Integral Grothendieck-Riemann-Roch theorem

We show that, in characteristic zero, the obvious integral version of the Grothendieck-Riemann-Roch formula obtained by clearing the denominators of the Todd and Chern characters is true (without having to divide the Chow groups by their torsion subgroups). The proof introduces an alternative to Grothendieck's strategy: we use resolution of singularities and the weak factorization theorem for birational maps.Comment: 24 page

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

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

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

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

Lie group weight multiplicities from conformal field theory

Dominant weight multiplicities of simple Lie groups are expressed in terms of the modular matrices of Wess-Zumino-Witten conformal field theories, and related objects. Symmetries of the modular matrices give rise to new relations among multiplicities. At least for some Lie groups, these new relations are strong enough to completely fix all multiplicities.Comment: 12 pages, Plain TeX, no figure

On character generators for simple Lie algebras

We study character generating functions (character generators) of simple Lie algebras. The expression due to Patera and Sharp, derived from the Weyl character formula, is first reviewed. A new general formula is then found. It makes clear the distinct roles of ``outside'' and ``inside'' elements of the integrity basis, and helps determine their quadratic incompatibilities. We review, analyze and extend the results obtained by Gaskell using the Demazure character formulas. We find that the fundamental generalized-poset graphs underlying the character generators can be deduced from such calculations. These graphs, introduced by Baclawski and Towber, can be simplified for the purposes of constructing the character generator. The generating functions can be written easily using the simplified versions, and associated Demazure expressions. The rank-two algebras are treated in detail, but we believe our results are indicative of those for general simple Lie algebras.Comment: 50 pages, 11 figure

Time-Frequency Transfer with Quantum Fields

Clock synchronisation relies on time-frequency transfer procedures which involve quantum fields. We use the conformal symmetry of such fields to define as quantum operators the time and frequency exchanged in transfer procedures and to describe their transformation under transformations to inertial or accelerated frames. We show that the classical laws of relativity are changed when brought in the framework of quantum theory.Comment: 4 page