We present a novel application of best N-term approximation theory in the framework of electronic structure calculations. The paper focusses on the description of electron correlations within a Jastrow-type ansatz for the wavefunction. As a starting point we discuss certain natural assumptions on the asymptotic behaviour of two-particle correlation functions ${ℱ}^{\left(2\right)}$ near electron-electron and electron-nuclear cusps. Based on Nitsche's characterization of best N-term approximation spaces $A_q^{\alpha }\left(H^1\right)$, we prove...

We discuss best N-term approximation spaces for one-electron wavefunctions ${\phi }_i$ and reduced density matrices ρ emerging from Hartree-Fock and density functional theory. The approximation spaces $A_q^{\alpha }\left(H^1\right)$ for anisotropic wavelet tensor product bases have been recently characterized by Nitsche in terms of tensor product Besov spaces. We have used the norm equivalence of these spaces to weighted ${\ell }_q$ spaces of wavelet coefficients to proof that both ${\phi }_i$ and ρ are in $A_q^{\alpha }\left(H^1\right)$ for all $\alpha >0$ with $\alpha =\frac{1}{q}-\frac{1}{2}$. Our proof is based on the...

One of the most interesting phenomena exhibited by ultracold quantum gases is the appearance of vortices when the gas is put in rotation. The talk will bring a survey of some recent progress in understanding this phenomenon starting from the many-body ground state of a Bose gas with short range interactions. Mathematically this amounts to describing solutions of a linear Schrödinger equation with a very large number of variables in terms of a nonlinear equation with few variables and analyzing the...