Dynamics of spin 1/2 quantum plasmas

The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron--ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out.Comment: 4 pages, 2 figures, to appear in Physical Review Letter

Fractional analytic index

For a finite rank projective bundle over a compact manifold, so associated to a torsion, Dixmier-Douady, 3-class, w, on the manifold, we define the ring of differential operators `acting on sections of the projective bundle' in a formal sense. In particular, any oriented even-dimensional manifold carries a projective spin Dirac operator in this sense. More generally the corresponding space of pseudodifferential operators is defined, with supports sufficiently close to the diagonal, i.e. the identity relation. For such elliptic operators we define the numerical index in an essentially analytic way, as the trace of the commutator of the operator and a parametrix and show that this is homotopy invariant. Using the heat kernel method for the twisted, projective spin Dirac operator, we show that this index is given by the usual formula, now in terms of the twisted Chern character of the symbol, which in this case defines an element of K-theory twisted by w; hence the index is a rational number but in general it is not an integer.Comment: 23 pages, Latex2e, final version, to appear in JD

Just in time: ‘momentary’ events in the making of Rosemary Butcher’s signature practices

The notions of ‘ephemerality’, of time and loss, are essentially spectatorial, in the case of live performance. For the performance-maker, the work of making “the work”, over time, has never been ephemeral. Spectators’ performances and those of makers are non-identical, not least in terms of performances’ times. The ‘signature practices’ of the mature expert practitioner tend to emerge just in time, and the work is serial, a momentary instantiation in an ongoing creative enquiry, whereas spectating, in the event, mistakes its experience for “the work itself”. We propose to argue that times, the immutable and the immanent, engage with particular ways of seeing, so as to produce ‘signature practices’, in expert performance-making registers. The processes tend to be punctuated a ‘momentary instantiation’ (Knorr Cetina, 2001): the timely performance outcome that seems initially to end the enquiry, but that will reveal, to the practitioner concerned, a further set of questions to be worked through

Elliptic operators on manifolds with singularities and K-homology

It is well known that elliptic operators on a smooth compact manifold are classified by K-homology. We prove that a similar classification is also valid for manifolds with simplest singularities: isolated conical points and fibered boundary. The main ingredients of the proof of these results are: an analog of the Atiyah-Singer difference construction in the noncommutative case and an analog of Poincare isomorphism in K-theory for our singular manifolds. As applications we give a formula in topological terms for the obstruction to Fredholm problems on manifolds with singularities and a formula for K-groups of algebras of pseudodifferential operators.Comment: revised version; 25 pages; section with applications expande