5,229 research outputs found
Ergodic Properties of Classical SU(2) Lattice Gauge Theory
We investigate the relationship between the Lyapunov exponents of periodic
trajectories, the average and fluctuations of Lyapunov exponents of ergodic
trajectories, and the ergodic autocorrelation time for the two-dimensional
hyperbola billiard. We then study the fluctuation properties of the ergodic
Lyapunov spectrum of classical SU(2) gauge theory on a lattice. Our results are
consistent with the notion that this system is globally hyperbolic. Among the
many powerful theorems applicable to such systems, we discuss one relating to
the fluctuations in the entropy growth rate.Comment: 21 pages, 7 figure
Billiards correlation functions
We discuss various experiments on the time decay of velocity autocorrelation
functions in billiards. We perform new experiments and find results which are
compatible with an exponential mixing hypothesis, first put forward by [FM]:
they do not seem compatible with the stretched exponentials believed, in spite
of [FM], to describe the mixing. The analysis led us to several byproducts: we
obtain information about the normal diffusive nature of the motion and we
consider the probability distribution of the number of collisions in time
(as t_m\to\io) finding a strong dependence on some geometric characteristics
of the locus of the billiards obstacles.Comment: 25 pages, 27 figures, POSTSCRIPT, not encoded, 730K. Keywords:
Billiards, correlation functions, velocity autocorrelation, diffusion
coefficients, Lorentz model, mixing, ergodic theory, chaos, Lyapunov
exponents, numerical experiment
Semiclassical form factor for spectral and matrix element fluctuations of multi-dimensional chaotic systems
We present a semiclassical calculation of the generalized form factor which
characterizes the fluctuations of matrix elements of the quantum operators in
the eigenbasis of the Hamiltonian of a chaotic system. Our approach is based on
some recently developed techniques for the spectral form factor of systems with
hyperbolic and ergodic underlying classical dynamics and f=2 degrees of
freedom, that allow us to go beyond the diagonal approximation. First we extend
these techniques to systems with f>2. Then we use these results to calculate
the generalized form factor. We show that the dependence on the rescaled time
in units of the Heisenberg time is universal for both the spectral and the
generalized form factor. Furthermore, we derive a relation between the
generalized form factor and the classical time-correlation function of the Weyl
symbols of the quantum operators.Comment: some typos corrected and few minor changes made; final version in PR
On a small-gain approach to distributed event-triggered control
In this paper the problem of stabilizing large-scale systems by distributed
controllers, where the controllers exchange information via a shared limited
communication medium is addressed. Event-triggered sampling schemes are
proposed, where each system decides when to transmit new information across the
network based on the crossing of some error thresholds. Stability of the
interconnected large-scale system is inferred by applying a generalized
small-gain theorem. Two variations of the event-triggered controllers which
prevent the occurrence of the Zeno phenomenon are also discussed.Comment: 30 pages, 9 figure
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