We find a canonical form for pure states of a general multipartite system, in which the constraints on the coordinates (with respect to a factorisable orthonormal basis) are simply that certain ones vanish and certain others are real. For identical particles they are invariant under permutations of the particles. As an application, we find the dimension of the generic local equivalence class.

We describe a method to investigate the mode shapes in turbulent pipe flow at a given wavenumber pair that are most responsive to harmonic forcing in the sense that the they correspond to the largest singular value in a Schmidt decomposition of the linear NavierStokes operator using the turbulent mean profile as the base flow. The ideas follow logically from the work of Sharma & McKeon (2009), ...

Gabor Matthäus, Stefan Nolte, Rico Hohmuth, Martin Voitsch, Wolfgang Richter, Boris Pradarutti, Stefan Riehemann, Gunther Notni, and Andreas Tünnermann Institute of Applied Physics, Friedrich-Schiller-University Jena, Max-Wien-Platz 1, Jena D-07743, Germany BATOP GmbH, Wildenbruchstrasse 15, Jena D-07745, Germany Fraunhofer Institute for Applied Optics and Precision Engineering, Albert-Einstein...

We consider the Schmidt decomposition of a bipartite density operator induced by the Hilbert-Schmidt scalar product, and we study the relation between the Schmidt coefficients and entanglement. First, we define the Schmidt equivalence classes of bipartite states. Each class consists of all the density operators (in a given bipartite Hilbert space) sharing the same set of Schmidt coefficients. N...

Research Update: Behind the high efficiency of hybrid perovskite solar cells Azhar Fakharuddin,1,2,a Francesca De Rossi,3,a Trystan M. Watson,3 Lukas Schmidt-Mende,1 and Rajan Jose4,a 1Department of Physics, University of Konstanz, D-78457 Konstanz, Germany 2School of Chemical and Materials Engineering, National University of Sciences and Technology, H-12, Islamabad, Pakistan 3College of Engine...

Incomparability of pure bipartite entangled states under deterministic LOCC is a very strange phenomena. We find two possible ways of getting our desired pure entangled state which is incomparable with the given input state, by collective LOCC with certainty. The first one is by providing some pure entanglement through the lower dimensional maximally-entangled states or using further less amoun...

* Parts of this contribution were presented as a lecture during the annual meeting of the Water Chemistry Division in the German Chemical Society (Fachgruppe Wasserchemie in der GDCh), Lindau, May 1997. ** Dr. Thomas Heberer, Dipl.-Lebensmittelchem. Kathrin Schmidt-Bäumler, Prof. Dr. Hans-Jürgen Stan, Institute of Food Chemistry, Technical University of Berlin, GustavMeyer-Allee 25, D-13355 Ber...

Let NSymm be the Hopf algebra of non-commutative symmetric functions (in an infinity of indeterminates): NSymm=Z 1 2 , ,... Z Z   . It is shown that an associative algebra A with a Hasse-Schmidt derivation 1 2 ( , , ,...) d id d d  on it is exactly the same as an NSymm module algebra. The primitives of NSymm act as ordinary derivations. There are many formulas for the generators Zi in terms ...