331 research outputs found
Limit theorems for random point measures generated by cooperative sequential adsorption
We consider a finite sequence of random points in a finite domain of a
finite-dimensional Euclidean space. The points are sequentially allocated in
the domain according to a model of cooperative sequential adsorption. The main
peculiarity of the model is that the probability distribution of a point
depends on previously allocated points. We assume that the dependence vanishes
as the concentration of points tends to infinity. Under this assumption the law
of large numbers, the central limit theorem and Poisson approximation are
proved for the generated sequence of random point measures.Comment: 17 page
Breakup Density in Spectator Fragmentation
Proton-proton correlations and correlations of protons, deuterons and tritons
with alpha particles from spectator decays following 197Au + 197Au collisions
at 1000 MeV per nucleon have been measured with two highly efficient detector
hodoscopes. The constructed correlation functions, interpreted within the
approximation of a simultaneous volume decay, indicate a moderate expansion and
low breakup densities, similar to assumptions made in statistical
multifragmentation models.
PACS numbers: 25.70.Pq, 21.65.+f, 25.70.Mn, 25.75.GzComment: 11 pages, LaTeX with 3 included figures; Also available from
http://www-kp3.gsi.de/www/kp3/aladin_publications.htm
Finite size effects and the order of a phase transition in fragmenting nuclear systems
We discuss the implications of finite size effects on the determination of
the order of a phase transition which may occur in infinite systems. We
introduce a specific model to which we apply different tests. They are aimed to
characterise the smoothed transition observed in a finite system. We show that
the microcanonical ensemble may be a useful framework for the determination of
the nature of such transitions.Comment: LateX, 5 pages, 5 figures; Fig. 1 change
Time Scales in Spectator Fragmentation
Proton-proton correlations and correlations of p-alpha, d-alpha, and t-alpha
from spectator decays following Au + Au collisions at 1000 AMeV have been
measured with an highly efficient detector hodoscope. The constructed
correlation functions indicate a moderate expansion and low breakup densities
similar to assumptions made in statistical multifragmentation models. In
agreement with a volume breakup rather short time scales were deduced employing
directional cuts in proton-proton correlations.
PACS numbers: 25.70.Pq, 21.65.+f, 25.70.MnComment: 8 pages, with 5 included figures; To appear in the proceedings of the
CRIS 2000 conference; Also available from
http://www-kp3.gsi.de/www/kp3/aladin_publications.htm
Thermal and Chemical Freeze-out in Spectator Fragmentation
Isotope temperatures from double ratios of hydrogen, helium, lithium,
beryllium, and carbon isotopic yields, and excited-state temperatures from
yield ratios of particle-unstable resonances in 4He, 5Li, and 8Be, were
determined for spectator fragmentation, following collisions of 197Au with
targets ranging from C to Au at incident energies of 600 and 1000 MeV per
nucleon. A deviation of the isotopic from the excited-state temperatures is
observed which coincides with the transition from residue formation to
multi-fragment production, suggesting a chemical freeze-out prior to thermal
freeze-out in bulk disintegrations.Comment: 14 pages, 10 figures, submitted to Phys. Rev. C, small changes as
suggested by the editors and referee
Tight Finite-Key Analysis for Quantum Cryptography
Despite enormous progress both in theoretical and experimental quantum
cryptography, the security of most current implementations of quantum key
distribution is still not established rigorously. One of the main problems is
that the security of the final key is highly dependent on the number, M, of
signals exchanged between the legitimate parties. While, in any practical
implementation, M is limited by the available resources, existing security
proofs are often only valid asymptotically for unrealistically large values of
M. Here, we demonstrate that this gap between theory and practice can be
overcome using a recently developed proof technique based on the uncertainty
relation for smooth entropies. Specifically, we consider a family of
Bennett-Brassard 1984 quantum key distribution protocols and show that security
against general attacks can be guaranteed already for moderate values of M.Comment: 11 pages, 2 figure
Application of Information Theory in Nuclear Liquid Gas Phase Transition
Information entropy and Zipf's law in the field of information theory have
been used for studying the disassembly of nuclei in the framework of the
isospin dependent lattice gas model and molecular dynamical model. We found
that the information entropy in the event space is maximum at the phase
transition point and the mass of the cluster show exactly inversely to its
rank, i.e. Zipf's law appears. Both novel criteria are useful in searching the
nuclear liquid gas phase transition experimentally and theoretically.Comment: 5 pages, 5 figure
Breakup Temperature of Target Spectators in Au + Au Collisions at E/A = 1000 MeV
Breakup temperatures were deduced from double ratios of isotope yields for
target spectators produced in the reaction Au + Au at 1000 MeV per nucleon.
Pairs of He and Li isotopes and pairs of He and H
isotopes (p, d and d, t) yield consistent temperatures after feeding
corrections, based on the quantum statistical model, are applied. The
temperatures rise with decreasing impact parameter from 4 MeV for peripheral to
about 10 MeV for the most central collisions.
The good agreement with the breakup temperatures measured previously for
projectile spectators at an incident energy of 600 MeV per nucleon confirms the
observed universality of the spectator decay at relativistic bombarding
energies. The measured temperatures also agree with the breakup temperatures
predicted by the statistical multifragmentation model. For these calculations a
relation between the initial excitation energy and mass was derived which gives
good simultaneous agreement for the fragment charge correlations.
The energy spectra of light charged particles, measured at =
150, exhibit Maxwellian shapes with inverse slope parameters much
higher than the breakup temperatures. The statistical multifragmentation model,
because Coulomb repulsion and sequential decay processes are included, yields
light-particle spectra with inverse slope parameters higher than the breakup
temperatures but considerably below the measured values. The systematic
behavior of the differences suggests that they are caused by
light-charged-particle emission prior to the final breakup stage.
PACS numbers: 25.70.Mn, 25.70.Pq, 25.75.-qComment: 29 pages, TeX with 11 included figures; Revised version accepted for
publication in Z. Phys. A Two additional figure
Isospin influences on particle emission and critical phenomenon in nuclear dissociation
Features of particle emission and critical point behavior are investigated as
functions of the isospin of disassembling sources and temperature at a moderate
freeze-out density for medium-size Xe isotopes in the framework of isospin
dependent lattice gas model. Multiplicities of emitted light particles,
isotopic and isobaric ratios of light particles show the strong dependence on
the isospin of the dissociation source, but double ratios of light isotope
pairs and the critical temperature determined by the extreme values of some
critical observables are insensitive to the isospin of the systems. Values of
the power law parameter of cluster mass distribution, mean multiplicity of
intermediate mass fragments (), information entropy () and Campi's
second moment () also show a minor dependence on the isospin of Xe
isotopes at the critical point. In addition, the slopes of the average
multiplicites of the neutrons (), protons (), charged particles
(), and IMFs (), slopes of the largest fragment mass number
(), and the excitation energy per nucleon of the disassembling source
() to temperature are investigated as well as variances of the
distributions of , , , , and . It
is found that they can be taken as additional judgements to the critical
phenomena.Comment: 9 Pages, 8 figure
Mass dependence of light nucleus production in ultrarelativistic heavy ion collisions
Light nuclei can be produced in the central reaction zone via coalescence in
relativistic heavy ion collisions. E864 at BNL has measured the production of
ten light nuclei with nuclear number of A=1 to A=7 at rapidity and
. Data were taken with a Au beam of momentum of 11.5 A
on a Pb or Pt target with different experimental settings. The
invariant yields show a striking exponential dependence on nuclear number with
a penalty factor of about 50 per additional nucleon. Detailed analysis reveals
that the production may depend on the spin factor of the nucleus and the
nuclear binding energy as well.Comment: (6 pages, 3 figures), some changes on text, references and figures'
lettering. To be published in PRL (13Dec1999
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