We determine the Chern characters of two projective modules over the fuzzy sphere and calculate the corresponding topological charges (Chern numbers). These turn out to have corrections—compared to the commutative limit—induced by the noncommutative structure of the three coordinates.

New fixed point results are presented for multivalued maps defined on subsets of a Fréchet space E. The proof relies on the notion of a pseudo open set, degree and index theory, and on viewing E as the projective limit of a sequence of Banach spaces.

By means of toric geometry we study hypersurfaces in weighted projective space of dimension four. In particular we compute for a given manifold its intrinsic topological coupling. We find that the result agrees with the calculation of the corresponding coupling on the mirror model in the large complex structure limit.

A smooth, projective, absolutely irreducible curve of genus 19 over F2 admitting an infinite S-class field tower is presented. Here S is a set of four F2-rational points on the curve. This is shown to imply that A(2) = limsup#X(F2)/g(X) ≥ 4/(19 − 1) ≈ 0.222. Here the limit is taken over curves X over F2 of genus g(X)→∞.

We provide a proof that when there is no forcing the recently introduced projective dynamics Monte Carlo algorithm gives the exact lifetime of the metastable state, within statistical uncertainties. We also show numerical evidence illustrating that for slow forcing the approach to the zero-forcing limit is rather rapid. The model studied numerically is the 3-dimensional 3-state Potts ferromagnet.

Using the recently discovered Clifford statistics we propose a simple model for the grand canonical ensemble of the carriers in the theory of fractional quantum Hall effect. The model leads to a temperature limit associated with the permutational degrees of freedom of such an ensemble. We also briefly review Schur’s theory of projective representations of the permutation groups. PACS numbers: 7...

We show that the sectional capacity of an adelic subset of a projective variety over a number field is a quasi-canonical limit of arithmetic top self-intersection numbers, and we establish the functorial properties of extremal plurisubharmonic Green’s functions. We also present a conjecture that the sectional capacity should be a top selfintersection number in an appropriate adelic arithmetic i...

The problem of the time arrival a quantum system in specified state is considered framework repeated measurement protocol and particular limit continuous measurements discussed. It shown that for choice system-detector coupling, Zeno effect avoided can be described effectively by non-Hermitian effective Hamiltonian. As specific example we consider evolution particle on one-dimensional lattice s...

We investigate the implementation of binary projective measurements with linear optics. This problem can be viewed as a single-shot discrimination of two orthogonal pure quantum states. We show that any two orthogonal states can be perfectly discriminated using only linear optics, photon counting, coherent ancillary states, and feedforward. The statement holds in the asymptotic limit of a large...