The n = 0 replica limit of U(n) and U(n)/SO(n) models

Recently the replica limit n = 0 of the U(n) and U(n)/SO(n) models have attracted interest since they describe the Anderson localization behaviour in the band-centre of a two-sublattice model. For n ≠ 0 the theories can be decomposed into one with symmetry U(1) and one for SU(n) and U(n)/SO(n). This does not no longer hold for n = 0. We show how the beta-functions and zeta-functions for operators without derivatives can be obtained in this limit from those of SU(n) and U(n)/SO(n) and draw consequences for these functions in this limit.     

Gauss laws in the sense of Bernstein and uniqueness of embedding into convolution semigroups on quantum groups and braided groups

Summary. The goal of this paper is to characterise certain probability laws on a class of quantum groups or braided groups that we will call nilpotent. First we introduce a braided analogue of the Heisenberg–Weyl group, which shall serve as standard example. We introduce Gaussian functionals on quantum groups or braided groups as functionals that satisfy an analogue of the Bernstein property, i.e. that the sum and difference of independent random variables are also independent. The corresponding functionals on the braided line, braided plane and a braided q-Heisenberg–Weyl group are determined. Section 5 deals with continuous convolution semigroups on nilpotent quantum groups and braided groups. We extend recent results proving the uniqueness of the embedding of an infinitely divisible probability law into a continuous convolution semigroup for simply connected nilpotent Lie groups to nilpotent quantum groups and braided groups. Finally, in Section 6 we give some indications how the semigroup approach of Heyer and Hazod to the Bernstein theorem on groups can be extended to quantum groups and braided groups. Received: 30 October 1996 / In revised form: 1 April 1997     

Phonons in Confinement and the Boson Peak Using Nuclear Inelastic Absorption

Hyperfine Interactions - We have applied nuclear inelastic absorption (NIA) to the molecular glass former dibutylphthalate/ferrocene, both in bulk and in nanoporous matrices having pore sizes of 50...     

Weight functions admitting repeated positive Kronrod quadrature

In this note it is shown that for weight functions of the formw(t)=(1 –t ²)^1/2/s _m (t), wheres _m is a polynomial of degreem which is positive on [–1, +1], successive Kronrod extension of a certain class ofN-point interpolation quadrature formulas, including theN-point Gauss-formula, is always possible and that each Kronrod extension has the positivity and interlacing property.