TY  - GEN
A1  - Flad, Heinz-Jürgen
A1  - Harutyunyan, Gohar
A1  - Schulze, Bert-Wolfgang
T1  - Singular analysis and coupled cluster theory
N2  - The primary motivation for systematic bases in first principles electronic structure simulations is to derive physical and chemical properties of molecules and solids with predetermined accuracy. This requires a detailed understanding of the asymptotic behaviour of many-particle Coulomb systems near coalescence points of particles. Singular analysis provides a convenient framework to study the asymptotic behaviour of wavefunctions near these singularities. In the present work, we want to introduce the mathematical framework of singular analysis and discuss a novel asymptotic parametrix construction for Hamiltonians of many-particle Coulomb systems. This corresponds to the construction of an approximate inverse of a Hamiltonian operator with remainder given by a so-called Green operator. The Green operator encodes essential asymptotic information and we present as our main result an explicit asymptotic formula for this operator. First applications to many-particle models in quantum chemistry are presented in order to demonstrate the feasibility of our approach. The focus is on the asymptotic behaviour of ladder diagrams, which provide the dominant contribution to shortrange correlation in coupled cluster theory. Furthermore, we discuss possible consequences of our asymptotic analysis with respect to adaptive wavelet approximation.
T3  - Zweitveröffentlichungen der Universität Potsdam : Mathematisch-Naturwissenschaftliche Reihe - 302 
Y1  - 2015
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-102306
SP  - 31530
EP  - 31541
ER  - 
TY  - INPR
A1  - Calvo, D.
A1  - Schulze, Bert-Wolfgang
T1  - Edge symbolic structures of second generation
N2  - Operators on a manifold with (geometric) singularities are degenerate in a natural way. They have a principal symbolic structure with contributions from the different strata of the configuration. We study the calculus of such operators on the level of edge symbols of second generation, based on specific quantizations of the corner-degenerate interior symbols, and show that this structure is preserved under compositions.
T3  - Preprint - (2005) 18 
KW  - Operators on manifolds with second order singularities
KW  - edge quantizations
KW  - continuity in Sobolev spaces with double weights
Y1  - 2005
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus-29940
ER  -