128 research outputs found
Computation of inflationary cosmological perturbations in the power-law inflationary model using the phase-integral method
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used
for computing cosmological perturbations in the power-law inflationary model.
The phase-integral formulas for the scalar and tensor power spectra are
explicitly obtained up to ninth-order of the phase-integral approximation. We
show that, the phase-integral approximation exactly reproduces the shape of the
power spectra for scalar and tensor perturbations as well as the spectral
indices. We compare the accuracy of the phase-integral approximation with the
results for the power spectrum obtained with the slow-roll and uniform
approximation methods.Comment: 16 pages, Revtex, to appear in Physical Review
Computation of inflationary cosmological perturbations in chaotic inflationary scenarios using the phase-integral method
The phase-integral approximation devised by Fr\"oman and Fr\"oman, is used
for computing cosmological perturbations in the quadratic chaotic inflationary
model. The phase-integral formulas for the scalar and tensor power spectra are
explicitly obtained up to fifth order of the phase-integral approximation. We
show that, the phase integral gives a very good approximation for the shape of
the power spectra associated with scalar and tensor perturbations as well as
the spectral indices. We find that the accuracy of the phase-integral
approximation compares favorably with the numerical results and those obtained
using the slow-roll and uniform approximation methods.Comment: 21 pages, RevTex, to appear in Phys. Rev
Asymptotic Spectroscopy of Rotating Black Holes
We calculate analytically the transmission and reflection amplitudes for
waves incident on a rotating black hole in d=4, analytically continued to
asymptotically large, nearly imaginary frequency. These amplitudes determine
the asymptotic resonant frequencies of the black hole, including quasinormal
modes, total-transmission modes and total-reflection modes. We identify these
modes with semiclassical bound states of a one-dimensional Schrodinger
equation, localized along contours in the complexified r-plane which connect
turning points of corresponding null geodesics. Each family of modes has a
characteristic temperature and chemical potential. The relations between them
provide hints about the microscopic description of the black hole in this
asymptotic regime.Comment: References adde
Critical view of WKB decay widths
A detailed comparison of the expressions for the decay widths obtained within
the semiclassical WKB approximation using different approaches to the tunneling
problem is performed. The differences between the available improved formulae
for tunneling near the top and the bottom of the barrier are investigated.
Though the simple WKB method gives the right order of magnitude of the decay
widths, a small number of parameters are often fitted. The need to perform the
fitting procedure remaining consistently within the WKB framework is emphasized
in the context of the fission model based calculations. Calculations for the
decay widths of some recently found super heavy nuclei using microscopic
alpha-nucleus potentials are presented to demonstrate the importance of a
consistent WKB calculation. The half-lives are found to be sensitive to the
density dependence of the nucleon-nucleon interaction and the implementation of
the Bohr-Sommerfeld quantization condition inherent in the WKB approach.Comment: 18 pages, Late
Alpha Decay Hindrance Factors: A Probe of Mean Field Wave Functions
A simple model to calculate alpha-decay Hindrance Factors is presented. Using
deformation values obtained from PES calculations as the only input, Hindrance
Factors for the alpha-decay of Rn- and Po-isotopes are calculated. It is found
that the intrinsic structure around the Fermi surface determined by the
deformed mean field plays an important role in determining the hindrance of
alpha-decay. The fair agreement between experimental and theoretical Hindrance
Factors suggest that the wave function obtained from the energy minima of the
PES calculations contains an important part of the correlations that play a
role for the alpha-decay. The calculated HF that emerges from these
calculations render a different interpretation than the commonly assumed
n-particle n-hole picture.Comment: 7 pages, 9 figure
The WKB Approximation without Divergences
In this paper, the WKB approximation to the scattering problem is developed
without the divergences which usually appear at the classical turning points. A
detailed procedure of complexification is shown to generate results identical
to the usual WKB prescription but without the cumbersome connection formulas.Comment: 13 pages, TeX file, to appear in Int. J. Theor. Phy
Energy evolution in time-dependent harmonic oscillator
The theory of adiabatic invariants has a long history, and very important
implications and applications in many different branches of physics,
classically and quantally, but is rarely founded on rigorous results. Here we
treat the general time-dependent one-dimensional harmonic oscillator, whose
Newton equation cannot be solved in general. We
follow the time-evolution of an initial ensemble of phase points with sharply
defined energy at time and calculate rigorously the distribution of
energy after time , which is fully (all moments, including the
variance ) determined by the first moment . For example,
, and all
higher even moments are powers of , whilst the odd ones vanish
identically. This distribution function does not depend on any further details
of the function and is in this sense universal. In ideal
adiabaticity , and the variance is
zero, whilst for finite we calculate , and for the
general case using exact WKB-theory to all orders. We prove that if is of class (all derivatives up to and including the order
are continuous) , whilst for class it is known to be exponential .Comment: 26 pages, 5 figure
Some properties of WKB series
We investigate some properties of the WKB series for arbitrary analytic
potentials and then specifically for potentials ( even), where more
explicit formulae for the WKB terms are derived. Our main new results are: (i)
We find the explicit functional form for the general WKB terms ,
where one has only to solve a general recursion relation for the rational
coefficients. (ii) We give a systematic algorithm for a dramatic simplification
of the integrated WKB terms that enter the energy
eigenvalue equation. (iii) We derive almost explicit formulae for the WKB terms
for the energy eigenvalues of the homogeneous power law potentials , where is even. In particular, we obtain effective algorithms to
compute and reduce the terms of these series.Comment: 18 pages, submitted to Journal of Physics A: Mathematical and Genera
Quantal Two-Centre Coulomb Problem treated by means of the Phase-Integral Method II. Quantization Conditions in the Symmetric Case Expressed in Terms of Complete Elliptic Integrals. Numerical Illustration
The contour integrals, occurring in the arbitrary-order phase-integral
quantization conditions given in a previous paper, are in the first- and
third-order approximations expressed in terms of complete elliptic integrals in
the case that the charges of the Coulomb centres are equal. The evaluation of
the integrals is facilitated by the knowledge of quasiclassical dynamics. The
resulting quantization conditions involving complete elliptic integrals are
solved numerically to obtain the energy eigenvalues and the separation
constants of the and states of the hydrogen molecule ion
for various values of the internuclear distance. The accuracy of the formulas
obtained is illustrated by comparison with available numerically exact results.Comment: 19 pages, RevTeX 4, 4 EPS figures, submitted to J. Math. Phy
Fundamental solution method applied to time evolution of two energy level systems: exact and adiabatic limit results
A method of fundamental solutions has been used to investigate transitions in
two energy level systems with no level crossing in a real time. Compact
formulas for transition probabilities have been found in their exact form as
well as in their adiabatic limit. No interference effects resulting from many
level complex crossings as announced by Joye, Mileti and Pfister (Phys. Rev.
{\bf A44} 4280 (1991)) have been detected in either case. It is argued that
these results of this work are incorrect. However, some effects of Berry's
phases are confirmed.Comment: LaTeX2e, 23 pages, 8 EPS figures. Style correcte
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