Double-Well Potential : The WKB Approximation with Phase Loss and Anharmonicity Effect

We derive a general WKB energy splitting formula in a double-well potential by incorporating both phase loss and anharmonicity effect in the usual WKB approximation. A bare application of the phase loss approach to the usual WKB method gives better results only for large separation between two potential minima. In the range of substantial tunneling, however, the phase loss approach with anharmonicity effect considered leads to a great improvement on the accuracy of the WKB approximation.Comment: 14 pages, revtex, 1 figure, will appear at Phys. Rev.

Parameter estimation using the genetic algorithm and its impact on quantitative precipitation forecast

In this study, optimal parameter estimations are performed for both physical and computational parameters in a mesoscale meteorological model, and their impacts on the quantitative precipitation forecasting (QPF) are assessed for a heavy rainfall case occurred at the Korean Peninsula in June 2005. Experiments are carried out using the PSU/NCAR MM5 model and the genetic algorithm (GA) for two parameters: the reduction rate of the convective available potential energy in the Kain-Fritsch (KF) scheme for cumulus parameterization, and the Asselin filter parameter for numerical stability. The fitness function is defined based on a QPF skill score. It turns out that each optimized parameter significantly improves the QPF skill. Such improvement is maximized when the two optimized parameters are used simultaneously. Our results indicate that optimizations of computational parameters as well as physical parameters and their adequate applications are essential in improving model performance

The Case for Hypercritical Accretion in M33 X-7

The spin parameter of the black hole in M33 X-7 has recently been measured to be a*=0.77+-0.05 (Liu et al. 2008). It has been proposed that the spin of the 15.65 M_sun black hole is natal. We show that this is not a viable evolutionary path given the observed binary orbital period of 3.45 days since the explosion that would produce a black hole with the cited spin parameter and orbital period would disrupt the binary. Furthermore, we show that the system has to be evolved through the hypercritical mass transfer of about 5 M_sun from the secondary star to the black hole.Comment: 4 page

Limits of Binaries That Can Be Characterized by Gravitational Microlensing

Due to the high efficiency of planet detections, current microlensing planet searches focus on high-magnification events. High-magnification events are sensitive to remote binary companions as well and thus a sample of wide-separation binaries are expected to be collected as a byproduct. In this paper, we show that characterizing binaries for a portion of this sample will be difficult due to the degeneracy of the binary-lensing parameters. This degeneracy arises because the perturbation induced by the binary companion is well approximated by the Chang-Refsdal lensing for binaries with separations greater than a certain limit. For binaries composed of equal mass lenses, we find that the lens binarity can be noticed up to the separations of $\sim 60$ times of the Einstein radius corresponding to the mass of each lens. Among these binaries, however, we find that the lensing parameters can be determined only for a portion of binaries with separations less than $\sim 20$ times of the Einstein radius.Comment: 5 pages, 3 figures, 1 tabl

Instantonic approach to triple well potential

By using a usual instanton method we obtain the energy splitting due to quantum tunneling through the triple well barrier. It is shown that the term related to the midpoint of the energy splitting in propagator is quite different from that of double well case, in that it is proportional to the algebraic average of the frequencies of the left and central wells.Comment: Revtex, 11 pages, Included one eps figur