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Register a new userSharp eigenvalue enclosures for the perturbed angular Kerr-Newman Dirac operator
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A certified strategy for determining sharp intervals of enclosure for the eigenvalues of matrix differential operators with singular coefficients is examined. The strategy relies on computing the second order spectrum relative to subspaces of continuous piecewise linear functions. For smooth perturbations of the angular Kerr-Newman Dirac operator, explicit rates of convergence due to regularity of the eigenfunctions are established. Existing benchmarks are validated and sharpened by several orders of magnitude in the unperturbed setting.
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This paper is concerned with methods for numerical computation of eigenvalue enclosures. We examine in close detail the equivalence between an extension of the Lehmann-Maehly-Goerisch method developed a few years ago by Zimmermann and Mertins, and a geometrically motivated method developed more recently by Davies and Plum. We extend various previously known results in the theory and establish explicit convergence estimates in both settings. The theoretical results are supported by two benchmark numerical experiments on the isotropic Maxwell eigenvalue problem.
We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange elements and unstructured meshes.
We prove new spectral enclosures for the non-real spectrum of a class of $2times2$ block operator matrices with self-adjoint operators $A$ and $D$ on the diagonal and operators $B$ and $-B^*$ as off-diagonal entries. One of our main results resembles Gershgorins circle theorem. The enclosures are applied to $J$-frame operators.
We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential mu for a given gauge configuration on the finite-volume lattice. First, we elaborate the Banks-Casher relations in the complex plane extended for the diquark condensate as well as the chiral condensate to relate the eigenvalue spectral density to the physical observable. Next, we evaluate the condensates and clarify the characteristic spectral change corresponding to the phase transition. Assuming the strong coupling limit, we exhibit the numerical results for a random gauge configuration in two-color QCD implemented by the staggered fermion formalism and confirm that our results agree well with the known estimate quantitatively. We then exploit our method in the case of the Wilson fermion formalism with two flavors. Also we elucidate the possibility of the Aoki (parity-flavor broken) phase and conclude from the point of view of the spectral density that the artificial pion condensation is not induced by the density effect in strong-coupling two-color QCD.
We use Heun type solutions given in cite{Suzuki} for the radial Teukolsky equation, written in the background metric of the Kerr-Newman-de Sitter geometry, to calculate the quasinormal frequencies for polynomial solutions and the reflection coefficient for waves coming from the de Sitter horizon and reflected at the outer horizon of the black hole.
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