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...

We study by direct numerical simulations the effects of Schmidt number ~Sc! on passive scalars mixed by forced isotropic and homogeneous turbulence. The scalar field is maintained statistically stationary by a uniform mean gradient. We consider the scaling of spectra, structure functions, local isotropy and intermittency. For moderately diffusive scalars with Sc51/8 and 1, the Taylor-scale Reyn...

Several combinatorical problems reduce to classifying certain families of difference sets. Schmidt, in [1], obtained strong new nonexistence results for this class of problem by applying algebraic number theory: a difference set can be related to a cyclotomic integer with bounded coefficients and a prescribed absolute value, and in many cases these integers can be number-theoretically proven no...

Measurements are presented on the influence of Schmidt number on the frequency of the mass transfer fluctuations at a solid boundary. The shape of the spectral function is similar at all Schmidt numbers. A relation between the mass transfer fluctuations and the fluctuating velocity field can be obtained only at high frequencies. A comparison of the scale and the frequency of the mass transfer f...

We present results from an experimental investigation of turbulent transport and molecular mixing of a Sc S 1 conserved scalar in the fully developed self-similar far field of a steady, axisymmetric, momentum-driven, free turbulent jet issuing into a quiescent medium. Our experiments cover the axial range from the jet exit to 350 diameters downstream, and span the range of Reynolds numbers from...

Computational Fluid Dynamics (CFD) has consolidated as a tool to provide understanding and quantitative information regarding many complex environmental flows. The accuracy and reliability of CFD modelling results oftentimes come under scrutiny because of issues in the implementation of and input data for those simulations. Regarding the input data, if an approach based on the Reynolds-Averaged...

Case taking is an art. In Homoeopathy “case and interrogation” involves unique technique so as to individualize a patient, i.e., how this patient different from other patients who are suffering with the same disease. This “art of case taking” explained in number books by many stalwarts theoretically, but still Physicians often find it quite difficult practically implementing at sick bed. The au...

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...