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...

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...

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...