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Asymptotology
About: Asymptotology is a research topic. Over the lifetime, 1319 publications have been published within this topic receiving 35831 citations.
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TL;DR: In this paper, the density of eigenvalues of a potential well is calculated in an asymptotic expansion for large geometrical size and explicit, readily calculable expressions for volume and surface contributions are obtained for the case of a spherical Woods-Saxon well.
8 citations
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8 citations
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01 Jan 1993TL;DR: In this article, the authors proved the asymptotic completeness of long-range quantum systems with respect to the clustering for N -body long-term quantum systems.
Abstract: It is well-known that the asymptotic completeness holds for short-range quantum systems. The first proof was given by Sigal-Soffer in reference [13] of Part I [9], which we refer to as reference [I.13], and the alternative proofs were obtained by Graf [I.8], Kitada [9], Derezinski [3], Tamura [I.17], and Yafaev [18]. In the present paper we shall prove the asymptotic clustering for N -body long-range quantum systems
8 citations
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TL;DR: In this article, a system of integro-differential equations with rapidly varying kernels, one of which has an unstable spectral value, is considered and an algorithm based on the method of normal forms is proposed for finding asymptotic solutions (of an arbitrary order).
Abstract: A system of integro-differential equations with rapidly varying kernels, one of which has an unstable spectral value, is considered. An algorithm based on the method of normal forms is proposed for finding asymptotic solutions (of an arbitrary order). The contrast structures (internal transition layers) in solutions to the problem are investigated by analyzing the leading term of the asymptotic expansion. It is shown that the contrast structures are caused by the instability of the spectral value and by the presence of inhomogeneity. The role of the kernels of the integral operators in the formation of contrast structures is clarified.
8 citations