Higher-order signature cocycles for subgroups of mapping class groups and homology cylinders

We define families of invariants for elements of the mapping class group of S, a compact orientable surface. Fix any characteristic subgroup H of pi_1(S) and restrict to J(H), any subgroup of mapping classes that induce the identity modulo H. To any unitary representation, r of pi_1(S)/H we associate a higher-order rho_r-invariant and a signature 2-cocycle sigma_r. These signature cocycles are shown to be generalizations of the Meyer cocycle. In particular each rho_r is a quasimorphism and each sigma_r is a bounded 2-cocycle on J(H). In one of the simplest non-trivial cases, by varying r, we exhibit infinite families of linearly independent quasimorphisms and signature cocycles. We show that the rho_r restrict to homomorphisms on certain interesting subgroups. Many of these invariants extend naturally to the full mapping class group and some extend to the monoid of homology cylinders based on S.Comment: 38 pages. This is final version for publication in IMRN, deleted some material and many references (sorry-at referee's insistence

Generation of field mediated three qubit entangled state shared by Alice and Bob

A scheme to generate shared tripartite entangled states, with two-trapped atoms in a cavity held by Alice (qubits A1 and A2) entangled to a single trapped atom in a remote lab owned by Bob (B), is proposed. The entanglement is generated through interaction of trapped atoms with two mode squeezed light shared by the two cavities. The proposed scheme is an extension of the proposal of ref. [W. Son, M. S. Kim, J. Lee, and D. Ahn, J. Mod. Opt. 49, 1739 (2002)], where the possibility of entangling two remote qubits using a bipartite continuous variable state was examined. While the global negativity detects the free entanglement of the three atom mixed state, the bound entanglement is detected by the negativity calculated from pure state decomposition of the state operator. The partial negativities calculated by selective partial transposition of the three atom mixed state detect the pairwise entanglement of qubit pairs A1B, A2B, and A1A2. The entanglement of three atoms is found to be W-like, no GHZ like quantum correlations being generated.Comment: 14 pages, 06 figures, section IV revised, Other minor changes to improve readabilit

An Exploration of the Perceptions of Elementary Principals on the Process and Benefits of the Principal Evaluation

An Exploration of the Perceptions of Elementary Principals on the Process and Benefits of the Principal Evaluation This qualitative case study investigated the principal evaluation process as described and experienced by principals and principal evaluators and the feedback provided in the principal evaluation process. The conceptual framework, VAL-Ed was used because it is grounded in research literature and is based on leadership standards. The participants were six elementary principals and three principal evaluators from each of the three participating districts. This study contradicted earlier research, in finding principal evaluations are aligned to professional standards and principals report their evaluation is beneficial. The study found the informal feedback that occurs during the evaluation process is perceived as more beneficial than the formal document. The study found principals were often concerned with the blurring of the lines of the evaluator\u27s role in the district and the role as evaluator. The study found a need to provide training for principal evaluators

Classification of Multipartite Entanglement via Negativity Fonts

Partial transposition of state operator is a well known tool to detect quantum correlations between two parts of a composite system. In this letter, the global partial transpose (GPT) is linked to conceptually multipartite underlying structures in a state - the negativity fonts. If K-way negativity fonts with non zero determinants exist, then selective partial transposition of a pure state, involving K of the N qubits (K leq N) yields an operator with negative eigevalues, identifying K-body correlations in the state. Expansion of GPT interms of K-way partially transposed (KPT) operators reveals the nature of intricate intrinsic correlations in the state. Classification criteria for multipartite entangled states, based on underlying structure of global partial transpose of canonical state, are proposed. Number of N-partite entanglement types for an N qubit system is found to be 2^{N-1}-N+2, while the number of major entanglement classes is 2^{N-1}-1. Major classes for three and four qubit states are listed. Subclasses are determined by the number and type of negativity fonts in canonical state.Comment: 5 pages, No figures, Corrected typo

The BCS theory of q-deformed nucleon pairs - qBCS

We construct a coherent state of q-deformed zero coupled nucleon pairs distributed in several single-particle orbits. Using a variational approach, the set of equations of qBCS theory, to be solved self consistently for occupation probabilities, gap parameter Delta, and the chemical potential lambda, is obtained. Results for valence nucleons in nuclear degenerate sdg major shell show that the strongly coupled zero angular momentum nucleon pairs can be substituted by weakly coupled q-deformed zero angular momentum nucleon pairs. A study of Sn isotopes reveals a well defined universe of (G, q) values, for which qBCS converges. While the qBCS and BCS show similar results for Gap parameter Delta in Sn isotopes, the ground state energies are lower in qBCS. The pairing correlations in N nucleon system, increase with increasing q (for q real).Comment: 8 pages, REVTEX, 3 eps figure

Generalized q-Deformed Symplectic sp(4) Algebra for Multi-shell Applications

A multi-shell generalization of a fermion representation of the q-deformed compact symplectic sp_q(4) algebra is introduced. An analytic form for the action of two or more generators of the Sp_q(4) symmetry on the basis states is determined and the result used to derive formulae for the overlap between number preserving states as well as for matrix elements of a model Hamiltonian. A second-order operator in the generators of Sp_q(4) is identified that is diagonal in the basis set and that reduces to the Casimir invariant of the sp(4) algebra in the non-deformed limit of the theory. The results can be used in nuclear structure applications to calculate beta-decay transition probabilities and to provide for a description of pairing and higher-order interactions in systems with nucleons occupying more than a single-j orbital.Comment: 10 page

Decoherence of tripartite states - a trapped ion coupled to an optical cavity

We investigate the non-dissipative decoherence of three qubit system obtained by manipulating the state of a trapped two-level ion coupled to an optical cavity. Modelling the environment as a set of noninteracting harmonic oscillators, analytical expressions for the state operator of tripartite composite system, the probability of generating maximally entangled GHZ state, and the population inversion have been obtained. The pointer observable is the energy of the isolated quantum system. Coupling to environment results in exponential decay of off diagonal matrix elements of the state operator with time as well as a phase decoherence of the component states. Numerical calculations to examine the time evolution of GHZ state generation probability and population inversion for different system environment coupling strengths are performed. Using negativity as an entanglement measure and linear entropy as a measure of mixedness, the entanglement dynamics of the tripartite system in the presence of decoherence is analysed.Comment: Revised version, errors corrected and references added. 12 pages, 6 figures, Presented at ICSSUR May 2005, Besancon, Franc