Analyticity of the density of electronic wavefunctions

We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in ${\mathbb R}^3$ away from the nuclei.Comment: 19 page

VR/Urban: SMSlingshot

In this paper we describe the concept and design objectives of VR/Urban's media intervention tool SMSlingshot, which was presented at the Riga White Night Arts Festival 2009 for the first time

The state space of short-range Ising spin glasses: the density of states

The state space of finite square and cubic Ising spin glass models is analysed in terms of the global and the local density of states. Systems with uniform and gaussian probability distribution of interactions are compared. Different measures for the local state density are presented and discussed. In particular the question whether the local density of states grows exponentially or not is considered. The direct comparison of global and local densities leads to consequences for the structure of the state space.Comment: 18 pages (including 6 figures); submitted to Z.f.Physik

Blockwise SVD with error in the operator and application to blind deconvolution

We consider linear inverse problems in a nonparametric statistical framework. Both the signal and the operator are unknown and subject to error measurements. We establish minimax rates of convergence under squared error loss when the operator admits a blockwise singular value decomposition (blockwise SVD) and the smoothness of the signal is measured in a Sobolev sense. We construct a nonlinear procedure adapting simultaneously to the unknown smoothness of both the signal and the operator and achieving the optimal rate of convergence to within logarithmic terms. When the noise level in the operator is dominant, by taking full advantage of the blockwise SVD property, we demonstrate that the block SVD procedure overperforms classical methods based on Galerkin projection or nonlinear wavelet thresholding. We subsequently apply our abstract framework to the specific case of blind deconvolution on the torus and on the sphere

ANALYTIC STRUCTURE OF SOLUTIONS TO MULTICONFIGURATION EQUATIONS

Abstract. We study the regularity at the positions of the (fixed) nuclei of solutions to (non-relativistic) multiconfiguration equations (including Hartree–Fock) of Coulomb systems. We prove the following: Let {ϕ1,..., ϕM} be any solution to the rank–M multiconfiguration equations for a molecule with L fixed nuclei at R1,..., RL ∈ R 3. Then, for any j ∈ {1,..., M}, k ∈ {1,..., L}, there exists a neighbourhood Uj,k ⊆ R 3 of Rk, and functions ϕ (1) j,k, ϕ(2) j,k, real analytic in Uj,k, such that ϕj(x) = ϕ (1) (2) j,k (x) + |x − Rk|ϕ j,k (x), x ∈ Uj,k. A similar result holds for the corresponding electron density. The proof uses the Kustaanheimo–Stiefel transformation, as applied in [9] to the study of the eigenfunctions of the Schrödinger operator of atoms and molecules near two-particle coalescence points. 1. Introduction an

Sol-Gel Derived Ferroelectric Nanoparticles Investigated by Piezoresponse Force Microscopy

Piezoresponse force microscopy (PFM) was used to investigate the ferroelectric properties of sol-gel derived LiNbO$_3$ nanoparticles. To determine the degree of ferroelectricity we took large-area images and performed statistical image-analysis. The ferroelectric behavior of single nanoparticles was verified by poling experiments using the PFM tip. Finally we carried out simultaneous measurements of the in-plane and the out-of-plane piezoresponse of the nanoparticles, followed by measurements of the same area after rotation of the sample by 90$^{\circ}$ and 180$^{\circ}$. Such measurements basically allow to determine the direction of polarization of every single particle

Family of Hermitian Low-Momentum Nucleon Interactions with Phase Shift Equivalence

Using a Schmidt orthogonalization transformation, a family of Hermitian low-momentum NN interactions is derived from the non-Hermitian Lee-Suzuki (LS) low-momentum NN interaction. As special cases, our transformation reproduces the Hermitian interactions for Okubo and Andreozzi. Aside from their common preservation of the deuteron binding energy, these Hermitian interactions are shown to be phase shift equivalent, all preserving the empirical phase shifts up to decimation scale Lambda. Employing a solvable matrix model, the Hermitian interactions given by different orthogonalization transformations are studied; the interactions can be very different from each other particularly when there is a strong intruder state influence. However, because the parent LS low-momentum NN interaction is only slightly non-Hermitian, the Hermitian low-momentum nucleon interactions given by our transformations, including the Okubo and Andreozzi ones, are all rather similar to each other. Shell model matrix elements given by the LS and several Hermitian low-momentum interactions are compared.Comment: 10 pages, 7 figure