Mathematical Sciences- Journal Articles

Permanent URI for this collection

https://hdl.handle.net/10468/89

Browse

Recent Submissions

Now showing 1 - 5 of 37
  • Thumbnail Image
    Item
    Feynman–Kac perturbation of C* quantum stochastic flows
    (Springer Nature, 2024-07-06) Belton, Alexander C. R.; Wills, Stephen J.
    The method of Feynman–Kac perturbation of quantum stochastic processes has a long pedigree, with the theory usually developed within the framework of processes on von Neumann algebras. In this work, the theory of operator spaces is exploited to enable a broadening of the scope to flows on C* algebras. Although the hypotheses that need to be verified in this general setting may seem numerous, we provide auxiliary results that enable this to be simplified in many of the cases which arise in practice. A wide variety of examples is provided by way of illustration.
  • Thumbnail Image
    Item
    Flows of constant mean curvature tori in the 3-sphere: The equivariant case
    (De Gruyter, 2015-09-05) Kilian, Martin; Schmidt, Martin U.; Schmitt, Nicholas
    We present a deformation for constant mean curvature tori in the 3-sphere. We show that the moduli space of equivariant constant mean curvature tori in the 3-sphere is connected, and we classify the minimal, the embedded, and the Alexandrov embedded tori therein.
  • Thumbnail Image
    Item
    Dressing CMC n-noids
    (Springer Nature Ltd., 2003-10-30) Kilian, Martin; Schmitt, N.; Sterling, I.; National Science Foundation; CEC
    The purpose of this paper is to construct CMC n-noids with bubbletons. We recall a specific class of dressing matrices, which we will refer to as simple factor dressing matrices, which in many known cases add bubbletons to a CMC surface. Our new surfaces are obtained by dressing known n-noids with embedded Delaunay ends by well chosen simple factor dressing matrices in such a way that the dressed surface is also a CMC n-noid.
  • Thumbnail Image
    Item
    On the generators of quantum stochastic operator cocycles
    (Polymat, 2007-01) Wills, Stephen J.
    The stochastic generators of Markov-regular operator cocycles on symmetric Fock space are studied in a variety of cases: positive cocycles, projection cocycles, and partially isometric cocycles. Moreover a class of transformations of positive contraction cocycles is exhibited which leads to a polar decomposition result.
  • Thumbnail Image
    Item
    Quantum stochastic operator cocycles via associated semigroups
    (Cambridge University Press, 2007-05-01) Lindsay, J. Martin; Wills, Stephen J.
    A recent characterisation of Fock-adapted contraction operator stochastic cocycles on a Hilbert space, in terms of their associated semigroups, yields a general principle for the construction of such cocycles by approximation of their stochastic generators. This leads to new existence results for quantum stochastic differential equations. We also give necessary and sufficient conditions for a cocycle to satisfy such an equation.