Related papers: Fractal AC circuits and propagating waves on fract…
We show that certain iteration systems lead to fractal measures admitting exact orthogonal harmonic analysis.
The Fraunhofer diffraction of quantum particles from materials with sharp electron-density edges or symmetric bond structures is ubiquitous. In contrast, diffraction from atoms with characteristic asymptotically-diffused electron…
Superconducting traveling-wave parametric amplifiers are a promising amplification technology suitable for applications in submillimeter astronomy. Their implementation relies on the use of Floquet transmission lines in order to create…
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and complex dimensions posed by Lapidus and van Frankenhuijsen…
We perform a real space renormalization group analysis to study the one electron eigenstates and the transmission coefficient across a 3-simplex fractal lattice of arbitrary size, in the presence of a magnetic field. In particular, we…
Propagation of elastic waves along the axis of cylindrical shells is of great current interest due to their ubiquitous presence and technological importance. Geometric imperfections and spatial variations of properties are inevitable in…
An exact method that analytically provides transfer matrices in finite networks of quasicrystalline approximants of any dimensionality is discussed. We use these matrices in two ways: a) to exactly determine the band structure of an…
We show that every interval in the homomorphism order of finite undirected graphs is either universal or a gap. Together with density and universality this "fractal" property contributes to the spectacular properties of the homomorphism…
In this article we study the energy level spectrum of fractals which have block-hierarchical structures. We develop a method to study the spectral properties in terms of linearization of spectral decimation procedure and verify it…
I construct perforated, "take-away" fractals that support short-distance power-law scaling with complex exponents for Dirac (spin-1/2) propagators. The construction relies on a fortuitous ansatz for Dirac boundary conditions at the surfaces…
We consider a measurement of finite-frequency current fluctuations, using a resonance circuit as a model for the detector. We arrive at an expression for the measurable response in terms of the current-current correlators which differs from…
The linear system of differential equations for determination of transmission and reflection amplytudes of scattered electron in the field of one dimensional arbitrary potential is obtained. It is shown that in general the scattering…
Fractional, anomalous diffusion in space-periodic potentials is investigated. The analytical solution for the effective, fractional diffusion coefficient in an arbitrary periodic potential is obtained in closed form in terms of two…
Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the…
We show that the lattice Boltzmann formalism can be used to describe wave propagation in a heterogeneous media, as well as solid-body-like systems and fracture propagation. Several fundamental properties of real fractures (such as…
The negative differential thermal conductance (NDTC) provides the key mechanism for realizing thermal transistors. This exotic effect has been the object of an extensive theoretical investigation, but the implementation is still limited to…
It is shown that conductance fluctuations due to phase coherent ballistic transport through a chaotic cavity generically are fractals. The graph of conductance vs. externally changed parameter, e.g. magnetic field, is a fractal with…
The procedure of evaluating of the spectrum for discrete periodic operators perturbed by operators of smaller dimensions is obtained. This result allows to obtain propagative, guided, localised spectra for different kind of physical…
If our aesthetic preferences are affected by fractal geometry of nature, scaling regularities would be expected to appear in all art forms, including music. While a variety of statistical tools have been proposed to analyze time series in…
Characterizing resonant scatterers is challenging because their poles and zeros usually lie away from the real-frequency axis, whereas most measurements sample only real frequencies and infer off-axis behavior from fitted models. Here we…