34,603 research outputs found
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
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
New DNLS Equations for Anharmonic Vibrational Impurities
We examine some new DNLS-like equations that arise when considering
strongly-coupled electron-vibration systems, where the local oscillator
potential is anharmonic. In particular, we focus on a single, rather general
nonlinear vibrational impurity and determine its bound state(s) and its
dynamical selftrapping properties.Comment: 16 pages, 5 figure
The attractive nonlinear delta-function potential
We solve the continuous one-dimensional Schr\"{o}dinger equation for the case
of an inverted {\em nonlinear} delta-function potential located at the origin,
obtaining the bound state in closed form as a function of the nonlinear
exponent. The bound state probability profile decays exponentially away from
the origin, with a profile width that increases monotonically with the
nonlinear exponent, becoming an almost completely extended state when this
approaches two. At an exponent value of two, the bound state suffers a
discontinuous change to a delta-like profile. Further increase of the exponent
increases again the width of the probability profile, although the bound state
is proven to be stable only for exponents below two. The transmission of plane
waves across the nonlinear delta potential increases monotonically with the
nonlinearity exponent and is insensitive to the sign of its opacity.Comment: submitted to Am. J. of Phys., sixteen pages, three figure
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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