Supersymmetric Biorthogonal Quantum Systems

We discuss supersymmetric biorthogonal systems, with emphasis given to the periodic solutions that occur at spectral singularities of PT symmetric models. For these periodic solutions, the dual functions are associated polynomials that obey inhomogeneous equations. We construct in detail some explicit examples for the supersymmetric pairs of potentials V_{+/-}(z) = -U(z)^2 +/- z(d/(dz))U(z) where U(z) = \sum_{k>0}u_{k}z^{k}. In particular, we consider the cases generated by U(z) = z and z/(1-z). We also briefly consider the effects of magnetic vector potentials on the partition functions of these systems.Comment: Changes are made to conform to the published version. In particular, some errors are corrected on pp 12-1

Active-sterile neutrino oscillations in the early Universe: asymmetry generation at low |delta m^2| and the Landau-Zener approximation

It is well established that active-sterile neutrino oscillations generate large neutrino asymmetries for very small mixing angles ($\sin^2 2\theta_0\lesssim 10^{-4}$), negative values of $\delta m^2$ and provided that $|\delta m^2|\gtrsim 10^{-4} {\rm eV^2}$. By numerically solving the quantum kinetic equations, we show that the generation still occurs at much lower values of $|\delta m^2|$. We also describe the borders of the generation at small mixing angles and show how our numerical results can be analytically understood within the framework of the Landau-Zener approximation thereby extending previous work based on the adiabatic limit. This approximate approach leads to a fair description of the MSW dominated regime of the neutrino asymmetry evolution and is also able to correctly reproduce its final value. We also briefly discuss the impact that neutrino asymmetry generation could have on big bang nucleosynthesis, CMBR and relic neutrinos.Comment: 29 pages, 8 figures; to appear on Phys. ReV. D; figure 7 added, new curves in figure 5a, new figure

Tensile and flexural properties of hybrid graphene oxide/epoxy carbon fibre reinforced composites.

In this study, nano-sized graphene oxide sheets were homogenously dispersed via sonication methods in epoxy followed by vacuum resin infusion for the fabrication of the epoxy, graphene oxide (GO) and micro-sized carbon fibre reinforced nanocomposites (EP/CF/GO). Graphene oxide concentrations ranging from 0.1 - 0.5 wt. % were studied to investigate the effect on tensile and flexural strength. It was observed that the tensile strength of the EP/CF decreased with the addition of GO but increased with GO weight concentration in the nanocomposites studied from 498MPa to 519 MPa for the inclusion of 0.1 to 0.5 wt.% GO respectively. The 0.5 wt. % EP/CF/GO recorded a 10% increase in Young's modulus compared to the classical epoxy / carbon fibre composites, and similar trend was observed for the flexural properties. However flexural strength of the GO samples did not surpass the control sample (epoxy /carbon fibre composites) with the 0.3 wt.% GO samples (EP/CF/GO) providing the greatest flexural strength of >580 MPa compared to the 0.1 wt.% and 0.5 wt.% GO samples

Further studies on relic neutrino asymmetry generation I: the adiabatic Boltzmann limit, non-adiabatic evolution, and the classical harmonic oscillator analogue of the quantum kinetic equations

We demonstrate that the relic neutrino asymmetry evolution equation derived from the quantum kinetic equations (QKEs) reduces to the Boltzmann limit that is dependent only on the instantaneous neutrino number densities, in the adiabatic limit in conjunction with sufficient damping. An original physical and/or geometrical interpretation of the adiabatic approximation is given, which serves as a convenient visual aid to understanding the sharply contrasting resonance behaviours exhibited by the neutrino ensemble in opposing collision regimes. We also present a classical analogue for the evolution of the difference in $\nu_{\alpha}$ and $\nu_s$ number densities which, in the Boltzmann limit, is akin to the behaviour of the generic reaction $A \rightleftharpoons B$ with equal forward and reverse reaction rate constants. A new characteristic quantity, the matter and collision-affected mixing angle of the neutrino ensemble, is identified here for the first time. The role of collisions is revealed to be twofold: (i) to wipe out the inherent oscillations, and (ii) to equilibrate the $\nu_{\alpha}$ and $\nu_s$ number densities in the long run. Studies on non-adiabatic evolution and its possible relation to rapid oscillations in lepton number generation also feature, with the introduction of an adiabaticity parameter for collision-affected oscillations.Comment: RevTeX, 38 pages including 8 embedded figure

Active-Sterile neutrino oscillations and BBN+CMBR constraints

We show how active-sterile neutrino oscillations in the early Universe can play an interesting role in explaining the current observations of CMBR anisotropies and light element abundances. We describe different possible phenomenological scenarios in the interpretation of present data and how active-sterile neutrino oscillations can provide a viable theoretical framework.Comment: Some changes, to appear in Phys. Rev.

On the sign of the neutrino asymmetry induced by active-sterile neutrino oscillations in the early Universe

We deal with the problem of the final sign of the neutrino asymmetry generated by active-sterile neutrino oscillations in the Early Universe solving the full momentum dependent quantum kinetic equations. We study the parameter region $10^{-2} \stackrel{<}{\sim} |\delta m^2|/eV^2\le 10^3$. For a large range of $\sin^2 2\theta_0$ values the sign of the neutrino asymmetry is fixed and does not oscillate. For values of mixing parameters in the region $10^{-6}\stackrel{<}{\sim}\sin^{2}2\theta_{0}\stackrel{<}{\sim} 3\times 10^{-4} ({\rm eV}^{2}/|\delta m^{2}|)$, the neutrino asymmetry appears to undergo rapid oscillations during the period where the exponential growth occurs. Our numerical results indicate that the oscillations are able to change the neutrino asymmetry sign. The sensitivity of the solutions and in particular of the final sign of lepton number to small changes in the initial conditions depends whether the number of oscillations is high enough. It is however not possible to conclude whether this effect is induced by the presence of a numerical error or is an intrinsic feature. As the amplitude of the statistical fluctuations is much lower than the numerical error, our numerical analysis cannot demonstrate the possibility of a chaotical generation of lepton domains. In any case this possibility is confined to a special region in the space of mixing parameters and it cannot spoil the compatibility of the $\nu_{\mu}\leftrightarrow\nu_{s}$ solution to the neutrino atmospheric data obtained assuming a small mixing of the $\nu_{s}$ with an ${\rm eV}-\tau$ neutrino.Comment: Typo's corrected, accepted for publication in Phys.Rev.

Big Bang Nucleosynthesis with Gaussian Inhomogeneous Neutrino Degeneracy

We consider the effect of inhomogeneous neutrino degeneracy on Big Bang nucleosynthesis for the case where the distribution of neutrino chemical potentials is given by a Gaussian. The chemical potential fluctuations are taken to be isocurvature, so that only inhomogeneities in the electron chemical potential are relevant. Then the final element abundances are a function only of the baryon-photon ratio $\eta$, the effective number of additional neutrinos $\Delta N_\nu$, the mean electron neutrino degeneracy parameter $\bar \xi$, and the rms fluctuation of the degeneracy parameter, $\sigma_\xi$. We find that for fixed $\eta$, $\Delta N_\nu$, and $\bar \xi$, the abundances of helium-4, deuterium, and lithium-7 are, in general, increasing functions of $\sigma_\xi$. Hence, the effect of adding a Gaussian distribution for the electron neutrino degeneracy parameter is to decrease the allowed range for $\eta$. We show that this result can be generalized to a wide variety of distributions for $\xi$.Comment: 9 pages, 3 figures, added discussion of neutrino oscillations, altered presentation of figure

Dynamical density-density correlations in one-dimensional Mott insulators

The dynamical density-density correlation function is calculated for the one-dimensional, half-filled Hubbard model extended with nearest neighbor repulsion using the Lanczos algorithm for finite size systems and analytically for large on site repulsion compared to hopping amplitudes. At the zone boundary an excitonic feature exists for any finite nearest neighbor repulsion and exhausts most of the spectral weight, even for parameters where no exciton is visible at zero momentum.Comment: 5 pages, REVTeX, epsf, 3 postscript figure

Update on neutrino mixing in the early Universe

From the current cosmological observations of CMB and nuclear abundances we show, with an analytic procedure, that the total effective number of extra neutrino species $\Delta N_{\nu}^{\rm tot}< 0.3$. We also describe the possible signatures of non standard effects that could be revealed in future CMB observations. This cosmological information is then applied to neutrino mixing models. Taking into account the recent results from the SNO and SuperKamiokande experiments, disfavouring pure active to sterile neutrino oscillations, we show that all 4 neutrino mixing models, both of 2+2 and 3+1 type, lead to a full thermalization of the sterile neutrino flavor. Moreover such a sterile neutrino production excludes the possibility of an electron neutrino asymmetry generation and we conclude that $\Delta N_{\nu}^{\rm tot}\simeq 1$, in disagreement with the cosmological bound. This result is valid under the assumption that the initial neutrino asymmetries are small. We suggest the existence of a second sterile neutrino flavor, with mixing properties such to generate a large electron neutrino asymmetry, as a possible way out.Comment: 29 pages, 3 figures; to appear on Phys.Rev.D; added discussion (at page 19) and references; typos correcte

Biorthogonal quantum mechanics

The Hermiticity condition in quantum mechanics required for the characterization of (a) physical observables and (b) generators of unitary motions can be relaxed into a wider class of operators whose eigenvalues are real and whose eigenstates are complete. In this case, the orthogonality of eigenstates is replaced by the notion of biorthogonality that defines the relation between the Hilbert space of states and its dual space. The resulting quantum theory, which might appropriately be called 'biorthogonal quantum mechanics', is developed here in some detail in the case for which the Hilbert-space dimensionality is finite. Specifically, characterizations of probability assignment rules, observable properties, pure and mixed states, spin particles, measurements, combined systems and entanglements, perturbations, and dynamical aspects of the theory are developed. The paper concludes with a brief discussion on infinite-dimensional systems. © 2014 IOP Publishing Ltd