Hyperuniformity and anti-hyperuniformity in one-dimensional substitution tilings

This work considers the scaling properties characterizing the hyperuniformity (or anti-hyperuniformity) of long-wavelength fluctuations in a broad class of one-dimensional substitution tilings. A simple argument is presented which predicts the exponent α governing the scaling of Fourier intensities at small wavenumbers, tilings with α > 0 being hyperuniform, and numerical computations confirm that the predictions are accurate for quasiperiodic tilings, tilings with singular continuous spectra and limit-periodic tilings. Quasiperiodic or singular continuous cases can be constructed with α arbitrarily close to any given value between −1 and 3. Limit-periodic tilings can be constructed with α between −1 and 1 or with Fourier intensities that approach zero faster than any power law.

On the Nature of Electronic Wave Functions in One-Dimensional Self-Similar and Quasiperiodic Systems

The interest in the precise nature of critical states and their role in the physics of aperiodic systems has witnessed a renewed interest in the last few years. In this work we present a review on the notion of critical wave functions and, in the light of the obtained results, we suggest the convenience of some conceptual revisions in order to properly describe the relationship between the transport properties and the wave functions distribution amplitudes for eigen functions belonging to singular continuous spectra related to both fractal and quasiperiodic distribution of atoms through the space.

STABLE CONTINUOUS SPECTRA FOR DIFFERENTIAL OPERATORS OF ARBITRARY ORDER

Perturbations of the continuous spectra of two self-adjoint operators H0 and H can be controlled by sandwiched differences of the form [Formula: see text] where ϕj(·) are bounded functions of the operators involved. If ϕj(H0) and ϕj(H) are integral operators, we give general integral conditions for the kernels, such that the continuous, the absolutely continuous and the singular continuous spectra of H0 and H coincide. The abstract operator theoretical conditions are applied for H0 in L 2(ℝd) of the form (-Δ)α/2, α∈ (0,2) and (-Δ)m, m∈ℕ. H is given as a perturbation of H0, where we allow perturbations by variable coefficients, potentials or obstacles.

STRANGE NONCHAOTIC ATTRACTORS FROM PERIODICALLY EXCITED CHUA'S CIRCUIT

In this paper, we discuss the existence of strange nonchaotic attractors for the Chua's circuit with periodical excitation. We have studied the Lyapunov exponents, Poincaré maps, singular continuous spectra of characterizing the attractors. The results show that the excited Chua's circuit does indeed have the strange nonchaotic behaviors.