47,416 research outputs found
Qualitative analysis of the dynamics of the time delayed Chua's circuit
IEEE TRANS. CIRCUITS SYST.
Pauli principle and chaos in a magnetized disk
We present results of a detailed quantum mechanical study of a gas of
noninteracting electrons confined to a circular boundary and subject to
homogeneous dc plus ac magnetic fields , with
). We earlier found a one-particle {\it classical}
phase diagram of the (scaled) Larmor frequency
{\rm vs} that
separates regular from chaotic regimes. We also showed that the quantum
spectrum statistics changed from Poisson to Gaussian orthogonal ensembles in
the transition from classically integrable to chaotic dynamics. Here we find
that, as a function of and , there are clear
quantum signatures in the magnetic response, when going from the
single-particle classically regular to chaotic regimes. In the quasi-integrable
regime the magnetization non-monotonically oscillates between diamagnetic and
paramagnetic as a function of . We quantitatively understand this behavior
from a perturbation theory analysis. In the chaotic regime, however, we find
that the magnetization oscillates as a function of but it is {\it always}
diamagnetic. Equivalent results are also presented for the orbital currents. We
also find that the time-averaged energy grows like in the
quasi-integrable regime but changes to a linear dependence in the chaotic
regime. In contrast, the results with Bose statistics are akin to the
single-particle case and thus different from the fermionic case. We also give
an estimate of possible experimental parameters were our results may be seen in
semiconductor quantum dot billiards.Comment: 22 pages, 7 GIF figures, Phys. Rev. E. (1999
Normal modes and time evolution of a holographic superconductor after a quantum quench
We employ holographic techniques to investigate the dynamics of the order
parameter of a strongly coupled superconductor after a perturbation that drives
the system out of equilibrium. The gravity dual that we employ is the Soliton background at zero temperature. We first analyze the normal
modes associated to the superconducting order parameter which are purely real
since the background has no horizon. We then study the full time evolution of
the order parameter after a quench. For sufficiently a weak and slow
perturbation we show that the order parameter undergoes simple undamped
oscillations in time with a frequency that agrees with the lowest normal model
computed previously. This is expected as the soliton background has no horizon
and therefore, at least in the probe and large limits considered, the
system will never return to equilibrium. For stronger and more abrupt
perturbations higher normal modes are excited and the pattern of oscillations
becomes increasingly intricate. We identify a range of parameters for which the
time evolution of the order parameter become quasi chaotic. The details of the
chaotic evolution depend on the type of perturbation used. Therefore it is
plausible to expect that it is possible to engineer a perturbation that leads
to the almost complete destruction of the oscillating pattern and consequently
to quasi equilibration induced by superposition of modes with different
frequencies.Comment: 10 pages, 7 figures, corrected typos, expanded section on chaotic
oscillations and new results for other quenc
Deterministic polarization chaos from a laser diode
Fifty years after the invention of the laser diode and fourty years after the
report of the butterfly effect - i.e. the unpredictability of deterministic
chaos, it is said that a laser diode behaves like a damped nonlinear
oscillator. Hence no chaos can be generated unless with additional forcing or
parameter modulation. Here we report the first counter-example of a
free-running laser diode generating chaos. The underlying physics is a
nonlinear coupling between two elliptically polarized modes in a
vertical-cavity surface-emitting laser. We identify chaos in experimental
time-series and show theoretically the bifurcations leading to single- and
double-scroll attractors with characteristics similar to Lorenz chaos. The
reported polarization chaos resembles at first sight a noise-driven mode
hopping but shows opposite statistical properties. Our findings open up new
research areas that combine the high speed performances of microcavity lasers
with controllable and integrated sources of optical chaos.Comment: 13 pages, 5 figure
Network analysis of chaotic dynamics in fixed-precision digital domain
When implemented in the digital domain with time, space and value discretized
in the binary form, many good dynamical properties of chaotic systems in
continuous domain may be degraded or even diminish. To measure the dynamic
complexity of a digital chaotic system, the dynamics can be transformed to the
form of a state-mapping network. Then, the parameters of the network are
verified by some typical dynamical metrics of the original chaotic system in
infinite precision, such as Lyapunov exponent and entropy. This article reviews
some representative works on the network-based analysis of digital chaotic
dynamics and presents a general framework for such analysis, unveiling some
intrinsic relationships between digital chaos and complex networks. As an
example for discussion, the dynamics of a state-mapping network of the Logistic
map in a fixed-precision computer is analyzed and discussed.Comment: 5 pages, 9 figure
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