1,660 research outputs found
Radiative damping and synchronization in a graphene-based terahertz emitter
We investigate the collective electron dynamics in a recently proposed
graphene-based terahertz emitter under the influence of the radiative damping
effect, which is included self-consistently in a molecular dynamics approach.
We show that under appropriate conditions synchronization of the dynamics of
single electrons takes place, leading to a rise of the oscillating component of
the charge current. The synchronization time depends dramatically on the
applied dc electric field and electron scattering rate, and is roughly
inversely proportional to the radiative damping rate that is determined by the
carrier concentration and the geometrical parameters of the device. The
emission spectra in the synchronized state, determined by the oscillating
current component, are analyzed. The effective generation of higher harmonics
for large values of the radiative damping strength is demonstrated.Comment: 9 pages, 7 figure
Transition to complete synchronization in phase coupled oscillators with nearest neighbours coupling
We investigate synchronization in a Kuramoto-like model with nearest
neighbour coupling. Upon analyzing the behaviour of individual oscillators at
the onset of complete synchronization, we show that the time interval between
bursts in the time dependence of the frequencies of the oscillators exhibits
universal scaling and blows up at the critical coupling strength. We also bring
out a key mechanism that leads to phase locking. Finally, we deduce forms for
the phases and frequencies at the onset of complete synchronization.Comment: 6 pages, 4 figures, to appear in CHAO
Exploring constrained quantum control landscapes
The broad success of optimally controlling quantum systems with external
fields has been attributed to the favorable topology of the underlying control
landscape, where the landscape is the physical observable as a function of the
controls. The control landscape can be shown to contain no suboptimal trapping
extrema upon satisfaction of reasonable physical assumptions, but this
topological analysis does not hold when significant constraints are placed on
the control resources. This work employs simulations to explore the topology
and features of the control landscape for pure-state population transfer with a
constrained class of control fields. The fields are parameterized in terms of a
set of uniformly spaced spectral frequencies, with the associated phases acting
as the controls. Optimization results reveal that the minimum number of phase
controls necessary to assure a high yield in the target state has a special
dependence on the number of accessible energy levels in the quantum system,
revealed from an analysis of the first- and second-order variation of the yield
with respect to the controls. When an insufficient number of controls and/or a
weak control fluence are employed, trapping extrema and saddle points are
observed on the landscape. When the control resources are sufficiently
flexible, solutions producing the globally maximal yield are found to form
connected `level sets' of continuously variable control fields that preserve
the yield. These optimal yield level sets are found to shrink to isolated
points on the top of the landscape as the control field fluence is decreased,
and further reduction of the fluence turns these points into suboptimal
trapping extrema on the landscape. Although constrained control fields can come
in many forms beyond the cases explored here, the behavior found in this paper
is illustrative of the impacts that constraints can introduce.Comment: 10 figure
Gauge Theory for Finite-Dimensional Dynamical Systems
Gauge theory is a well-established concept in quantum physics,
electrodynamics, and cosmology. This theory has recently proliferated into new
areas, such as mechanics and astrodynamics. In this paper, we discuss a few
applications of gauge theory in finite-dimensional dynamical systems with
implications to numerical integration of differential equations. We distinguish
between rescriptive and descriptive gauge symmetry. Rescriptive gauge symmetry
is, in essence, re-scaling of the independent variable, while descriptive gauge
symmetry is a Yang-Mills-like transformation of the velocity vector field,
adapted to finite-dimensional systems. We show that a simple gauge
transformation of multiple harmonic oscillators driven by chaotic processes can
render an apparently "disordered" flow into a regular dynamical process, and
that there exists a remarkable connection between gauge transformations and
reduction theory of ordinary differential equations. Throughout the discussion,
we demonstrate the main ideas by considering examples from diverse engineering
and scientific fields, including quantum mechanics, chemistry, rigid-body
dynamics and information theory
Many-Body Theory of Synchronization by Long-Range Interactions
Synchronization of coupled oscillators on a -dimensional lattice with the
power-law coupling and randomly distributed intrinsic
frequency is analyzed. A systematic perturbation theory is developed to
calculate the order parameter profile and correlation functions in powers of
. For , the system exhibits a sharp
synchronization transition as described by the conventional mean-field theory.
For , the transition is smeared by the quenched disorder, and the
macroscopic order parameter \Av\psi decays slowly with as |\Av\psi|
\propto g_0^2.Comment: 4 pages, 2 figure
Scaling and singularities in the entrainment of globally-coupled oscillators
The onset of collective behavior in a population of globally coupled
oscillators with randomly distributed frequencies is studied for phase
dynamical models with arbitrary coupling. The population is described by a
Fokker-Planck equation for the distribution of phases which includes the
diffusive effect of noise in the oscillator frequencies. The bifurcation from
the phase-incoherent state is analyzed using amplitude equations for the
unstable modes with particular attention to the dependence of the nonlinearly
saturated mode on the linear growth rate . In general
we find where is the
diffusion coefficient and is the mode number of the unstable mode. The
unusual factor arises from a singularity in the cubic term of
the amplitude equation.Comment: 11 pages (Revtex); paper submitted to Phys. Rev. Let
Exact Phase Solutions of Nonlinear Oscillators on Two-dimensional Lattice
We present various exact solutions of a discrete complex Ginzburg-Landau
(CGL) equation on a plane lattice, which describe target patterns and spiral
patterns and derive their stability criteria. We also obtain similar solutions
to a system of van der Pol's oscillators.Comment: Latex 11 pages, 17 eps file
The dynamics of correlated novelties
One new thing often leads to another. Such correlated novelties are a
familiar part of daily life. They are also thought to be fundamental to the
evolution of biological systems, human society, and technology. By opening new
possibilities, one novelty can pave the way for others in a process that
Kauffman has called "expanding the adjacent possible". The dynamics of
correlated novelties, however, have yet to be quantified empirically or modeled
mathematically. Here we propose a simple mathematical model that mimics the
process of exploring a physical, biological or conceptual space that enlarges
whenever a novelty occurs. The model, a generalization of Polya's urn, predicts
statistical laws for the rate at which novelties happen (analogous to Heaps'
law) and for the probability distribution on the space explored (analogous to
Zipf's law), as well as signatures of the hypothesized process by which one
novelty sets the stage for another. We test these predictions on four data sets
of human activity: the edit events of Wikipedia pages, the emergence of tags in
annotation systems, the sequence of words in texts, and listening to new songs
in online music catalogues. By quantifying the dynamics of correlated
novelties, our results provide a starting point for a deeper understanding of
the ever-expanding adjacent possible and its role in biological, linguistic,
cultural, and technological evolution
Collective synchronization in populations of globally coupled phase oscillators with drifting frequencies
We generalize the Kuramoto model for coupled phase oscillators by allowing
the frequencies to drift in time according to Ornstein-Uhlenbeck dynamics. Such
drifting frequencies were recently measured in cellular populations of
circadian oscillator and inspired our work. Linear stability analysis of the
Fokker-Planck equation for an infinite population is amenable to exact solution
and we show that the incoherent state is unstable passed a critical coupling
strength K_c(\ga, \sigf), where \ga is the inverse characteristic drifting
time and \sigf the asymptotic frequency dispersion. Expectedly agrees
with the noisy Kuramoto model in the large \ga (Schmolukowski) limit but
increases slower as \ga decreases. Asymptotic expansion of the solution for
\ga\to 0 shows that the noiseless Kuramoto model with Gaussian frequency
distribution is recovered in that limit. Thus varying a single parameter allows
to interpolate smoothly between two regimes: one dominated by the frequency
dispersion and the other by phase diffusion.Comment: 5 pages, 5 figures, accepted in Phys. Rev.
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