Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · cond-mat/9901156

Electronic and dynamic properties of a one-dimensional Thue-Morse chain

Gi-Yeong Oh
View original source ↗Read source document ↗Export metadata ↓

Abstract

We study the electronic and dynamic properties of a one-dimensional Thue-Morse chain within the framework of the transfer model. By means of direct diagonalization of the Hamiltonian matrix we first show that the trace map of the transfer matrices is exactly the same as that in the diagonal model. Then, by calculating several quantities such as the wave function, the Lyapunov exponent, and the Landauer resistivity, we show that all the electronic states are extended despite the singular continuity of the energy spectrum. Our results indicate that the electronic properties of the Thue-Morse chain is independent of the kind of the model, which is contrary to the result of Chakrabarti et al. [Phys. Rev. Lett. 74, 1403 (1995)]. To deepen our understanding, we study the dynamics of an electronic wave packet and show that the wave packet spreads superdiffusively for long times with dynamic indices intermediate between periodic and quasiperiodic chains. Several features of dynamics distinctive from the case of the Fibonacci chain are discussed. We also study the effects of electron-phonon interaction on the dynamics of the wave packet by taking into account a kind of nonlinear interaction. Degree of dynamic localization is shown to be crucially dependent on the strength of the hopping energy and the nonlinear interaction parameter.

Explore related subjects

cond-mat.dis-nncond-mat.soft

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Gi-Yeong Oh. 1999-01-18. Electronic and dynamic properties of a one-dimensional Thue-Morse chain. https://arxiv.org/abs/cond-mat/9901156

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Irrationality Measure Controls Long-Wavelength Charge Fluctuations in Quasiperiodic Systems

Quasiperiodic order is characterized by irrational frequencies whose rational approximability known as irrationality measure defines distinct arithmetic classes. We establish that this arithmetic classification has direct physical consequences for long-wavelength charge fluctuations. In translation-covariant quasiperiodic systems, the infrared scaling of charge fluctuation is governed by the interplay between the irrationality exponent of irrational frequency and the large-harmonic decay of the hull charge profile: the latter determines the available charge weight, while the former controls how efficiently that weight is transferred to the infrared. Consequently, all algebraic irrational frequencies share the same arithmetic scaling, whereas exceptionally well-approximable transcendental frequencies can exhibit strongly enhanced infrared fluctuation scaling. We further prove that occupied states separated from the Fermi level by a gap stable throughout the hull contribute only an analytic infrared background, leaving the nontrivial scaling to near-Fermi states. Our results extend to general translation-covariant multi-frequency quasiperiodic systems.

cond-mat.dis-nn↗
arXiv2026

Curvature-Induced Geometric Universality in Non-Hermitian Anderson Transitions

In Euclidean space, universality classes of Anderson transitions are primarily determined by symmetry and spatial dimensionality. Here, we present evidence for a geometry-controlled universality class of non-Hermitian Anderson transitions on hyperbolic-like lattices. In this setting, critical behavior is influenced by the large-scale hyperbolic geometry, characterized by negative curvature, exponential volume growth, and a non-Euclidean notion of spatial scaling. Finite-size scaling of participation ratios across several distinct \( \{p,q\} \) tilings reveals one-parameter scaling collapses with a common critical exponent \( \nu\simeq1 \) within numerical accuracy. A complementary phenomenological coarse-grained Landau-Ginzburg analysis shows how exponential correlation-volume growth suppresses critical fluctuations, offering a rationale for the observed mean-field-like scaling. Our results suggest that spatial curvature can act as an additional organizing principle for Anderson-transition universality beyond the conventional dimensionality- and symmetry-based classification.

cond-mat.dis-nn↗
arXiv2026

Finite-rank multiplicative perturbations of rotationally invariant non-Hermitian random matrices

We study finite-rank multiplicative deformations of rotationally invariant non-Hermitian random matrices. More precisely, we consider models of the form $\mathbf{A}(\mathbf{I}+\mathbf{T})$, where $\mathbf{A}$ is a large rotationally invariant non-Hermitian random matrix, $\mathbf{T}$ is a finite-rank normal perturbation, and $\mathbf{I}$ denotes the identity matrix. We characterize the emergence of outlier eigenvalues, their fluctuations, and the associated eigenvector overlaps. Our results provide a multiplicative non-Hermitian counterpart to the classical Baik--Ben Arous--P\'ech\'e framework.

cond-mat.dis-nn↗