139 research outputs found
Semiclassical approach to the line shape
We extend the results of Bakalov D., B.Jeziorski, T.Korona, K.Szalewicz,
E.Tchoukova, Phys. Rev. Lett. {\bf 84} (2000) 2350, on one-photon electric
dipole transition line shift and broadening to the case of two-photon
transitions. As an example we consider the laser induced transition in
antiprotonic helium produced in helium gas target. The transition is between
antiprotonic helium states and . PACS 32.70.Jz,
34.20.Gj, 36.10.-kComment: 12 page
Multidomain spectral method for the Gauss hypergeometric function
We present a multidomain spectral approach for Fuchsian ordinary differential equations in the particular case of the hypergeometric equation. Our hybrid approach uses Frobeniusâ method and Moebius transformations in the vicinity of each of the singular points of the hypergeometric equation, which leads to a natural decomposition of the real axis into domains. In each domain, solutions to the hypergeometric equation are constructed via the well-conditioned ultraspherical spectral method. The solutions are matched at the domain boundaries to lead to a solution which is analytic on the whole compactified real line RâȘâ , except for the singular points and cuts of the Riemann surface on which the solution is defined. The solution is further extended to the whole Riemann sphere by using the same approach for ellipses enclosing the singularities. The hypergeometric equation is solved on the ellipses with the boundary data from the real axis. This solution is continued as a harmonic function to the interior of the disk by solving the Laplace equation in polar coordinates with an optimal complexity Fourierâultraspherical spectral method. In cases where logarithms appear in the solution, a hybrid approach involving an analytical treatment of the logarithmic terms is applied. We show for several examples that machine precision can be reached for a wide class of parameters, but also discuss almost degenerate cases where this is not possible
On the Bound States in a Non-linear Quantum Field Theory of a Spinor Field with Higher Derivatives
We consider a model of quantum field theory with higher derivatives for a
spinor field with quartic selfinteraction. With the help of the Bethe-Salpeter
equation we study the problem of the two particle bound states in the "chain"
approximation. The existence of a scalar bound state is established.Comment: 14 pages, no figures, LaTe
Classification of integrable two-component Hamiltonian systems of hydrodynamic type in 2+1 dimensions
Hamiltonian systems of hydrodynamic type occur in a wide range of
applications including fluid dynamics, the Whitham averaging procedure and the
theory of Frobenius manifolds. In 1+1 dimensions, the requirement of the
integrability of such systems by the generalised hodograph transform implies
that integrable Hamiltonians depend on a certain number of arbitrary functions
of two variables. On the contrary, in 2+1 dimensions the requirement of the
integrability by the method of hydrodynamic reductions, which is a natural
analogue of the generalised hodograph transform in higher dimensions, leads to
finite-dimensional moduli spaces of integrable Hamiltonians. In this paper we
classify integrable two-component Hamiltonian systems of hydrodynamic type for
all existing classes of differential-geometric Poisson brackets in 2D,
establishing a parametrisation of integrable Hamiltonians via
elliptic/hypergeometric functions. Our approach is based on the Godunov-type
representation of Hamiltonian systems, and utilises a novel construction of
Godunov's systems in terms of generalised hypergeometric functions.Comment: Latex, 34 page
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