Yang-Mills equation for stable Higgs sheaves

We establish a Kobayashi-Hitchin correspondence for the stable Higgs sheaves on a compact Kaehler manifold. Using it, we also obtain a Kobayashi-Hitchin correspondence for the stable Higgs G-sheaves, where G is any complex reductive linear algebraic group

Universal Control of Nuclear Spins Via Anisotropic Hyperfine Interactions

We show that nuclear spin subsystems can be completely controlled via microwave irradiation of resolved anisotropic hyperfine interactions with a nearby electron spin. Such indirect addressing of the nuclear spins via coupling to an electron allows us to create nuclear spin gates whose operational time is significantly faster than conventional direct addressing methods. We experimentally demonstrate the feasibility of this method on a solid-state ensemble system consisting of one electron and one nuclear spin.Comment: RevTeX4, 8 pages, 8 figure

Entropic Test of Quantum Contextuality

We study the contextuality of a three-level quantum system using classical conditional entropy of measurement outcomes. First, we analytically construct the minimal configuration of measurements required to reveal contextuality. Next, an entropic contextual inequality is formulated, analogous to the entropic Bell inequalities derived by Braunstein and Caves in [Phys. Rev. Lett. {\bf 61}, 662 (1988)], that must be satisfied by all non-contextual theories. We find optimal measurements for violation of this inequality. The approach is easily extendable to higher dimensional quantum systems and more measurements. Our theoretical findings can be verified in the laboratory with current technology.Comment: 4 pages, 4 figure

Optimal Cloning and Singlet Monogamy

The inability to produce two perfect copies of an unknown state is inherently linked with the inability to produce maximal entanglement between multiple spins. Despite this, there is no quantitative link between how much entanglement can be generated between spins (known as monogamy), and how well an unknown state can be cloned. This situation is remedied by giving a set of sufficient conditions such that the optimal Completely Positive map can be implemented as a teleportation operation into a standard, reference, state. The case of arbitrary 1 to N asymmetric cloning of d-dimensional spins can then be solved exactly, yielding the concept of `singlet monogamy'. The utility of this relation is demonstrated by calculating properties of Heisenberg systems, and contrasting them with the results from standard monogamy arguments.Comment: 4 pages, 1 figure. v2: conjecture upgraded to proof and generalized to arbitrary local hilbert space dimensions. v3: published versio

Decay of highly-correlated spin states in a dipolar-coupled solid

We have measured the decay of NMR multiple quantum coherence intensities both under the internal dipolar Hamiltonian as well as when this interaction is effectively averaged to zero, in the cubic calcium fluoride (CaF2) spin system and the pseudo one-dimensional system of fluoroapatite. In calcium fluoride the decay rates depend both on the number of correlated spins in the cluster, as well as on the coherence number. For smaller clusters, the decays depend strongly on coherence number, but this dependence weakens as the size of the cluster increases. The same scaling was observed when the coherence distribution was measured in both the usual Zeeman or z basis and the x basis. The coherence decay in the one dimensional fluoroapatite system did not change significantly as a function of the multiple quantum growth time, in contrast to the calcium fluoride case. While the growth of coherence orders is severely restricted in this case, the number of correlated spins should continue to grow, albeit more slowly. All coherence intensities were observed to decay as Gaussian functions in time. In all cases the standard deviation of the observed decay appeared to scale linearly with coherence number.Comment: 7 pages, 9 figures. submitted to PR

On semistable principal bundles over a complex projective manifold, II

Let (X, \omega) be a compact connected Kaehler manifold of complex dimension d and E_G a holomorphic principal G-bundle on X, where G is a connected reductive linear algebraic group defined over C. Let Z (G) denote the center of G. We prove that the following three statements are equivalent: (1) There is a parabolic subgroup P of G and a holomorphic reduction of the structure group of E_G to P (say, E_P) such that the bundle obtained by extending the structure group of E_P to L(P)/Z(G) (where L(P) is the Levi quotient of P) admits a flat connection; (2) The adjoint vector bundle ad(E_G) is numerically flat; (3) The principal G-bundle E_G is pseudostable, and the degree of the charateristic class c_2(ad(E_G) is zero.Comment: 15 page

Check-Up of Planet Earth at the Turn of the Millennium: Anticipated New Phase in Earth Sciences

Langley's remarkable solar and lunar spectra collected from Mt. Whitney inspired Arrhenius to develop the first quantitative climate model in 1896. In 1999, NASA's Earth Observing AM Satellite (EOS-AM) will repeat Langley's experiment, but for the entire planet, thus pioneering calibrated spectral observations from space. Conceived in response to real environmental problems, EOS-AM, in conjunction with other international satellite efforts, will fill a major gap in current efforts by providing quantitative global data sets with a resolution of few kilometers on the physical, chemical and biological elements of the earth system. Thus, like Langley's data, EOS-AM can revolutionize climate research by inspiring a new generation of climate system models and enable us to assess the human impact on the environment

Exploring grassroots innovation phenomenon through the lived experience of an Indian grassroots innovator.

Purpose – The purpose of this paper is to stir the deliberation on understanding grassroots innovation (GI) phenomenon through the lived experience approach and attempt to address the existing void in current literature. Design/methodology/approach – This paper outlines a human science research approach for studying the subjective reality embedded in the GI phenomenon. Such an approach provides a better and more bottom-up understanding of the underlying individual and interpersonal dynamics shaping the GI. Findings – This study provides a richer understanding of the underlying individual and interpersonal dynamics shaping the GI phenomena. This may serve as an aid for future research on scaling, managing GI and developing entrepreneurial capabilities of the grassroots innovators (GIrs). The study also confirms that no single unilateral theory can fully explain the lived experiences of the GIrs at the ideation, opportunity recognition, prototyping and scaling stage of GI. Rather, it is quintessential to have an integrated holistic perspective for understanding GI. This study also highlights the importance of hermeneutic phenomenology in pro-poor innovation research and practice in the near future. Research limitations/implications – This paper’s main limitation is whether the findings can be generalized in a wider context. The authors acknowledge this limitation. However, the purpose of this study is not to generalize the findings but rather provide a contextual understanding of what constitutes the lived experiences of GI. The authors recommend that a future study covering greater number of GIrs across India be undertaken to gain a better appreciation of the bigger picture. Originality/value – Systematic approaches for tapping into GI are conspicuously non-existent and hence a contextual understanding through the proposed holistic lens will assist in thriving of the GI phenomena in South Asian countries such as India