length which decreases with perturbation strength. In the second one, multifractality is affected at all scales and disappears uniformly for a strong enough perturbation. Our refined analysis shows that subtle variants of these scenarios can be present in certain cases. This study could guide experimental implementations in order to observe quantum multifractality in real systems.

20 pages, 27 figures

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• Higher order spacing ratios in random matrix theory and complex quantum systems
• Quantum localization measures in phase space
• Chaos-Assisted Long-Range Tunneling for Quantum Simulation
• Multifractality of open quantum systems
• Symmetry Violation of Quantum Multifractality: Gaussian fluctuations versus Algebraic Localization
• Quantum multifractality as a probe of phase space in the Dicke model
• Coherent Forward Scattering Peak and Multifractality