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Discrete transformation for three-wave problems is constructed in explicit form. Generalization of this system on the matrix case in three dimensional space together with corresponding discrete transformation is presented also. © 2003 American Institute of Physics.
The scattering of scalar waves by objects located inside a waveguide or a cavity is discussed using the method of pseudopotentials. Pseudopotentials were introduced to simulate short-range potentials in quantum mechanics and proved useful in many-body problems and in problems involving...
We consider several types of integrals that arise in the context of quantum field theory that factor into a holomorphic and antiholomorphic piece. This gives rise to a conformal block representations for some of the integrals. © 2003 American Institute of Physics.
We discuss a concept of particle localization which is motivated from quantum field theory, and has been proposed by Brunetti, Guido and Longo and by Schroer. It endows the single-particle Hilbert space with a family of real subspaces indexed by the space–time regions, with certain specific...
The homogeneous Bloch equation reduces to the Riccati equation. By linearizing the Riccati equation, a set of three solutions of the homogeneous Bloch equation is found. The fundamental matrix becomes singular. We clarify the utility and limitation of our approach to solve the homogeneous Bloch...
We derive topological algebras for two-dimensional models admitting a d = δ , b d = δ , b decomposition (with b b the BRST operator). In general, the topological algebra we obtain is not derived from the twisting of an N = 2 N = 2 supersymmetry algebra. We show, for the particular case of an...
In this paper we present a mathematical investigation of the phenomenon of dynamical localization in a class of quasi-periodically and periodically time-dependent two-level systems. Our results are based on a sort of “renormalization” procedure, which is developed here in a systematic way in...
In this article, we present a rigorous proof of the isotope effect within the theory of Bardeen–Cooper–Schrieffer for isotropic superconductors. We show that, when the interaction kernel is a positive constant, the isotope effect is exact; when the interaction kernel is a positive function...
For noncritical energies, the asymptotic behavior of the scattering phase and of the time-delay are known to be described by a Weyl type formula and the Breit–Wigner formula, respectively. We consider here the case of critical energy levels in dimension 1. We obtain the semiclassical...
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