Generalized spin Sutherland systems revisited

We present generalizations of the spin Sutherland systems obtained earlier by Blom and Langmann and by Polychronakos in two different ways: from SU(n) Yang--Mills theory on the cylinder and by constraining geodesic motion on the N-fold direct product of SU(n) with itself, for any N>1. Our systems are in correspondence with the Dynkin diagram automorphisms of arbitrary connected and simply connected compact simple Lie groups. We give a finite-dimensional as well as an infinite-dimensional derivation and shed light on the mechanism whereby they lead to the same classical integrable systems. The infinite-dimensional approach, based on twisted current algebras (alias Yang--Mills with twisted boundary conditions), was inspired by the derivation of the spinless Sutherland model due to Gorsky and Nekrasov. The finite-dimensional method relies on Hamiltonian reduction under twisted conjugations of N-fold direct product groups, linking the quantum mechanics of the reduced systems to representation theory similarly as was explored previously in the N=1 case.Comment: 21 page

On second order Thom-Boardman singularities

In this paper we derive closed formulas for the Thom polynomials of two families of second order Thom-Boardman singularities \Sigma^{i,j}. The formulas are given as linear combinations of Schur polynomials, and all coefficients are nonnegative.Comment: 15 pages, 1 figure; minor updates and correction

Derivations of the trigonometric BC(n) Sutherland model by quantum Hamiltonian reduction

The BC(n) Sutherland Hamiltonian with coupling constants parametrized by three arbitrary integers is derived by reductions of the Laplace operator of the group U(N). The reductions are obtained by applying the Laplace operator on spaces of certain vector valued functions equivariant under suitable symmetric subgroups of U(N)\times U(N). Three different reduction schemes are considered, the simplest one being the compact real form of the reduction of the Laplacian of GL(2n,C) to the complex BC(n) Sutherland Hamiltonian previously studied by Oblomkov.Comment: 30 pages, LateX; v2: final version with minor stylistic modification

Spinning particles in Taub-NUT space

The geodesic motion of pseudo-classical spinning particles in Euclidean Taub-NUT space is analysed. The constants of motion are expressed in terms of Killing-Yano tensors. Some previous results from the literature are corrected.Comment: LaTeX, 8 page

Optical Detection of a Single Nuclear Spin

We propose a method to optically detect the spin state of a 31-P nucleus embedded in a 28-Si matrix. The nuclear-electron hyperfine splitting of the 31-P neutral-donor ground state can be resolved via a direct frequency discrimination measurement of the 31-P bound exciton photoluminescence using single photon detectors. The measurement time is expected to be shorter than the lifetime of the nuclear spin at 4 K and 10 T.Comment: 4 pages, 3 figure

Magnetic fullerenes inside single-wall carbon nanotubes

C59N magnetic fullerenes were formed inside single-wall carbon nanotubes by vacuum annealing functionalized C59N molecules encapsulated inside the tubes. A hindered, anisotropic rotation of C59N was deduced from the temperature dependence of the electron spin resonance spectra near room temperature. Shortening of spin-lattice relaxation time, T_1, of C59N indicates a reversible charge transfer toward the host nanotubes above $\sim 350$ K. Bound C59N-C60 heterodimers are formed at lower temperatures when C60 is co-encapsulated with the functionalized C59N. In the 10-300 K range, T_1 of the heterodimer shows a relaxation dominated by the conduction electrons on the nanotubes

Error Rate of the Kane Quantum Computer CNOT Gate in the Presence of Dephasing

We study the error rate of CNOT operations in the Kane solid state quantum computer architecture. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off diagonal elements of the system's density matrix. Using available spin echo decay data, the CNOT error rate is estimated at approsimately 10^{-3}.Comment: New version includes substantial additional data and merges two old figures into one. (12 pages, 6 figures