Schur Q-functions and degeneracy locus formulas for morphisms with symmetries

We give closed-form formulas for the fundamental classes of degeneracy loci associated with vector bundle maps given locally by (not necessary square) matrices which are symmetric (resp. skew-symmetric) w.r.t. the main diagonal. Our description uses essentially Schur Q-polynomials of a bundle, and is based on a certain push-forward formula for these polynomials in a Grassmann bundle.Comment: 22 pages, AMSTEX, misprints corrected, exposition improved. to appear in the Proceedings of Intersection Theory Conference in Bologna, "Progress in Mathematics", Birkhause

Classification of double flag varieties of complexity 0 and 1

A classification of double flag varieties of complexity 0 and 1 is obtained. An application of this problem to decomposing tensor products of irreducible representations of semisimple Lie groups is considered

Spectral geometry of κ\kappa-Minkowski space

After recalling Snyder's idea of using vector fields over a smooth manifold as `coordinates on a noncommutative space', we discuss a two dimensional toy-model whose `dual' noncommutative coordinates form a Lie algebra: this is the well known $\kappa$-Minkowski space. We show how to improve Snyder's idea using the tools of quantum groups and noncommutative geometry. We find a natural representation of the coordinate algebra of $\kappa$-Minkowski as linear operators on an Hilbert space study its `spectral properties' and discuss how to obtain a Dirac operator for this space. We describe two Dirac operators. The first is associated with a spectral triple. We prove that the cyclic integral of M. Dimitrijevic et al. can be obtained as Dixmier trace associated to this triple. The second Dirac operator is equivariant for the action of the quantum Euclidean group, but it has unbounded commutators with the algebra.Comment: 23 pages, expanded versio

On Nichols algebras over SL(2,Fq) and GL(2,Fq)

We compute necessary conditions on Yetter-Drinfeld modules over the groups SL(2,Fq) and GL(2,Fq) to generate finite dimensional Nichols algebras. This is a first step towards a classification of pointed Hopf algebras with a group of group-likes isomorphic to one of these groups.Comment: Major exposition revision, including referees remarks. To appear in J. Math. Phys. 13 page

Higher su(N) tensor products

We extend our recent results on ordinary su(N) tensor product multiplicities to higher su(N) tensor products. Particular emphasis is put on four-point couplings where the tensor product of four highest weight modules is considered. The number of times the singlet occurs in the decomposition is the associated multiplicity. In this framework, ordinary tensor products correspond to three-point couplings. As in that case, the four-point multiplicity may be expressed explicitly as a multiple sum measuring the discretised volume of a convex polytope. This description extends to higher-point couplings as well. We also address the problem of determining when a higher-point coupling exists, i.e., when the associated multiplicity is non-vanishing. The solution is a set of inequalities in the Dynkin labels.Comment: 17 pages, LaTe

Independent individual addressing of multiple neutral atom qubits with a MEMS beam steering system

We demonstrate a scalable approach to addressing multiple atomic qubits for use in quantum information processing. Individually trapped 87Rb atoms in a linear array are selectively manipulated with a single laser guided by a MEMS beam steering system. Single qubit oscillations are shown on multiple sites at frequencies of ~3.5 MHz with negligible crosstalk to neighboring sites. Switching times between the central atom and its closest neighbor were measured to be 6-7 us while moving between the central atom and an atom two trap sites away took 10-14 us.Comment: 9 pages, 3 figure

Calibration of <i>Herschel</i> SPIRE FTS observations at different spectral resolutions

The SPIRE Fourier Transform Spectrometer on-board the Herschel Space Observatory had two standard spectral resolution modes for science observations: high resolution (HR) and low resolution (LR), which could also be performed in sequence (H+LR). A comparison of the HR and LR resolution spectra taken in this sequential mode revealed a systematic discrepancy in the continuum level. Analysing the data at different stages during standard pipeline processing demonstrates that the telescope and instrument emission affect HR and H+LR observations in a systematically different way. The origin of this difference is found to lie in the variation of both the telescope and instrument response functions, while it is triggered by fast variation of the instrument temperatures. As it is not possible to trace the evolution of the response functions using housekeeping data from the instrument subsystems, the calibration cannot be corrected analytically. Therefore, an empirical correction for LR spectra has been developed, which removes the systematic noise introduced by the variation of the response functions

Analytical Form of the Deuteron Wave Function Calculated within the Dispersion Approach

We present a convenient analytical parametrization of the deuteron wave function calculated within dispersion approach as a discrete superposition of Yukawa-type functions, in both configuration and momentum spaces.Comment: 3 pages, 2 figure; several minor corrections adde

Connection Conditions and the Spectral Family under Singular Potentials

To describe a quantum system whose potential is divergent at one point, one must provide proper connection conditions for the wave functions at the singularity. Generalizing the scheme used for point interactions in one dimension, we present a set of connection conditions which are well-defined even if the wave functions and/or their derivatives are divergent at the singularity. Our generalized scheme covers the entire U(2) family of quantizations (self-adjoint Hamiltonians) admitted for the singular system. We use this scheme to examine the spectra of the Coulomb potential $V(x) = - e^2 / | x |$ and the harmonic oscillator with square inverse potential $V(x) = (m \omega^2 / 2) x^2 + g/x^2$, and thereby provide a general perspective for these models which have previously been treated with restrictive connection conditions resulting in conflicting spectra. We further show that, for any parity invariant singular potentials $V(-x) = V(x)$, the spectrum is determined solely by the eigenvalues of the characteristic matrix $U \in U(2)$.Comment: TeX, 18 page

Multi-photon transitions between energy levels in a current-biased Josephson tunnel junction

The escape of a small current-biased Josephson tunnel junction from the zero voltage state in the presence of weak microwave radiation is investigated experimentally at low temperatures. The measurements of the junction switching current distribution indicate the macroscopic quantum tunneling of the phase below a cross-over temperature of $T^{\star} \approx 280 \rm{mK}$. At temperatures below $T^{\star}$ we observe both single-photon and \emph{multi-photon} transitions between the junction energy levels by applying microwave radiation in the frequency range between $10 \rm{GHz}$ and $38 \rm{GHz}$ to the junction. These observations reflect the anharmonicity of the junction potential containing only a small number of levels.Comment: 4 pages, 5 figure