The Experts below are selected from a list of 222 Experts worldwide ranked by ideXlab platform

Ewa Weinmüller - One of the best experts on this subject based on the ideXlab platform.

  • Collocation methods for boundary value problems with an Essential Singularity
    Lecture Notes in Computer Science, 2004
    Co-Authors: Winfried Auzinger, Othmar Koch, Ewa Weinmüller
    Abstract:

    We investigate collocation methods for the efficient solution of singular boundary value problems with an Essential Singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a Singularity of the first kind, is less robust with respect to an Essential Singularity than a classical strategy based on mesh halving.

  • LSSC - Collocation methods for boundary value problems with an Essential Singularity
    Large-Scale Scientific Computing, 2004
    Co-Authors: Winfried Auzinger, Othmar Koch, Ewa Weinmüller
    Abstract:

    We investigate collocation methods for the efficient solution of singular boundary value problems with an Essential Singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a Singularity of the first kind, is less robust with respect to an Essential Singularity than a classical strategy based on mesh halving.

Francesco Ravanini - One of the best experts on this subject based on the ideXlab platform.

  • Essential Singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
    Physical Review B, 2011
    Co-Authors: Elisa Ercolessi, Stefano Evangelisti, Fabio Franchini, Francesco Ravanini
    Abstract:

    We study the Renyi entropy of the one-dimensional XYZ spin-1/2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tri-critical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an Essential Singularity. At these non-conformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models.

Winfried Auzinger - One of the best experts on this subject based on the ideXlab platform.

  • Collocation methods for boundary value problems with an Essential Singularity
    Lecture Notes in Computer Science, 2004
    Co-Authors: Winfried Auzinger, Othmar Koch, Ewa Weinmüller
    Abstract:

    We investigate collocation methods for the efficient solution of singular boundary value problems with an Essential Singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a Singularity of the first kind, is less robust with respect to an Essential Singularity than a classical strategy based on mesh halving.

  • LSSC - Collocation methods for boundary value problems with an Essential Singularity
    Large-Scale Scientific Computing, 2004
    Co-Authors: Winfried Auzinger, Othmar Koch, Ewa Weinmüller
    Abstract:

    We investigate collocation methods for the efficient solution of singular boundary value problems with an Essential Singularity. We give numerical evidence that this approach indeed yields high order solutions. Moreover, we discuss the issue of a posteriori error estimation for the collocation solution. An estimate based on the defect correction principle, which has been successfully applied to problems with a Singularity of the first kind, is less robust with respect to an Essential Singularity than a classical strategy based on mesh halving.

Pedro Schlottmann - One of the best experts on this subject based on the ideXlab platform.

  • Non-Fermi-liquid behavior of impurity spins in the anisotropic Heisenberg chain
    Nuclear Physics B, 1999
    Co-Authors: Pedro Schlottmann
    Abstract:

    We consider a U(1)-invariant model consisting of the integrable anisotropic Heisenberg chain of arbitrary spin S embedding an impurity of spin S′. The impurity is assumed located on the mth link of the chain and interacting only with both neighboring sites. The coupling of the impurity to the lattice can be tuned by the impurity rapidity. The model is then integrable as a function of two continuous parameters (the anisotropy and the impurity rapidity) and two discrete variables (the spins S and S′). The thermodynamic Bethe ansatz equations are derived and used to analyze the small field and low temperature properties. Three situations have to be distinguished: (i) If S′ = S the impurity just corresponds to one more site in the chain. (ii) If S′ > S the impurity spin is only partially compensated at T = 0 and the entropy has an Essential Singularity at T = H = 0. (iii) If S′ < S the impurity is overcompensated, and again the entropy has an Essential Singularity at T = H = 0. The Essential Singularity gives rise to a quantum critical point and hence non-Fermi-liquid-like behavior as H and T tend to zero. While cases (i) and (iii) are analogous to the n-channel Kondo problem, case (ii) differs considerably as a consequence of critical behavior induced by the anisotropy.

John Stalker - One of the best experts on this subject based on the ideXlab platform.