6,186 research outputs found
Ripples in a string coupled to Glauber spins
Each oscillator in a linear chain (a string) interacts with a local Ising
spin in contact with a thermal bath. These spins evolve according to Glauber
dynamics. Below a critical temperature, a rippled state in the string is
accompanied by a nonzero spin polarization. The system is shown to form ripples
in the string which, for slow spin relaxation, vibrates rapidly about
quasi-stationary states described as snapshots of a coarse-grained stroboscopic
map. For moderate observation times, ripples are observed irrespective of the
final thermodynamically stable state (rippled or not).Comment: 5 pages, 2 figure
Axisymmetric pulse recycling and motion in bulk semiconductors
The Kroemer model for the Gunn effect in a circular geometry (Corbino disks)
has been numerically solved. The results have been interpreted by means of
asymptotic calculations. Above a certain onset dc voltage bias, axisymmetric
pulses of the electric field are periodically shed by an inner circular
cathode. These pulses decay as they move towards the outer anode, which they
may not reach. As a pulse advances, the external current increases continuously
until a new pulse is generated. Then the current abruptly decreases, in
agreement with existing experimental results. Depending on the bias, more
complex patterns with multiple pulse shedding are possible.Comment: 8 pages, 15 figure
Chaotic motion of space charge wavefronts in semiconductors under time-independent voltage bias
A standard drift-diffusion model of space charge wave propagation in
semiconductors has been studied numerically and analytically under dc voltage
bias. For sufficiently long samples, appropriate contact resistivity and
applied voltage - such that the sample is biased in a regime of negative
differential resistance - we find chaos in the propagation of nonlinear fronts
(charge monopoles of alternating sign) of electric field. The chaos is always
low-dimensional, but has a complex spatial structure; this behavior can be
interpreted using a finite dimensional asymptotic model in which the front
(charge monopole) positions and the electrical current are the only dynamical
variables.Comment: 12 pages, 8 figure
Nonequilibrium free energy, H theorem and self-sustained oscillations for Boltzmann-BGK descriptions of semiconductor superlattices
Semiconductor superlattices (SL) may be described by a Boltzmann-Poisson
kinetic equation with a Bhatnagar-Gross-Krook (BGK) collision term which
preserves charge, but not momentum or energy. Under appropriate boundary and
voltage bias conditions, these equations exhibit time-periodic oscillations of
the current caused by repeated nucleation and motion of charge dipole waves.
Despite this clear nonequilibrium behavior, if we `close' the system by
attaching insulated contacts to the superlattice and keeping its voltage bias
to zero volts, we can prove the H theorem, namely that a free energy
of the kinetic equations is a Lyapunov functional (, ). Numerical simulations confirm that the free energy decays to its
equilibrium value for a closed SL, whereas for an `open' SL under appropriate
dc voltage bias and contact conductivity oscillates in time with the
same frequency as the current self-sustained oscillations.Comment: 15 pages, 3 figures, minor revision of latex fil
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.
Symmetric hyperbolic systems for Bianchi equations
We obtain a family of first-order symmetric hyperbolic systems for the
Bianchi equations. They have only physical characteristics: the light cone and
timelike hypersurfaces. In the proof of the hyperbolicity, new positivity
properties of the Bel tensor are used.Comment: latex, 7 pages, accepted for publication in Class. Quantum Gra
Generalized drift-diffusion model for miniband superlattices
A drift-diffusion model of miniband transport in strongly coupled
superlattices is derived from the single-miniband Boltzmann-Poisson transport
equation with a BGK (Bhatnagar-Gross-Krook) collision term. We use a consistent
Chapman-Enskog method to analyze the hyperbolic limit, at which collision and
electric field terms dominate the other terms in the Boltzmann equation. The
reduced equation is of the drift-diffusion type, but it includes additional
terms, and diffusion and drift do not obey the Einstein relation except in the
limit of high temperatures.Comment: 4 pages, 3 figures, double-column revtex. To appear as RC in PR
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
Universality of the Gunn effect: self-sustained oscillations mediated by solitary waves
The Gunn effect consists of time-periodic oscillations of the current flowing
through an external purely resistive circuit mediated by solitary wave dynamics
of the electric field on an attached appropriate semiconductor. By means of a
new asymptotic analysis, it is argued that Gunn-like behavior occurs in
specific classes of model equations. As an illustration, an example related to
the constrained Cahn-Allen equation is analyzed.Comment: 4 pages,3 Post-Script figure
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
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