Distance between exact and approximate distributions of partial maxima under power normalization

We obtain the distance between the exact and approximate distributions of partial maxima of a random sample under power normalization. It is observed that the Hellinger distance and variational distance between the exact and approximate distributions of partial maxima under power normalization is the same as the corresponding distances under linear normalization.Comment: Published at http://dx.doi.org/10.15559/15-VMSTA42 in the Modern Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA) by VTeX (http://www.vtex.lt/

Visualisation of an entangled channel spin-1 system

Co-variance matrix formalism gives powerful entanglement criteria for continuous as well as finite dimensional systems. We use this formalism to study a mixed channel spin-1 system which is well known in nuclear reactions. A spin-j state can be visualized as being made up of 2j spinors which are represented by a constellation of 2j points on a Bloch sphere using Majorana construction. We extend this formalism to visualize an entangled mixed spin-1 system.Comment: 4 pages,4 figure

SU(2) Invariants of Symmetric Qubit States

Density matrix for N-qubit symmetric state or spin-j state (j = N/2) is expressed in terms of the well known Fano statistical tensor parameters. Employing the multiaxial representation [1], wherein a spin-j density matrix is shown to be characterized by j(2j+1) axes and 2j real scalars, we enumerate the number of invariants constructed out of these axes and scalars. These invariants are explicitly calculated in the particular case of pure as well as mixed spin-1 state.Comment: 7 pages, 1 fi

Spin Squeezing of Superposition of Biaxial State and two qubit Bell State

In this study we investigate the spin squeezing in superposition of a Biaxial state [1,2] and Bell state. Numerical and analytical solutions for the length of mean spin, mean spin direction and spin squeezing are given. It is shown that both the mean spin direction and spin squeezing parameter are determined by the coefficients of superposition and the relative phase.Comment: Int. J. Theor. Phys. (2013

Photodisintegration of aligned deuterons at astrophysical energies using linearly polarized photons

Following the model independent approach to deuteron photodisintegration with linearly polarized $\gamma-$rays, we show that the measurements of the tensor analyzing powers on aligned deuterons along with the differential cross section involve five different linear combinations of the isovector $E1^j_v; j=0,1,2$ amplitudes interfering with the isoscalar $M1_s$ and $E2_s$ amplitudes. This is of current interest in view of the recent experimental finding \cite{blackston1} that the three $E1^j_v$ amplitudes are distinct and also the reported experimental observation \cite{sawatzky} on the front-back (polar angle) asymmetry in the differential cross section.Comment: 12 page

Squeezing of a coupled state of two spinors

The notion of spin squeezing involves reduction in the uncertainty of a component of the spin vector below a certain limit. This aspect has been studied earlier for pure and mixed states of definite spin. In this paper, this study has been extended to coupled spin states which do not possess sharp spin value. A general squeezing criterion has been obtained by requiring that a direct product state for two spinors is not squeezed. The squeezing aspect of entangled states is studied in relation to their spin- spin correlations.Comment: Typeset in LaTeX 2e using the style iopart, packages iopams,times,amssymb,graphicx; 17 pages, 5 eps figure file

Squeezing in Multivariate Spin Systems

In contrast to the canonically conjugate variates $q$,$p$ representing the position and momentum of a particle in the phase space distributions, the three Cartesian components, $J_{x}$,$J_{y}$, $J_{z}$ of a spin-$j$ system constitute the mutually non-commuting variates in the quasi-probabilistic spin distributions. It can be shown that a univariate spin distribution is never squeezed and one needs to look into either bivariate or trivariate distributions for signatures of squeezing. Several such distributions result if one considers different characteristic functions or moments based on various correspondence rules. As an example, discrete probability distribution for an arbitrary spin-1 assembly is constructed using Wigner-Weyl and Margenau-Hill correspondence rules. It is also shown that a trivariate spin-1 assembly resulting from the exposure of nucleus with non-zero quadrupole moment to combined electric quadrupole field and dipole magnetic field exhibits squeezing in cerain cases.Comment: 13 pages, 1 Table, Presented at ICSSUR-05, Franc

Microrheological Studies of Regenerated Silk Fibroin Solution by Video Microscopy

We have carried out studies on the rheological properties of regenerated silk fibroin (RSF) solution using video microscopy. The degummed silk from the Bombyx mori silkworm was used to prepare RSF solution by dissolving it in calcium nitrate tetrahydrate-methanol solvent. Measurements were carried out by tracking the position of an embedded micron-sized polystyrene bead within the RSF solution through video imaging. The time dependent mean squared displacement (MSD) of the bead in solution and hence, the complex shear modulus of this solution was calculated from the bead's position information. An optical tweezer was used to transport and locate the bead at any desired site within the micro-volume of the sample, to facilitate the subsequent free-bead video analysis. We present here the results of rheological measurements of the silk polymer network in solution over a frequency range, whose upper limit is the frame capture rate of our camera, at full resolution. By examining the distribution of MSD of beads at different locations within the sample volume, we demonstrate that this probe technique enables us to detect local inhomogeneties at micrometer length scales, not detectable either by a rheometer or from diffusing wave spectroscopy.Comment: 5 page

Crystal structure of 3-benzoyl-2-[(5-bromo-2-Hydroxy-3-methoxybenzylidene)amino]-4,5,6,7-tetrahydrobenzo[b]thiophene

In the cyclo­hexene ring of the title compound, C23H20BrNO3S, the -(CH2)4- atoms are positionally disordered [occupancy ratio = 0.753 (6):0.247 (6)]. The ring has a half-chair conformation for both the major and minor components. The dihedral angles between the mean plane of the thio­phene ring and those of the benzene and phenyl rings are 35.2 (4) and 57.7 (3)°, respectively. The planes of the two aryl rings are twisted with respect to each other by 86.4 (6)°. In the mol­ecule, there is an O-H...N hydrogen bond forming an S(6) ring motif. In the crystal, mol­ecules are linked via C-H...O hydrogen bonds, forming chains parallel to [100].Publisher PDFPeer reviewe

Entangling capabilities of Symmetric two qubit gates

Our work addresses the problem of generating maximally entangled two spin-1/2 (qubit) symmetric states using NMR, NQR, Lipkin-Meshkov-Glick Hamiltonians. Time evolution of such Hamiltonians provides various logic gates which can be used for quantum processing tasks. Pairs of spin-1/2's have modeled a wide range of problems in physics. Here we are interested in two spin-1/2 symmetric states which belong to a subspace spanned by the angular momentum basis {|j = 1, {\mu}>; {\mu} = +1, 0,-1}. Our technique relies on the decomposition of a Hamiltonian in terms of SU(3) generators. In this context, we define a set of linearly independent, traceless, Hermitian operators which provides an alternate set of SU(n) generators. These matrices are constructed out of angular momentum operators Jx,Jy,Jz. We construct and study the properties of perfect entanglers acting on a symmetric subspace i.e., spin-1 operators that can generate maximally entangled states from some suitably chosen initial separable states in terms of their entangling power.Comment: 12 page