294 research outputs found
On the Mixing of Diffusing Particles
We study how the order of N independent random walks in one dimension evolves
with time. Our focus is statistical properties of the inversion number m,
defined as the number of pairs that are out of sort with respect to the initial
configuration. In the steady-state, the distribution of the inversion number is
Gaussian with the average ~N^2/4 and the standard deviation sigma N^{3/2}/6.
The survival probability, S_m(t), which measures the likelihood that the
inversion number remains below m until time t, decays algebraically in the
long-time limit, S_m t^{-beta_m}. Interestingly, there is a spectrum of
N(N-1)/2 distinct exponents beta_m(N). We also find that the kinetics of
first-passage in a circular cone provides a good approximation for these
exponents. When N is large, the first-passage exponents are a universal
function of a single scaling variable, beta_m(N)--> beta(z) with
z=(m-)/sigma. In the cone approximation, the scaling function is a root of a
transcendental equation involving the parabolic cylinder equation, D_{2
beta}(-z)=0, and surprisingly, numerical simulations show this prediction to be
exact.Comment: 9 pages, 6 figures, 2 table
Complete positivity of nonlinear evolution: A case study
Simple Hartree-type equations lead to dynamics of a subsystem that is not
completely positive in the sense accepted in mathematical literature. In the
linear case this would imply that negative probabilities have to appear for
some system that contains the subsystem in question. In the nonlinear case this
does not happen because the mathematical definition is physically unfitting as
shown on a concrete example.Comment: extended version, 3 appendices added (on mixed states, projection
postulate, nonlocality), to be published in Phys. Rev.
Kakucs-Balla-domb. A case study in the absolute and relative chronology of the Vatya culture
Measurement of the quasi-elastic axial vector mass in neutrino-oxygen interactions
The weak nucleon axial-vector form factor for quasi-elastic interactions is
determined using neutrino interaction data from the K2K Scintillating Fiber
detector in the neutrino beam at KEK. More than 12,000 events are analyzed, of
which half are charged-current quasi-elastic interactions nu-mu n to mu- p
occurring primarily in oxygen nuclei. We use a relativistic Fermi gas model for
oxygen and assume the form factor is approximately a dipole with one parameter,
the axial vector mass M_A, and fit to the shape of the distribution of the
square of the momentum transfer from the nucleon to the nucleus. Our best fit
result for M_A = 1.20 \pm 0.12 GeV. Furthermore, this analysis includes updated
vector form factors from recent electron scattering experiments and a
discussion of the effects of the nucleon momentum on the shape of the fitted
distributions.Comment: 14 pages, 10 figures, 6 table
The realisation of voicing assimilation rules in Hungarian spontaneous and read speech: Case studies
Complex geoarcheological investigation at the Székelyudvarhely-Kadicsfalva/Cãdiseni site (Romania)
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