Trotter product formulae for ∗*-automorphisms of quantum lattice systems

We consider the dynamics $t\mapsto\tau_t$ of an infinite quantum lattice system that is generated by a local interaction. If the interaction decomposes into a finite number of terms that are themselves local interactions, we show that $\tau_t$ can be efficiently approximated by a product of $n$ automorphisms, each of them being an alternating product generated by the individual terms. For any integer $m$, we construct a product formula (in the spirit of Trotter) such that the approximation error scales as $n^{-m}$. Our bounds hold in norm, pointwise for algebra elements that are sufficiently well approximated by finite volume observables.Comment: Published in Annales Henri Poincar\'

Sensitivity to social exclusion in major depressive disorder (MDD) predicts therapeutic outcome after in-patient treatment

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Atom Interferometry in Space: Thermal Management and Magnetic Shielding

Atom interferometry is an exciting tool to probe fundamental physics. It is considered especially apt to test the universality of free fall by using two different sorts of atoms. The increasing sensitivity required for this kind of experiment sets severe requirements on its environments, instrument control, and systematic effects. This can partially be mitigated by going to space as was proposed, for example, in the Spacetime Explorer and Quantum Equivalence Principle Space Test (STE-QUEST) mission. However, the requirements on the instrument are still very challenging. For example, the specifications of the STE-QUEST mission imply that the Feshbach coils of the atom interferometer are allowed to change their radius only by about 260 nm or 2.6E-4% due to thermal expansion although they consume an average power of 22 W. Also Earth's magnetic field has to be suppressed by a factor of 10E5. We show in this article that with the right design such thermal and magnetic requirements can indeed be met and that these are not an impediment for the exciting physics possible with atom interferometers in space.Comment: v2: minor changes to agree with published version; 8 pages, 6 figure

Begreppet Början. En begreppsstyrd undersökning av det svenska ordförrådets förändring under 500 år

Every concept has a lexicon. How this lexicon changes over time is the main focus of this article. The concept of Beginning is investigated over a period of 500 years. All words in the lexical field, both the living and the obsolete ones, are represented in the study. A method consisting of several steps is presented to reach the “profile” of the concept and to grasp the interaction of first elements (i.e. prefixes and adverbs) and roots over time

En databaserad begreppsordbok för den äldre svenskan

Artikeln redovisar ett försök att utarbeta en databaserad, begreppsklassificerad ordbok för den äldre och yngre nysvenskan. Ordboken bygger på Rogets "Thesaurus" (och dess svenska motsvarighet: B ring) och Dahlgrens "Glossarium". Ett av huvudsyftena med ordboken är att den skall vara utgångspunkten i skapandet av en strukturell, synkronisk och historisk ordbok