13,583 research outputs found
Shot-noise statistics in diffusive conductors
We study the full probability distribution of the charge transmitted through
a mesoscopic diffusive conductor during a measurement time T. We have
considered a semi-classical model, with an exclusion principle in a discretized
single-particle phase-space. In the large T limit, numerical simulations show a
universal probability distribution which agrees very well with the quantum
mechanical prediction of Lee, Levitov and Yakovets [PRB {51} 4079 (1995)] for
the charge counting statistics. Special attention is given to its third
cumulant, including an analysis of finite size effects and of some experimental
constraints for its accurate measurement.Comment: Submitted to Eur. Phys. J. B (Jan. 2002
Scars on quantum networks ignore the Lyapunov exponent
We show that enhanced wavefunction localization due to the presence of short
unstable orbits and strong scarring can rely on completely different
mechanisms. Specifically we find that in quantum networks the shortest and most
stable orbits do not support visible scars, although they are responsible for
enhanced localization in the majority of the eigenstates. Scarring orbits are
selected by a criterion which does not involve the classical Lyapunov exponent.
We obtain predictions for the energies of visible scars and the distributions
of scarring strengths and inverse participation ratios.Comment: 5 pages, 2 figure
Random fluctuation leads to forbidden escape of particles
A great number of physical processes are described within the context of
Hamiltonian scattering. Previous studies have rather been focused on
trajectories starting outside invariant structures, since the ones starting
inside are expected to stay trapped there forever. This is true though only for
the deterministic case. We show however that, under finitely small random
fluctuations of the field, trajectories starting inside Arnold-Kolmogorov-Moser
(KAM) islands escape within finite time. The non-hyperbolic dynamics gains then
hyperbolic characteristics due to the effect of the random perturbed field. As
a consequence, trajectories which are started inside KAM curves escape with
hyperbolic-like time decay distribution, and the fractal dimension of a set of
particles that remain in the scattering region approaches that for hyperbolic
systems. We show a universal quadratic power law relating the exponential decay
to the amplitude of noise. We present a random walk model to relate this
distribution to the amplitude of noise, and investigate this phenomena with a
numerical study applying random maps.Comment: 6 pages, 6 figures - Up to date with corrections suggested by
referee
Recommendations and illustrations for the evaluation of photonic random number generators
The never-ending quest to improve the security of digital information
combined with recent improvements in hardware technology has caused the field
of random number generation to undergo a fundamental shift from relying solely
on pseudo-random algorithms to employing optical entropy sources. Despite these
significant advances on the hardware side, commonly used statistical measures
and evaluation practices remain ill-suited to understand or quantify the
optical entropy that underlies physical random number generation. We review the
state of the art in the evaluation of optical random number generation and
recommend a new paradigm: quantifying entropy generation and understanding the
physical limits of the optical sources of randomness. In order to do this, we
advocate for the separation of the physical entropy source from deterministic
post-processing in the evaluation of random number generators and for the
explicit consideration of the impact of the measurement and digitization
process on the rate of entropy production. We present the Cohen-Procaccia
estimate of the entropy rate as one way to do this. In order
to provide an illustration of our recommendations, we apply the Cohen-Procaccia
estimate as well as the entropy estimates from the new NIST draft standards for
physical random number generators to evaluate and compare three common optical
entropy sources: single photon time-of-arrival detection, chaotic lasers, and
amplified spontaneous emission
Random bits, true and unbiased, from atmospheric turbulence
Random numbers represent a fundamental ingredient for numerical simulation,
games, informa- tion science and secure communication. Algorithmic and
deterministic generators are affected by insufficient information entropy. On
the other hand, suitable physical processes manifest intrinsic unpredictability
that may be exploited for generating genuine random numbers with an entropy
reaching the ideal limit. In this work, we present a method to extract genuine
random bits by using the atmospheric turbulence: by sending a laser beam along
a 143Km free-space link, we took advantage of the chaotic behavior of air
refractive index in the optical propagation. Random numbers are then obtained
by converting in digital units the aberrations and distortions of the received
laser wave-front. The generated numbers, obtained without any post-processing,
pass the most selective randomness tests. The core of our extracting algorithm
can be easily generalized for other physical processes
Quantum Graphs: A model for Quantum Chaos
We study the statistical properties of the scattering matrix associated with
generic quantum graphs. The scattering matrix is the quantum analogue of the
classical evolution operator on the graph. For the energy-averaged spectral
form factor of the scattering matrix we have recently derived an exact
combinatorial expression. It is based on a sum over families of periodic orbits
which so far could only be performed in special graphs. Here we present a
simple algorithm implementing this summation for any graph. Our results are in
excellent agreement with direct numerical simulations for various graphs.
Moreover we extend our previous notion of an ensemble of graphs by considering
ensemble averages over random boundary conditions imposed at the vertices. We
show numerically that the corresponding form factor follows the predictions of
random-matrix theory when the number of vertices is large---even when all bond
lengths are degenerate. The corresponding combinatorial sum has a structure
similar to the one obtained previously by performing an energy average under
the assumption of incommensurate bond lengths.Comment: 8 pages, 3 figures. Contribution to the conference on Dynamics of
Complex Systems, Dresden (1999
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