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Schwetz, T., Tortola, M., & Valle, J. W. F. (2011). Where we are on theta(13): addendum to 'Global neutrino data and recent reactor fluxes: status of three-flavor oscillation parameters'. New J. Phys., 13, 109401–5pp.
Abstract: In this addendum to Schwetz et al (2011 New J. Phys. 13 063004), we consider the recent results from long-baseline nu(mu) -> nu(e) searches at the Tokai to Kamioka (T2K) and Main Injector Neutrino Oscillation Search (MINOS) experiments and investigate their implications for the mixing angle theta(13) and the leptonic Dirac CP phase delta. By combining the 2.5 sigma indication for a nonzero value of theta(13) coming from the T2K data with global neutrino oscillation data, we obtain a significance for theta(13) > 0 of about 3 sigma with best fit points sin(2) theta(13) = 0.013 (0.016) for normal (inverted) neutrino mass ordering. These results depend somewhat on assumptions concerning the analysis of reactor neutrino data.
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Hinarejos, M., Bañuls, M. C., & Perez, A. (2015). Wigner formalism for a particle on an infinite lattice: dynamics and spin. New J. Phys., 17, 013037–16pp.
Abstract: The recently proposed Wigner function for a particle in an infinite lattice (Hinarejos M, Banuls MC and Perez A 2012 New J. Phys. 14 103009) is extended here to include an internal degree of freedom as spin. This extension is made by introducing a Wigner matrix. The formalism is developed to account for dynamical processes, with or without decoherence. We show explicit solutions for the case of Hamiltonian evolution under a position-dependent potential, and for evolution governed by a master equation under some simple models of decoherence, for which the Wigner matrix formalism is well suited. Discrete processes are also discussed. Finally, we discuss the possibility of introducing a negativity concept for the Wigner function in the case where the spin degree of freedom is included.
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Hinarejos, M., Perez, A., & Bañuls, M. C. (2012). Wigner function for a particle in an infinite lattice. New J. Phys., 14, 103009–19pp.
Abstract: We study the Wigner function for a quantum system with a discrete, infinite-dimensional Hilbert space, such as a spinless particle moving on a one-dimensional infinite lattice. We discuss the peculiarities of this scenario and of the associated phase-space construction, propose a meaningful definition of the Wigner function in this case and characterize the set of pure states for which it is non-negative. We propose a measure of non-classicality for states in this system, which is consistent with the continuum limit. The prescriptions introduced here are illustrated by applying them to localized and Gaussian states and to their superpositions.
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