17,432 research outputs found
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
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
Nonlinear Impurity in a Lattice: Dispersion Effects
We examine the bound state(s) associated with a single cubic nonlinear
impurity, in a one-dimensional tight-binding lattice, where hopping to
first--and--second nearest neighbors is allowed. The model is solved in closed
form {\em v\`{\i}a} the use of the appropriate lattice Green function and a
phase diagram is obtained showing the number of bound states as a function of
nonlinearity strength and the ratio of second to first nearest--neighbor
hopping parameters. Surprisingly, a finite amount of hopping to second nearest
neighbors helps the formation of a bound state at smaller (even vanishingly
small) nonlinearity values. As a consequence, the selftrapping transition can
also be tuned to occur at relatively small nonlinearity strength, by this
increase in the lattice dispersion.Comment: 24 pages, 10 figure
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
Ideal Gas in a Finite Container
The thermodynamics of an ideal gas enclosed in a box of volume a1 x a2 x a3
at temperature T is considered. The canonical partition function of the system
is expressed in terms of complete elliptic integrals of the first kind, whose
argument obeys a transcendental equation. For high and low temperatures we
derive explicitly the main finite-volume corrections to the standard
thermodynamic quantities.Comment: 13 pages total (Latex source), including one table and one ps figur
Exponential versus linear amplitude decay in damped oscillators
We comment of the widespread belief among some undergraduate students that
the amplitude of any harmonic oscillator in the presence of any type of
friction, decays exponentially in time. To dispel that notion, we compare the
amplitude decay for a harmonic oscillator in the presence of (i) viscous
friction and (ii) dry friction. It is shown that, in the first case, the
amplitude decays exponentially with time while in the second case, it decays
linearly with time.Comment: 3 pages, 1 figure, accepted in Phys. Teac
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