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Dynamical instabilities in density-dependent hadronic relativistic models
Unstable modes in asymmetric nuclear matter (ANM) at subsaturation densities
are studied in the framework of relativistic mean-field density-dependent
hadron models. The size of the instabilities that drive the system are
calculated and a comparison with results obtained within the non-linear Walecka
model is presented. The distillation and anti-distillation effects are
discussed.Comment: 8 pages, 8 Postscript figures. Submitted for publication in Phys.
Rev.
Hamilton-Jacobi Approach for Power-Law Potentials
The classical and relativistic Hamilton-Jacobi approach is applied to the
one-dimensional homogeneous potential, , where and
are continuously varying parameters. In the non-relativistic case, the
exact analytical solution is determined in terms of , and the total
energy . It is also shown that the non-linear equation of motion can be
linearized by constructing a hypergeometric differential equation for the
inverse problem . A variable transformation reducing the general problem
to that one of a particle subjected to a linear force is also established. For
any value of , it leads to a simple harmonic oscillator if , an
"anti-oscillator" if , or a free particle if E=0. However, such a
reduction is not possible in the relativistic case. For a bounded relativistic
motion, the first order correction to the period is determined for any value of
. For , it is found that the correction is just twice that one
deduced for the simple harmonic oscillator (), and does not depend on the
specific value of .Comment: 12 pages, Late
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