Related papers: Hierarchical Band Gaps in Complex Periodic Systems
Some properties of diagonal binomial coefficients were studied in respect to frequency of their units digits. An approach was formulated that led to use of difference tables to predict if certain units digits can appear in the values of…
In this paper we study spectral sets which are unions of finitely many intervals in R. We show that any spectrum associated with such a spectral set is periodic, with the period an integral multiple of the measure of the set. As a…
We find that the frequency spectra of layered phononic and photonic composites admit a universal struc- ture, independent of the geometry of the periodic-cell and the specific physical properties. We show that this representation extends to…
In contrast to the usual quantum systems which have at most a finite number of open spectral gaps if they are periodic in more than one direction, periodic quantum graphs may have gaps arbitrarily high in the spectrum. This property of…
The spectral gap of local random quantum circuits is a fundamental property that determines how close the moments of the circuit's unitaries match those of a Haar random distribution. When studying spectral gaps, it is common to bound these…
Spectral gaps in the vibrational modes of disordered solids are key design elements in the synthesis and control of phononic metamaterials that exhibit a plethora of novel elastic and mechanical properties. However, reliably producing these…
We discuss spectral properties of an periodic quantum graph consisting of an array of rings coupled either tightly or loosely through connecting links, assuming that the vertex coupling is manifestly non-invariant with respect to the time…
We consider a semi-periodic two-dimensional Schr\"odinger operator which is cut at an angle. When the cut is commensurate with the periodic lattice, the spectrum of the operator has the band-gap Bloch structure. We prove that in the…
Using the time periodic ABCD parameters, an expression for the dispersion relation of space-time modulated structures is obtained. The relation is valid for general structures even when the spatial granularity is comparable to the operating…
We calculate the photonic band gap of triply periodic bicontinuous cubic structures and of tubular structures constructed from the skeletal graphs of triply periodic minimal surfaces. The effect of the symmetry and topology of the periodic…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
We consider elastic waves in a two-dimensional periodic lattice network of Timoshenko-type beams. We show that for general configurations involving certain highly-contrasting components a high-contrast modification of the homogenization…
Wave motion in a continuous elastic rod with a periodically attached inertial-amplification mechanism is investigated. The mechanism has properties similar to an "inerter" typically used in vehicle suspensions, however here it is…
The transmissivity of a one-dimensional random system that is periodic on average is studied. It is shown that the transmission coefficient for frequencies corresponding to a gap in the band structure of the average periodic system…
We analyze the phonon spectra of periodic structures formed by two-dimensional mixtures of dipolar colloidal particles. These mixtures display an enormous variety of complex ordered configurations [J. Fornleitner {\it et al.}, Soft Matter…
Bloch wavefunctions are used to derive dispersion relations for water wave propagation in the presence of an infinite array of periodically arranged surface scatterers. For one dimensional periodicity (stripes), band gaps for wavevectors in…
In this work, we present a computational analysis of the planar wave propagation behavior of a one-dimensional periodic multi-stable cellular material. Wave propagation in these materials is interesting because they combine the ability of…
We consider quantum lattice Hamiltonians and derive recursive spectral relations bridging successive particle number sectors. One relation gives conditions under which the charge gap dominates the neutral gap. We verify these conditions…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…
The existence and construction of periodic approximations with convergent spectra is crucial in solid state physics for the spectral study of corresponding Schr\"odinger operators. In a forthcoming work [9] (arXiv:1709.00975) this task was…