Inverse spin-s portrait and representation of qudit states by single probability vectors

Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j+1)(4j+1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere. Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits (j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and (2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.Comment: 23 pages, 4 figures, PDF LaTeX, submitted to the Journal of Russian Laser Researc

Laminar fluid flow in microchannels with complex shape

This paper was presented at the 4th Micro and Nano Flows Conference (MNF2014), which was held at University College, London, UK. The conference was organised by Brunel University and supported by the Italian Union of Thermofluiddynamics, IPEM, the Process Intensification Network, the Institution of Mechanical Engineers, the Heat Transfer Society, HEXAG - the Heat Exchange Action Group, and the Energy Institute, ASME Press, LCN London Centre for Nanotechnology, UCL University College London, UCL Engineering, the International NanoScience Community, www.nanopaprika.eu.Laminar flow of newton incompressible fluid with constant viscosity in system of channels (Fig.1) is considered. It’s demonstrated that there are infinitely many stationary solutions with same boundary conditions. Possible flow fields and ways of practical realization are studied. Solutions are investigated numerically, scheme of calculation is described partially in [1, 2]

Proalgebraic crossed modules of quasirational presentations

We introduce the concept of quasirational relation modules for discrete and pro-$p$ presentations of discrete and pro-$p$ groups and show that aspherical presentations and their subpresentations are quasirational. In the pro-$p$-case quasirationality of pro-$p$-groups with a single defining relation holds. For every quasirational (pro-$p$)relation module we construct the so called $p$-adic rationalization, which is a pro-fd-module $\overline{R}\widehat{\otimes}\mathbb{Q}_p= \varprojlim R/[R,R\mathcal{M}_n]\otimes\mathbb{Q}_p$. We provide the isomorphisms $\overline{R^{\wedge}_w}(\mathbb{Q}_p)=\overline{R}\widehat{\otimes}\mathbb{Q}_p$ and $\overline{R_u}(\mathbb{Q}_p)=\mathcal{O}(G_u)^*$, where $R^{\wedge}_w$ and $R^{\wedge}_u$ stands for continuous prounipotent completions and corresponding prounipotent presentations correspondingly. We show how $\overline{R^{\wedge}_{w}}$ embeds into a sequence of abelian prounipotent groups. This sequence arises naturally from a certain prounipotent crossed module, the latter bring concrete examples of proalgebraic homotopy types. The old-standing open problem of Serre, slightly corrected by Gildenhuys, in its modern form states that pro-$p$-groups with a single defining relation are aspherical. Our results give a positive feedback to the question of Serre.Comment: This is a corrected version of the paper which appeared in the Extended Abstracts Spring 2015, Interactions between Representation Theory, Algebraic Topology and Commutative Algebra, Research Perspectives CRM Barcelona, Vol.5, 201

Room-temperature ferromagnetism in graphite driven by 2D networks of point defects

Ferromagnetism in carbon-based materials is appealing for both applications and fundamental science purposes because carbon is a light and bio-compatible material that contains only s and p electrons in contrast to traditional ferromagnets based on 3d or 4f electrons. Here we demonstrate direct evidence for ferromagnetic order locally at defect structures in highly oriented pyrolytic graphite (HOPG) with magnetic force microscopy and in bulk magnetization measurements at room temperature. Magnetic impurities have been excluded as the origin of the magnetic signal after careful analysis supporting an intrinsic magnetic behavior of carbon. The observed ferromagnetism has been attributed to originate from unpaired electron spins localized at grain boundaries of HOPG. Grain boundaries form two-dimensional arrays of point defects, where their spacing depends on the mutual orientation of two grains. Depending on the distance between these point defects, scanning tunneling spectroscopy of grain boundaries showed two intense split localized states for small distances between defects (< 4 nm) and one localized state at the Fermi level for large distances between defects (> 4 nm).Comment: 19 pages, 5 figure

The 35S U5 snRNP is generated from the activated spliceosome during In vitro splicing

Primary gene transcripts of eukaryotes contain introns, which are removed during processing by splicing machinery. Biochemical studies In vitro have identified a specific pathway in which introns are recognised and spliced out. This occurs by progressive formation of spliceosomal complexes designated as E, A, B, and C. The composition and structure of these spliceosomal conformations have been characterised in many detail. In contrast, transitions between the complexes and the intermediates of these reactions are currently less clear. We have previously isolated a novel 35S U5 snRNP from HeLa nuclear extracts. The protein composition of this particle differed from the canonical 20S U5 snRNPs but was remarkably similar to the activated B* spliceosomes. Based on this observation we have proposed a hypothesis that 35S U5 snRNPs represent a dissociation product of the spliceosome after both transesterification reactions are completed. Here we provide experimental evidence that 35S U5 snRNPs are generated from the activated B* spliceosomes during In vitro splicing

Languages ordered by the subword order

We consider a language together with the subword relation, the cover relation, and regular predicates. For such structures, we consider the extension of first-order logic by threshold- and modulo-counting quantifiers. Depending on the language, the used predicates, and the fragment of the logic, we determine four new combinations that yield decidable theories. These results extend earlier ones where only the language of all words without the cover relation and fragments of first-order logic were considered

Scaling Separability Criterion: Application To Gaussian States

We introduce examples of three- and four-mode entangled Gaussian mixed states that are not detected by the scaling and Peres-Horodecki separability criteria. The presented modification of the scaling criterion resolves this problem. Also it is shown that the new criterion reproduces the main features of the scaling pictures for different cases of entangled states, while the previous versions lead to completely different outcomes. This property of the presented scheme is evidence of its higher generality.Comment: 7 pages, 4 figure

Electronic Instability in a Zero-Gap Semiconductor: The Charge-DensityWave in (TaSe4)(2)I

We report a comprehensive study of the paradigmatic quasi-1D compound (TaSe4)(2)I performed by means of angle-resolved photoemission spectroscopy (ARPES) and first-principles electronic structure calculations. We find it to be a zero-gap semiconductor in the nondistorted structure, with non-negligible interchain coupling. Theory and experiment support a Peierls-like scenario for the charge-density wave formation below T-CDW = 263 K, where the incommensurability is a direct consequence of the finite interchain coupling. The formation of small polarons, strongly suggested by the ARPES data, explains the puzzling semiconductor-to-semiconductor transition observed in transport at T-CDW.open114sciescopu

On the homomorphism order of labeled posets

Partially ordered sets labeled with k labels (k-posets) and their homomorphisms are examined. We give a representation of directed graphs by k-posets; this provides a new proof of the universality of the homomorphism order of k-posets. This universal order is a distributive lattice. We investigate some other properties, namely the infinite distributivity, the computation of infinite suprema and infima, and the complexity of certain decision problems involving the homomorphism order of k-posets. Sublattices are also examined.Comment: 14 page