553 research outputs found
The nonlinear magnetoinductive dimer
We examine a nonlinear magnetoinductive dimer and compute its linear and
nonlinear symmetric, antisymmetric and asymmetric modes in closed-form, in the
rotating-wave approximation. A linear stability analysis of these modes reveals
that the asymmetric mode is always stable, for any allowed value of the
coupling parameter and for both, hard and soft nonlinearity. A numerical
computation of the dimer dynamics reveals a magnetic energy selftrapping whose
threshold increases for increasing dimer coupling.Comment: 4 double-column pages, 6 figures, submitte
Flat bands and PT-symmetry in quasi-one-dimensional lattices
We examine the effect of adding PT-symmetric gain and loss terms to quasi 1D
lattices (ribbons) that possess flat bands. We focus on three representative
cases: (a) The Lieb ribbon, (b) The kagome ribbon, and (c) The stub Ribbon. In
general we find that the effect on the flat band depends strongly on the
geometrical details of the lattice being examined. One interesting and novel
result that emerge from an analytical calculation of the band structure of the
Lieb ribbon including gain and loss, is that its flat band survives the
addition of PT-symmetry for any amount of gain and loss, while for the other
two lattices, any presence of gain and loss destroys the flat bands. For all
three ribbons, there are finite stability windows whose size decreases with the
strength of the gain and loss parameter. For the Lieb and kagome cases, the
size of this window converges to a finite value. The existence of finite
stability windows, plus the constancy of the Lieb flat band are in marked
contrast to the behavior of a pure one-dimensional lattice.Comment: 5 pages, 5 figure
LOcalized modes on an Ablowitz-Ladik nonlinear impurity
We study localized modes on a single Ablowitz-Ladik impurity embedded in the
bulk or at the surface of a one-dimensional linear lattice. Exact expressions
are obtained for the bound state profile and energy. Dynamical excitation of
the localized mode reveals exponentially-high amplitude oscillations of the
spatial profile at the impurity location. The presence of a surface increases
the minimum nonlinearity to effect a dynamical selftrapping.Comment: 11 pages, 6 figures, accepted in PL
Compact modes in quasi one dimensional coupled magnetic oscillators
In this work we study analytically and numerically the spectrum and
localization properties of three quasi-one-dimensional (ribbons) split-ring
resonator arrays which possess magnetic flatbands, namely, the stub, Lieb and
kagome lattices, and how their spectra is affected by the presence of
perturbations that break the delicate geometrical interference needed for a
magnetic flatband to exist. We find that the Stub and Lieb ribbons are stable
against the three types of perturbations considered here, while the kagome
ribbon is, in general, unstable. When losses are incorporated, all flatbands
remain dispersionless but become complex, with the kagome ribbon exhibiting the
highest loss rate.Comment: 11 pages, 15 figure
Discrete embedded modes in the continuum in 2D lattices
We study the problem of constructing bulk and surface embedded modes (EMs)
inside the quasi-continuum band of a square lattice, using a potential
engineering approach \`a la Wigner and von Neumann. Building on previous
results for the one-dimensional (1D) lattice, and making use of separability,
we produce examples of two-dimensional envelope functions and the
two-dimensional (2D) potentials that produce them. The 2D embedded mode decays
like a stretched exponential, with a supporting potential that decays as a
power law. The separability process can cause that a 1D impurity state (outside
the 1D band) can give rise to a 2D embedded mode (inside the band). The
embedded mode survives the addition of random perturbations of the potential;
however, this process introduces other localized modes inside the band, and
causes a general tendency towards localization of the perturbed modes.Comment: 7 pages, 6 figure
Fractional electrical impurity
We examine the localized mode and the transmission of plane waves across a
capacitive impurity of strength , in a 1D bi-inductive electrical
transmission line where the usual discrete Laplacian is replaced by a
fractional one characterized by a fractional exponent . In the absence of
the impurity, the plane wave dispersion is computed in closed form in terms of
hypergeometric functions. It is observed that the bandwidth decreases steadily,
as decreases towards zero, reaching a minimum width at . The localized
mode energy and spatial profiles are computed in close form v\`{i}a lattice
Green functions. The profiles show a remnant of the staggered-unstaggered
symmetry that is common in non-fractional chains. The width of the localized
mode decreases with decreasing , becoming completely localized at the
impurity site at . The transmission coefficient of plane waves across the
impurity is qualitatively similar to its non-fractional counterpart (),
except at low values (). For a fixed exponent , the transmission
decreases with increasing Comment: 6 pages, 6 figure
Fractionality and PT-symmetry in an electrical transmission line
We examine the stability of a 1D electrical transmission line in the
simultaneous presence of PT-symmetry and fractionality. The array contains a
binary gain/loss distribution and a fractional Laplacian
characterized by a fractional exponent . For an infinite periodic
chain, the spectrum is computed in closed form, and its imaginary sector is
examined to determine the stable/unstable regions as a function of the
gain/loss strength and fractional exponent. In contrast to the non-fractional
case where all eigenvalues are complex for any gain/loss, here we observe that
a stable region can exist when gain/loss is small, and the fractional exponent
is below a critical value, . As the fractional
exponent is decreased further, the spectrum acquires a gap with two nearly-flat
bands. We also examined numerically the case of a finite chain of size N.
Contrary to what happens in the infinite chain, here the stable region always
lies above a critical value . An increase in
gain/loss or always reduces the width of this stable region until it
disappears completely.Comment: 6 pages, 6 figure
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