3,338 research outputs found
Lepton pair production by high-energy neutrino in an external electromagnetic field
The process of the lepton pair production by a neutrino propagating in an
external electromagnetic field is investigated in the framework of the Standard
Model. Relatively simple exact expression for the probability as the single
integral is obtained, which is suitable for a quantitative analysis.Comment: 9 pages, LATEX, 2 PS figures, submitted to Modern Physics Letters
Exchange-assisted tunneling in the classical limit
The exchange interaction and correlations may produce a power-law decay
instead of the usual exponential decrease of the wave function under potential
barrier. The exchange-assisted tunneling vanishes in the classical limit,
however, the dependence on the Planck constant h is different from that for a
conventional single-particle tunneling
Nanoparticles as a possible moderator for an ultracold neutron source
Ultracold and very cold neutrons (UCN and VCN) interact strongly with
nanoparticles due to the similarity of their wavelengths and nanoparticles
sizes. We analyze the hypothesis that this interaction can provide efficient
cooling of neutrons by ultracold nanoparticles at certain experimental
conditions, thus increasing the density of UCN by many orders of magnitude. The
present analytical and numerical description of the problem is limited to the
model of independent nanoparticles at zero temperature. Constraints of
application of this model are discussed
Exponential bounds for the probability deviations of sums of random fields
Non-asymptotic exponential upper bounds for the deviation probability for a sum of independent random fields are obtained under Bernstein's condition and assumptions formulated in terms of Kolmogorov's metric entropy. These estimations are constructive in the sense that all the constants involved are given explicitly. In the case of moderately large deviations, the upper bounds have optimal log-asymptotices. The exponential estimations are extended to the local and global continuity modulus for sums of independent samples of a random field
Chaplygin ball over a fixed sphere: explicit integration
We consider a nonholonomic system describing a rolling of a dynamically
non-symmetric sphere over a fixed sphere without slipping. The system
generalizes the classical nonholonomic Chaplygin sphere problem and it is shown
to be integrable for one special ratio of radii of the spheres. After a time
reparameterization the system becomes a Hamiltonian one and admits a separation
of variables and reduction to Abel--Jacobi quadratures. The separating
variables that we found appear to be a non-trivial generalization of
ellipsoidal (spheroconical) coordinates on the Poisson sphere, which can be
useful in other integrable problems.
Using the quadratures we also perform an explicit integration of the problem
in theta-functions of the new time.Comment: This is an extended version of the paper to be published in Regular
and Chaotic Dynamics, Vol. 13 (2008), No. 6. Contains 20 pages and 2 figure
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