21 research outputs found
Study of Spectral Statistics of Classically Integrable Systems
In this work we present the results of a study of spectral statistics for a
classically integrable system, namely the rectangle billiard. We show that the
spectral statistics are indeed Poissonian in the semiclassical limit for almost
all such systems, the exceptions being the atypical rectangles with rational
squared ratio of its sides, and of course the energy ranges larger than L_{\rm
max}=\hbar / T_0T_0L_{\rm max} \to \inftyE \to \infty$.Comment: 5 pages, 4 figures, PTP LaTeX style, to be published in the
proceedings of the conference/summer school 'Let's Face Chaos through
Nonlinear Dynamics', Maribor, Slovenia, June/July 1999, eds. M. Robnik et
al., Prog. Theor. Phys. Suppl. (Kyoto) 139 (2000
On the stability of classical chaotic motion under system's perturbations
We study in detail the time behavior of classical fidelity for chaotic
systems. We show in particular that the asymptotic decay, depending on system
dynamical properties, can be either exponential, with a rate determined by the
gap in the discretized Perron-Frobenius operator, or algebraic, with the same
power as for correlation functions decay. Therefore the decay of fidelity is
strictly connected to correlations decay.Comment: 4 pages, 5 figures, revtex; revised title, abstract and introduction,
with minor modifications in the main tex
Experimental study of generic billiards with microwave resonators
In this work we study the eigenstates and the energy spectra of a generic
billiard system with the use of microwave resonators. This is possible due to
the exact correspondence between the Schroedinger equation and the electric
field equations of the lowest modes in thin microwave resonators. We obtain a
good agreement between the numerical (exact) and experimental eigenstates,
while the short range experimental spectral statistics show the expected
Brody-like behaviour in this energy range, as opposed to the Berry-Robnik
picture which is valid only in the semiclassical region of sufficiently small
effective Planck's constant.Comment: 13 pages, 10 figures (in .GIF format), high quality pictures
available upon request, PTP LaTeX style, to be published in the proceedings
of the conference/summer school 'Let's Face Chaos through Nonlinear
Dynamics', Maribor, Slovenia, June/July 1999, eds. M. Robnik et al., Prog.
Theor. Phys. Suppl. (Kyoto) 139 (2000
Dispersion interactions in stratified anisotropic and optically active media at all separations
We propose a method to calculate dispersion interactions in a system composed
of a one dimensional layering of finite thickness anisotropic and optically
active slabs. The result is expressed within the algebra of 4x4 matrices and is
demonstrated to be equivalent to the known limits of isotropic, nonretarded and
uniaxial dispersion interactions. The method is also capable of handling
dielectric media with smoothly varying anisotropy axes.Comment: 10 pages, 3 figures, revte
Turbulence transition in the asymptotic suction boundary layer
We study the transition to turbulence in the asymptotic suction boundary
layer (ASBL) by direct numerical simulation. Tracking the motion of
trajectories intermediate between laminar and turbulent states we can identify
the invariant object inside the laminar-turbulent boundary, the edge state. In
small domains, the flow behaves like a travelling wave over short time
intervals. On longer times one notes that the energy shows strong bursts at
regular time intervals. During the bursts the streak structure is lost, but it
reforms, translated in the spanwise direction by half the domain size. Varying
the suction velocity allows to embed the flow into a family of flows that
interpolate between plane Couette flow and the ASBL. Near the plane Couette
limit, the edge state is a travelling wave. Increasing the suction, the
travelling wave and a symmetry-related copy of it undergo a saddle-node
infinite-period (SNIPER) bifurcation that leads to bursting and
discrete-symmetry shifts. In wider domains, the structures localize in the
spanwise direction, and the flow in the active region is similar to the one in
small domains. There are still periodic bursts at which the flow structures are
shifted, but the shift-distance is no longer connected to a discrete symmetry
of the flow geometry. Two different states are found by edge tracking
techniques, one where structures are shifted to the same side at every burst
and one where they are alternatingly shifted to the left and to the right.Comment: Conference TSFP8, Poitiers 2013. TSFP-8 conference proceedings 2013,
http://www.tsfp-conference.org/proceedings
Decay of the classical Loschmidt echo in integrable systems
We study both analytically and numerically the decay of fidelity of classical
motion for integrable systems. We find that the decay can exhibit two
qualitatively different behaviors, namely an algebraic decay, that is due to
the perturbation of the shape of the tori, or a ballistic decay, that is
associated with perturbing the frequencies of the tori. The type of decay
depends on initial conditions and on the shape of the perturbation but, for
small enough perturbations, not on its size. We demonstrate numerically this
general behavior for the cases of the twist map, the rectangular billiard, and
the kicked rotor in the almost integrable regime.Comment: 8 pages, 3 figures, revte