94,938 research outputs found
Some properties of the resonant state in quantum mechanics and its computation
The resonant state of the open quantum system is studied from the viewpoint
of the outgoing momentum flux. We show that the number of particles is
conserved for a resonant state, if we use an expanding volume of integration in
order to take account of the outgoing momentum flux; the number of particles
would decay exponentially in a fixed volume of integration. Moreover, we
introduce new numerical methods of treating the resonant state with the use of
the effective potential. We first give a numerical method of finding a
resonance pole in the complex energy plane. The method seeks an energy
eigenvalue iteratively. We found that our method leads to a super-convergence,
the convergence exponential with respect to the iteration step. The present
method is completely independent of commonly used complex scaling. We also give
a numerical trick for computing the time evolution of the resonant state in a
limited spatial area. Since the wave function of the resonant state is
diverging away from the scattering potential, it has been previously difficult
to follow its time evolution numerically in a finite area.Comment: 20 pages, 12 figures embedde
SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop
SecDec is a program which can be used for the factorization of dimensionally
regulated poles from parametric integrals, in particular multi-loop integrals,
and the subsequent numerical evaluation of the finite coefficients. Here we
present version 3.0 of the program, which has major improvements compared to
version 2: it is faster, contains new decomposition strategies, an improved
user interface and various other new features which extend the range of
applicability.Comment: 46 pages, version to appear in Comput.Phys.Com
Machine Precision Evaluation of Singular and Nearly Singular Potential Integrals by Use of Gauss Quadrature Formulas for Rational Functions
A new technique for machine precision evaluation of singular and nearly singular potential integrals with 1/R singularities is presented. The numerical quadrature scheme is based on a new rational expression for the integrands, obtained by a cancellation procedure. In particular, by using library routines for Gauss quadrature of rational functions readily available in the literature, this new expression permits the exact numerical integration of singular static potentials associated with polynomial source distributions. The rules to achieve the desired numerical accuracy for singular and nearly singular static and dynamic potential integrals are presented and discussed, and several numerical examples are provide
SecDec: A general program for sector decomposition
We present a program for the numerical evaluation of multi-dimensional
polynomial parameter integrals. Singularities regulated by dimensional
regularisation are extracted using iterated sector decomposition. The program
evaluates the coefficients of a Laurent series in the regularisation parameter.
It can be applied to multi-loop integrals in Euclidean space as well as other
parametric integrals, e.g. phase space integrals.Comment: 42 pages, 12 figures. Replaced by published version. Cuba library
included in the progra
The Sivashinsky equation for corrugated flames in the large-wrinkle limit
Sivashinsky's (1977) nonlinear integro-differential equation for the shape of
corrugated 1-dimensional flames is ultimately reducible to a 2N-body problem,
involving the 2N complex poles of the flame slope. Thual, Frisch & Henon (1985)
derived singular linear integral equations for the pole density in the limit of
large steady wrinkles , which they solved exactly for monocoalesced
periodic fronts of highest amplitude of wrinkling and approximately otherwise.
Here we solve those analytically for isolated crests, next for monocoalesced
then bicoalesced periodic flame patterns, whatever the (large-) amplitudes
involved. We compare the analytically predicted pole densities and flame shapes
to numerical results deduced from the pole-decomposition approach. Good
agreement is obtained, even for moderately large Ns. The results are extended
to give hints as to the dynamics of supplementary poles. Open problems are
evoked
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