834 research outputs found
Hamiltonian chaos in a coupled BEC -- optomechanical cavity system
We study a hybrid optomechanical system consisting of a Bose-Einstein
condensate (BEC) trapped inside a single-mode optical cavity with a moving
end-mirror. The intracavity light field has a dual role: it excites a momentum
side-mode of the condensate, and acts as a nonlinear spring that couples the
vibrating mirror to that collective density excitation. We present the dynamics
in a regime where the intracavity optical field, the mirror, and the side-mode
excitation all display bistable behavior. In this regime we find that the
dynamics of the system exhibits Hamiltonian chaos for appropriate initial
conditions.Comment: 5 figure
The charge shuttle as a nanomechanical ratchet
We consider the charge shuttle proposed by Gorelik {\em et al.} driven by a
time-dependent voltage bias. In the case of asymmetric setup, the system
behaves as a rachet. For pure AC drive, the rectified current shows a complex
frequency dependent response characterized by frequency locking at fracional
values of the external frequency. Due to the non-linear dynamics of the
shuttle, the rachet effect is present also for very low frequencies.Comment: 4 pages, 4 figure
Quantum entanglement between a nonlinear nanomechanical resonator and a microwave field
We consider a theoretical model for a nonlinear nanomechanical resonator
coupled to a superconducting microwave resonator. The nanomechanical resonator
is driven parametrically at twice its resonance frequency, while the
superconducting microwave resonator is driven with two tones that differ in
frequency by an amount equal to the parametric driving frequency. We show that
the semi-classical approximation of this system has an interesting fixed point
bifurcation structure. In the semi-classical dynamics a transition from stable
fixed points to limit cycles is observed as one moves from positive to negative
detuning. We show that signatures of this bifurcation structure are also
present in the full dissipative quantum system and further show that it leads
to mixed state entanglement between the nanomechanical resonator and the
microwave cavity in the dissipative quantum system that is a maximum close to
the semi-classical bifurcation. Quantum signatures of the semi-classical
limit-cycles are presented.Comment: 36 pages, 18 figure
Transitions to improved confinement regimes induced by changes in heating in zero-dimensional models for tokamak plasmas
It is shown that rapid substantial changes in heating rate can induce
transitions to improved energy confinement regimes in zero-dimensional models
for tokamak plasma phenomenology. We examine for the first time the effect of
step changes in heating rate in the models of E-J.Kim and P.H.Diamond,
Phys.Rev.Lett. 90, 185006 (2003) and M.A.Malkov and P.H.Diamond, Phys.Plasmas
16, 012504 (2009) which nonlinearly couple the evolving temperature gradient,
micro-turbulence and a mesoscale flow; and in the extension of H.Zhu,
S.C.Chapman and R.O.Dendy, Phys.Plasmas 20, 042302 (2013), which couples to a
second mesoscale flow component. The temperature gradient rises, as does the
confinement time defined by analogy with the fusion context, while
micro-turbulence is suppressed. This outcome is robust against variation of
heating rise time and against introduction of an additional variable into the
model. It is also demonstrated that oscillating changes in heating rate can
drive the level of micro-turbulence through a period-doubling path to chaos,
where the amplitude of the oscillatory component of the heating rate is the
control parameter.Comment: 8 pages, 14 figure
Generalising the logistic map through the -product
We investigate a generalisation of the logistic map as (, )
where stands for a generalisation of the ordinary product, known as
-product [Borges, E.P. Physica A {\bf 340}, 95 (2004)]. The usual product,
and consequently the usual logistic map, is recovered in the limit ,
The tent map is also a particular case for . The
generalisation of this (and others) algebraic operator has been widely used
within nonextensive statistical mechanics context (see C. Tsallis, {\em
Introduction to Nonextensive Statistical Mechanics}, Springer, NY, 2009). We
focus the analysis for at the edge of chaos, particularly at the
first critical point , that depends on the value of . Bifurcation
diagrams, sensitivity to initial conditions, fractal dimension and rate of
entropy growth are evaluated at , and connections with
nonextensive statistical mechanics are explored.Comment: 12 pages, 23 figures, Dynamics Days South America. To be published in
Journal of Physics: Conference Series (JPCS - IOP
Computing the multifractal spectrum from time series: An algorithmic approach
We show that the existing methods for computing the f(\alpha) spectrum from a
time series can be improved by using a new algorithmic scheme. The scheme
relies on the basic idea that the smooth convex profile of a typical f(\alpha)
spectrum can be fitted with an analytic function involving a set of four
independent parameters. While the standard existing schemes [16, 18] generally
compute only an incomplete f(\alpha) spectrum (usually the top portion), we
show that this can be overcome by an algorithmic approach which is automated to
compute the Dq and f(\alpha) spectrum from a time series for any embedding
dimension. The scheme is first tested with the logistic attractor with known
f(\alpha) curve and subsequently applied to higher dimensional cases. We also
show that the scheme can be effectively adapted for analysing practcal time
series involving noise, with examples from two widely different real world
systems. Moreover, some preliminary results indicating that the set of four
independant parameters may be used as diagnostic measures is also included.Comment: 10 pages, 16 figures, submitted to CHAO
Quantum integrability and nonintegrability in the spin-boson model
We study the spectral properties of a spin-boson Hamiltonian that depends on
two continuous parameters (interaction strength) and
(integrability switch). In the classical limit this
system has two distinct integrable regimes, and . For
each integrable regime we can express the quantum Hamiltonian as a function of
two action operators. Their eigenvalues (multiples of ) are the natural
quantum numbers for the complete level spectrum. This functional dependence
cannot be extended into the nonintegrable regime . Here level
crossings are prohibited and the level spectrum is naturally described by a
single (energy sorting) quantum number. In consequence, the tracking of
individual eigenstates along closed paths through both regimes leads to
conflicting assignments of quantum numbers. This effect is a useful and
reliable indicator of quantum chaos -- a diagnostic tool that is independent of
any level-statistical analysis
Fractal and chaotic solutions of the discrete nonlinear Schr\"odinger equation in classical and quantum systems
We discuss stationary solutions of the discrete nonlinear Schr\"odinger
equation (DNSE) with a potential of the type which is generically
applicable to several quantum spin, electron and classical lattice systems. We
show that there may arise chaotic spatial structures in the form of
incommensurate or irregular quantum states. As a first (typical) example we
consider a single electron which is strongly coupled with phonons on a
chain of atoms --- the (Rashba)--Holstein polaron model. In the adiabatic
approximation this system is conventionally described by the DNSE. Another
relevant example is that of superconducting states in layered superconductors
described by the same DNSE. Amongst many other applications the typical example
for a classical lattice is a system of coupled nonlinear oscillators. We
present the exact energy spectrum of this model in the strong coupling limit
and the corresponding wave function. Using this as a starting point we go on to
calculate the wave function for moderate coupling and find that the energy
eigenvalue of these structures of the wave function is in exquisite agreement
with the exact strong coupling result. This procedure allows us to obtain
(numerically) exact solutions of the DNSE directly. When applied to our typical
example we find that the wave function of an electron on a deformable lattice
(and other quantum or classical discrete systems) may exhibit incommensurate
and irregular structures. These states are analogous to the periodic,
quasiperiodic and chaotic structures found in classical chaotic dynamics
Ensemble averages and nonextensivity at the edge of chaos of one-dimensional maps
Ensemble averages of the sensitivity to initial conditions and the
entropy production per unit time of a {\it new} family of one-dimensional
dissipative maps, , and of the known
logistic-like maps, , are numerically studied, both
for {\it strong} (Lyapunov exponent ) and {\it weak} (chaos
threshold, i.e., ) chaotic cases. In all cases we verify that (i)
both and {\it linearly}
increase with time for (and only for) a special value of , ,
and (ii) the {\it slope} of {\it coincide},
thus interestingly extending the well known Pesin theorem. For strong chaos,
, whereas at the edge of chaos, .Comment: 5 pages, 5 figure
Visualizing the logistic map with a microcontroller
The logistic map is one of the simplest nonlinear dynamical systems that
clearly exhibit the route to chaos. In this paper, we explored the evolution of
the logistic map using an open-source microcontroller connected to an array of
light emitting diodes (LEDs). We divided the one-dimensional interval
into ten equal parts, and associated and LED to each segment. Every time an
iteration took place a corresponding LED turned on indicating the value
returned by the logistic map. By changing some initial conditions of the
system, we observed the transition from order to chaos exhibited by the map.Comment: LaTeX, 6 pages, 3 figures, 1 listin
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