737 research outputs found
Rational points on X_0^+ (p^r)
We show how the recent isogeny bounds due to \'E. Gaudron and G. R\'emond
allow to obtain the triviality of X_0^+ (p^r)(Q), for r>1 and p a prime
exceeding 2.10^{11}. This includes the case of the curves X_split (p). We then
prove, with the help of computer calculations, that the same holds true for p
in the range 10 < p < 10^{14}, p\neq 13. The combination of those results
completes the qualitative study of such sets of rational points undertook in
previous papers, with the exception of p=13.Comment: 16 pages, no figur
Remarks on the representation theory of the Moyal plane
We present an explicit construction of a unitary representation of the
commutator algebra satisfied by position and momentum operators on the Moyal
plane.Comment: 10 pages, minor changes, refs. adde
Neutrino mixing and masses in a left-right model with mirror fermions
In the framework of a left-right model containing mirror fermions with gauge
group SU(3),
we estimate the neutrino masses, which are found to be consistent with their
experimental bounds and hierarchy. We evaluate the decay rates of the Lepton
Flavor Violation (LFV) processes , and . We obtain upper limits for the
flavor-changing branching ratios in agreement with their present experimental
bounds. We also estimate the decay rates of heavy Majorana neutrinos in the
channels , and , which are roughly equal for large values of the heavy
neutrino mass. Starting from the most general Majorana neutrino mass matrix,
the smallness of active neutrino masses turns out from the interplay of the
hierarchy of the involved scales and the double application of seesaw
mechanism. An appropriate parameterization on the structure of the neutrino
mass matrix imposing a symmetric mixing of electron neutrino with muon and tau
neutrinos leads to Tri-bimaximal mixing matrix for light neutrinos.Comment: Accepted by European Physical Journal
Basic properties of nonlinear stochastic Schr\"{o}dinger equations driven by Brownian motions
The paper is devoted to the study of nonlinear stochastic Schr\"{o}dinger
equations driven by standard cylindrical Brownian motions (NSSEs) arising from
the unraveling of quantum master equations. Under the Born--Markov
approximations, this class of stochastic evolutions equations on Hilbert spaces
provides characterizations of both continuous quantum measurement processes and
the evolution of quantum systems. First, we deal with the existence and
uniqueness of regular solutions to NSSEs. Second, we provide two general
criteria for the existence of regular invariant measures for NSSEs. We apply
our results to a forced and damped quantum oscillator.Comment: Published in at http://dx.doi.org/10.1214/105051607000000311 the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
On the noncommutative eikonal
We study the eikonal approximation to quantum mechanics on the Moyal plane.
Instead of using a star product, the analysis is carried out in terms of
operator-valued wavefunctions depending on noncommuting, operator-valued
coordinates.Comment: 18 page
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