5,870 research outputs found
Exact solution of the Schr\"{o}dinger equation for an hydrogen atom at the interface between the vacuum and a topologically insulating surface
When an hydrogen atom is brought near to the interface between
-media, the quantum-mechanical motion of the electron will be affected
by the electromagnetic interaction between the atomic charges and the
-interface, which is described by an axionic extension of Maxwell
electrodynamics in the presence of a boundary. In this paper we investigate the
atom-surface interaction effects upon the energy levels and wave functions of
an hydrogen atom placed at the interface between a -medium and the
vacuum. In the approximation considered, the Schr\"{o}dinger equation can be
exactly solved by separation of variables in terms of hypergeometic functions
for the angular part and hydrogenic functions for the radial part. In order to
make such effects apparent we deal with unrealistic high values of the
-parameter. We also compute the energy shifts using perturbation theory
for a particular small value of and we demonstrate that they are in a
very good agreement with the ones obtained from the exact solution.Comment: 20 pages, 17 figures, 6 tables, Accepted for publication in the
European Physics Journal
Chaos in resonant-tunneling superlattices
Spatio-temporal chaos is predicted to occur in n-doped semiconductor
superlattices with sequential resonant tunneling as their main charge transport
mechanism. Under dc voltage bias, undamped time-dependent oscillations of the
current (due to the motion and recycling of electric field domain walls) have
been observed in recent experiments. Chaos is the result of forcing this
natural oscillation by means of an appropriate external microwave signal.Comment: 3 pages, LaTex, RevTex, 3 uuencoded figures (1.2M) are available upon
request from [email protected], to appear in Phys.Rev.
Current-voltage characteristic and stability in resonant-tunneling n-doped semiconductor superlattices
We review the occurrence of electric-field domains in doped superlattices
within a discrete drift model. A complete analysis of the construction and
stability of stationary field profiles having two domains is carried out. As a
consequence, we can provide a simple analytical estimation for the doping
density above which stable stable domains occur. This bound may be useful for
the design of superlattices exhibiting self-sustained current oscillations.
Furthermore we explain why stable domains occur in superlattices in contrast to
the usual Gunn diode.Comment: Tex file and 3 postscript figure
A moment based approach to the dynamical solution of the Kuramoto model
We examine the dynamics of the Kuramoto model with a new analytical approach.
By defining an appropriate set of moments the dynamical equations can be
exactly closed. We discuss some applications of the formalism like the
existence of an effective Hamiltonian for the dynamics. We also show how this
approach can be used to numerically investigate the dynamical behavior of the
model without finite size effects.Comment: 6 pages, 5 figures, Revtex file, to appear in J. Phys.
Nonlinear stochastic discrete drift-diffusion theory of charge fluctuations and domain relocation times in semiconductor superlattices
A stochastic discrete drift-diffusion model is proposed to account for the
effects of shot noise in weakly coupled, highly doped semiconductor
superlattices. Their current-voltage characteristics consist of a number stable
multistable branches corresponding to electric field profiles displaying two
domains separated by a domain wall. If the initial state corresponds to a
voltage on the middle of a stable branch and a sudden voltage is switched so
that the final voltage corresponds to the next branch, the domains relocate
after a certain delay time. Shot noise causes the distribution of delay times
to change from a Gaussian to a first passage time distribution as the final
voltage approaches that of the end of the first current branch. These results
agree qualitatively with experiments by Rogozia {\it et al} (Phys. Rev. B {\bf
64}, 041308(R) (2001)).Comment: 9 pages, 12 figures, 2 column forma
Temperature dependence of current self-oscillations and electric field domains in sequential tunneling doped superlattices
We examine how the current--voltage characteristics of a doped weakly coupled
superlattice depends on temperature. The drift velocity of a discrete drift
model of sequential tunneling in a doped GaAs/AlAs superlattice is calculated
as a function of temperature. Numerical simulations and theoretical arguments
show that increasing temperature favors the appearance of current
self-oscillations at the expense of static electric field domain formation. Our
findings agree with available experimental evidence.Comment: 7 pages, 5 figure
Edge dislocations in crystal structures considered as traveling waves of discrete models
The static stress needed to depin a 2D edge dislocation, the lower dynamic
stress needed to keep it moving, its velocity and displacement vector profile
are calculated from first principles. We use a simplified discrete model whose
far field distortion tensor decays algebraically with distance as in the usual
elasticity. An analytical description of dislocation depinning in the strongly
overdamped case (including the effect of fluctuations) is also given. A set of
parallel edge dislocations whose centers are far from each other can depin
a given one provided , where is the average inter-dislocation
distance divided by the Burgers vector of a single dislocation. Then a limiting
dislocation density can be defined and calculated in simple cases.Comment: 10 pages, 3 eps figures, Revtex 4. Final version, corrected minor
error
Dynamics of Electric Field Domains and Oscillations of the Photocurrent in a Simple Superlattice Model
A discrete model is introduced to account for the time-periodic oscillations
of the photocurrent in a superlattice observed by Kwok et al, in an undoped 40
period AlAs/GaAs superlattice. Basic ingredients are an effective negative
differential resistance due to the sequential resonant tunneling of the
photoexcited carriers through the potential barriers, and a rate equation for
the holes that incorporates photogeneration and recombination. The
photoexciting laser acts as a damping factor ending the oscillations when its
power is large enough. The model explains: (i) the known oscillatory static I-V
characteristic curve through the formation of a domain wall connecting high and
low electric field domains, and (ii) the photocurrent and photoluminescence
time-dependent oscillations after the domain wall is formed. In our model, they
arise from the combined motion of the wall and the shift of the values of the
electric field at the domains. Up to a certain value of the photoexcitation,
the non-uniform field profile with two domains turns out to be metastable:
after the photocurrent oscillations have ceased, the field profile slowly
relaxes toward the uniform stationary solution (which is reached on a much
longer time scale). Multiple stability of stationary states and hysteresis are
also found. An interpretation of the oscillations in the photoluminescence
spectrum is also given.Comment: 34 pages, REVTeX 3.0, 10 figures upon request, MA/UC3M/07/9
Effects of noise on hysteresis and resonance width in graphene and nanotubes resonators
We investigate the role that noise plays in the hysteretic dynamics of a
suspended nanotube or a graphene sheet subject to an oscillating force. We find
that not only the size but also the position of the hysteresis region in these
systems can be controlled by noise. We also find that nano-resonators act as
noise rectifiers: by increasing the noise in the setup, the resonance width of
the characteristic peak in these systems is reduced and, as a result, the
quality factor is increased.Comment: 15 pages, 6 figures. Sent to PRB (in revision
Symmetric hyperbolic systems for a large class of fields in arbitrary dimension
Symmetric hyperbolic systems of equations are explicitly constructed for a
general class of tensor fields by considering their structure as r-fold forms.
The hyperbolizations depend on 2r-1 arbitrary timelike vectors. The importance
of the so-called "superenergy" tensors, which provide the necessary symmetric
positive matrices, is emphasized and made explicit. Thereby, a unified
treatment of many physical systems is achieved, as well as of the sometimes
called "higher order" systems. The characteristics of these symmetric
hyperbolic systems are always physical, and directly related to the null
directions of the superenergy tensor, which are in particular principal null
directions of the tensor field solutions. Generic energy estimates and
inequalities are presented too.Comment: 24 pages, no figure
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