13,114 research outputs found
Tail asymptotics of the Brownian signature
The signature of a path \gamma is a sequence whose n-th term is the order-n iterated integrals of \gamma. It arises from solving multidimensional linear differential equations driven by \gamma. We are interested in relating the path properties of \gamma with its signature. If \gamma is C1, then an elegant formula of Hambly and Lyons relates the length of \gamma to the tail asymptotics of the signature.
We show an analogous formula for the multidimensional Brownian motion,with the quadratic variation playing a similar role to the length. In the proof, we study the hyperbolic development of Brownian motion and also
obtain a new subadditive estimate for the asymptotic of signature, which may be of independent interest. As a corollary, we strengthen the existing uniqueness results for the signatures of Brownian motion
Proton rich nuclei at and beyond the proton drip line in the Relativistic Mean Field theory
Ground state properties of proton-rich odd- nuclei in the region are studied in the relativistic mean field (RMF) theory. The RMF
equations are solved by using the expansion method in the Harmonic-Oscillator
basis. In the particle-particle channel, we use the state-dependent BCS method
with a zero-range -force, which has been proved to be effective even
for neutron-rich nuclei. All the ground state properties, including the
one-proton separation energies, the ground state deformations, the last
occupied proton orbits and the locations of proton drip line, are calculated.
Good agreement with both the available experimental data and the predictions of
the RHB method are obtained.Comment: the version to appear in Progress of Theoretical Physics, more
discussions adde
Masses, Deformations and Charge Radii--Nuclear Ground-State Properties in the Relativistic Mean Field Model
We perform a systematic study of the ground-state properties of all the
nuclei from the proton drip line to the neutron drip line throughout the
periodic table employing the relativistic mean field model. The TMA parameter
set is used for the mean-field Lagrangian density, and a state-dependent BCS
method is adopted to describe the pairing correlation. The ground-state
properties of a total of 6969 nuclei with and from the
proton drip line to the neutron drip line, including the binding energies, the
separation energies, the deformations, and the rms charge radii, are calculated
and compared with existing experimental data and those of the FRDM and HFB-2
mass formulae. This study provides the first complete picture of the current
status of the descriptions of nuclear ground-state properties in the
relativistic mean field model. The deviations from existing experimental data
indicate either that new degrees of freedom are needed, such as triaxial
deformations, or that serious effort is needed to improve the current
formulation of the relativistic mean field model.Comment: 16 pages, 5 figures, to appear in Progress of Theoretical Physic
A systematic study of neutron magic nuclei with N = 8, 20, 28, 50, 82, and 126 in the relativistic mean field theory
We perform a systematic study of all the traditional neutron magic nuclei
with = 8, 20, 28, 50, 82, and 126, from the neutron drip line to the proton
drip line. We adopt the deformed relativistic mean field (RMF) theory as our
framework and treat pairing correlations by a simple BCS method with a
zero-range -force. Remarkable agreement with the available experimental
data is obtained for the binding energies, the two- and one-proton separation
energies, and the nuclear charge radii. The calculated nuclear deformations are
compared with the available experimental data and the predictions of the FRDM
mass formula and the HFBCS-1 mass formula. We discuss, in particular, the
appearance of sub-shell magic nuclei by observing irregular behavior in the
two- and one-proton separation energies.Comment: the version to appear in Journal of Physics G; more references adde
Relativistic mean field theory for deformed nuclei with pairing correlations
We develop a relativistic mean field (RMF) description of deformed nuclei
with the pairing correlations in the BCS approximation. The treatment of the
pairing correlations for nuclei with the Fermi surface being close to the
threshold of unbound states needs a special attention. To this end, we take the
delta function interaction for the pairing interaction with the hope to pick up
those states with the wave function being concentrated in the nuclear region
and perform the standard BCS approximation for the single particle states
generated by the RMF theory with deformation. We apply the RMF + BCS method to
the Zr isotopes and obtain a good description of the binding energies and the
nuclear radii of nuclei from the proton drip line to the neutron drip line.Comment: the version to be published in Progress of Theoretical Physic
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