Differentiable potentials and metallic states in disordered one-dimensional systems

Abstract

We provide evidence that as a general rule Anderson localization effects become weaker as the degree of differentiability of the disordered potential increases. In one dimension a band of metallic states exists provided that the disordered potential is sufficiently correlated and has some minimum degree of differentiability. Several examples are studied in detail. In agreement with the one parameter scaling theory the motion in the metallic region is ballistic if the spectral density is smooth. Finally, we study the most promising settings to observe these results in the context of cold atoms.

5 pages, 3 figures, journal version

References in corpus (12)

• Anderson localization of a non-interacting Bose-Einstein condensate
• Direct observation of Anderson localization of matter-waves in a controlled disorder
• Localization and Mobility Edge in One-Dimensional Potentials with Correlated Disorder
• Transition from localized to extended eigenstates in the ensemble of power-law random banded matrices
• Anderson Localization of Expanding Bose-Einstein Condensates in Random Potentials
• Non-universality of Anderson localization in short-range correlated disorder
• Absolute Continuity of the Integrated Density of States for the Almost Mathieu Operator with Non-Critical Coupling
• Delocalisation phenomena in one-dimensional models with long-range correlated disorder: a perturbative approach
• Effect of Long Range Disorder on Electron Motion in Two Dimensions
• Multifractality of Hamiltonians with power-law transfer terms
• Fractional derivatives of random walks: Time series with long-time memory
• On the statistics of superlocalized states in self-affine disordered potentials

Cited by in corpus (23)

• Anomalous Localization in Low-Dimensional Systems with Correlated Disorder
• One-dimensional quasicrystals with power-law hopping
• Self-dual quasiperiodic systems with power-law hopping
• Lyapunov exponent for the laser speckle potential: a weak disorder expansion
• Induced Delocalization by Correlation and Interaction in the one-dimensional Anderson Model
• Anticorrelations from power-law spectral disorder and conditions for an Anderson transition
• Anderson localization and momentum-space entanglement
• A proposed signature of Anderson localization and correlation-induced delocalization in an N-leg optical lattice
• Tailoring Anderson localization by disorder correlations in 1D speckle potentials
• Supersymmetry method for interacting chaotic and disordered systems: the SYK model
• Correlation-Strength Driven Anderson Metal-Insulator Transition
• Lyapunov exponents in 1d disordered system with long-range memory
• Localization in fractal and multifractal media
• Generalized Lyapunov Exponent and Transmission Statistics in One-dimensional Gaussian Correlated Potentials
• Iterative Method for Generating Correlated Binary Sequences
• The Role of Power-Law Correlated Disorder in the Anderson Metal-Insulator Transition
• A Metal-Insulator transition induced by Random Dipoles
• Numerical study of the transverse localization of waves in one-dimensional lattices with randomly distributed gain and loss: Effect of disorder correlations
• Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping
• Non-Gaussian Spatial Correlations Dramatically Weaken Localization
• Localization in One-Dimensional Tight-Binding Model with Chaotic Binary Sequences
• Universal scheme to generate metal-insulator transition in disordered systems
• Delocalization in One-Dimensional Tight-Binding Models with Fractal Disorder II: Existence of Mobility Edge