62,250 research outputs found
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
Heat capacity of square-well fluids of variable width
We have obtained by Monte Carlo NVT simulations the constant-volume excess
heat capacity of square-well fluids for several temperatures, densities and
potential widths. Heat capacity is a thermodynamic property much more sensitive
to the accuracy of a theory than other thermodynamic quantities, such as the
compressibility factor. This is illustrated by comparing the reported
simulation data for the heat capacity with the theoretical predictions given by
the Barker-Henderson perturbation theory as well as with those given by a
non-perturbative theoretical model based on Baxter's solution of the
Percus-Yevick integral equation for sticky hard spheres. Both theories give
accurate predictions for the equation of state. By contrast, it is found that
the Barker-Henderson theory strongly underestimates the excess heat capacity
for low to moderate temperatures, whereas a much better agreement between
theory and simulation is achieved with the non-perturbative theoretical model,
particularly for small well widths, although the accuracy of the latter worsens
for high densities and low temperatures, as the well width increases.Comment: 11 pages, 4 figures; figures now include additional perturbation
data; to be published in Mol. Phy
Controlled localization of interacting bosons in a disordered optical lattice
We show that tunneling and localization properties of interacting ultracold
atoms in an optical lattice can be controlled by adiabatically turning on a
fast oscillatory force even in the presence of disorder. Our calculations are
based on the exact solution of the time-dependent Schroedinger equation, using
the Floquet formalism. Implications of our findings for larger systems and the
possibility of controlling the phase diagram of disordered-interacting bosonic
systems are discussed.Comment: 7 pages 7 fig
Is CDM an effective CCDM cosmology?
We show that a cosmology driven by gravitationally induced particle
production of all non-relativistic species existing in the present Universe
mimics exactly the observed flat accelerating CDM cosmology with just
one dynamical free parameter. This kind of scenario includes the creation cold
dark matter (CCDM) model [Lima, Jesus & Oliveira, JCAP 011(2010)027] as a
particular case and also provides a natural reduction of the dark sector since
the vacuum component is not needed to accelerate the Universe. The new cosmic
scenario is equivalent to CDM both at the background and perturbative
levels and the associated creation process is also in agreement with the
universality of the gravitational interaction and equivalence principle.
Implicitly, it also suggests that the present day astronomical observations
cannot be considered the ultimate proof of cosmic vacuum effects in the evolved
Universe because CDM may be only an effective cosmology.Comment: 6 pages, 2 figures, changes in the abstract, introduction, new
references and typo correction
Pair correlation function of short-ranged square-well fluids
We have performed extensive Monte Carlo simulations in the canonical (NVT)
ensemble of the pair correlation function for square-well fluids with well
widths ranging from 0.1 to 1.0, in units of the diameter
of the particles. For each one of these widths, several densities and
temperatures in the ranges and
, where is the
critical temperature, have been considered. The simulation data are used to
examine the performance of two analytical theories in predicting the structure
of these fluids: the perturbation theory proposed by Tang and Lu [Y. Tang and
B. C.-Y. Lu, J. Chem. Phys. {\bf 100}, 3079, 6665 (1994)] and the
non-perturbative model proposed by two of us [S. B. Yuste and A. Santos, J.
Chem. Phys. {\bf 101}, 2355 (1994)]. It is observed that both theories
complement each other, as the latter theory works well for short ranges and/or
moderate densities, while the former theory does for long ranges and high
densities.Comment: 10 pages, 10 figure
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