Fluctuation-stable generalized entropy probes of spectral heterogeneity

Abstract

Generalized entropy measures are widely used to characterize localization and multifractality, and the regime \(q>1\) is often empirically found to exhibit improved numerical stability and cleaner scaling behavior. Here, we develop a fluctuation-stability framework for generalized entropy diagnostics and show that weak-amplitude spectral fluctuations are amplified for \(q<1\) and suppressed for \(q>1\), thereby providing a theoretical basis for the physically robust \(q>1\) regime. A thermodynamic scaling analysis further identifies an asymptotically stable regime beyond a critical threshold. As an application, we introduce the entropy-gradient susceptibility \(χ_q\) as a coarse-grained probe of spectral heterogeneity. Using the Aubry-André and generalized Aubry-André models, we demonstrate that \(χ_q\) sharply distinguishes homogeneous localization transitions from mobility-edge coexistence regimes. Our results establish fluctuation stability as a guiding principle for generalized entropy diagnostics in quasiperiodic systems.

arXiv commentFinal version: 9 pages, 3 figures, Accepted for publication in Phys. Lett. A

References in corpus (17)

• Nearest neighbor tight binding models with an exact mobility edge in one dimension
• Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• One dimensional quasiperiodic mosaic lattice with exact mobility edges
• One-dimensional quasicrystals with power-law hopping
• Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
• Reentrant Localization Transition in a Quasiperiodic Chain
• Anomalous mobility edges in one-dimensional quasiperiodic models
• Statistics of Lyapunov exponent in 1-D random periodic-on-average systems
• Self-dual quasiperiodic systems with power-law hopping
• Non-equilibrium phase diagram of a 1D quasiperiodic system with a single-particle mobility edge
• Fraction of delocalized eigenstates in the long-range Aubry-André-Harper model
• Hidden dualities in 1D quasiperiodic lattice models
• Localization transition in weakly-interacting Bose superfluids in one-dimensional quasiperdiodic lattices
• Scrambling and Lyapunov Exponent in Unitary Networks with Tunable Interactions
• Electronic properties of the 1D Frenkel-Kontorova model
• Comment on ``Periodic wave functions and number of extended states in random dimer systems'