Lattice Point Generating Functions and Symmetric Cones

We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a finite reflection group. We obtain general expressions for the multivariate generating functions of such cones, and work out the specific cases of a symmetry group of type A (previously known) and types B and D (new). We obtain several applications of the special cases in type B, including identities involving permutation statistics and lecture hall partitions.Comment: 19 page

The vector-valued big q-Jacobi transform

Big $q$-Jacobi functions are eigenfunctions of a second order $q$-difference operator $L$. We study $L$ as an unbounded self-adjoint operator on an $L^2$-space of functions on $\mathbb R$ with a discrete measure. We describe explicitly the spectral decomposition of $L$ using an integral transform $\mathcal F$ with two different big $q$-Jacobi functions as a kernel, and we construct the inverse of $\mathcal F$.Comment: 35 pages, corrected an error and typo

Spherical Deconstruction

We present evidence that N=1* SUSY Yang-Mills provides a deconstruction of a six-dimensional gauge theory compactified on a two-sphere. The six-dimensional theory is a twisted compactification of N=(1,1) SUSY Yang-Mills theory of the type considered by Maldacena and Nunez (MN). In particular, we calculate the full classical spectrum of the N=1* theory with gauge group U(N) in its Higgs vacuum. In the limit N goes to infinity, we find an exact agreement with the Kaluza-Klein spectrum of the MN compactification.Comment: 16 page

Propagator of a Charged Particle with a Spin in Uniform Magnetic and Perpendicular Electric Fields

We construct an explicit solution of the Cauchy initial value problem for the time-dependent Schroedinger equation for a charged particle with a spin moving in a uniform magnetic field and a perpendicular electric field varying with time. The corresponding Green function (propagator) is given in terms of elementary functions and certain integrals of the fields with a characteristic function, which should be found as an analytic or numerical solution of the equation of motion for the classical oscillator with a time-dependent frequency. We discuss a particular solution of a related nonlinear Schroedinger equation and some special and limiting cases are outlined.Comment: 17 pages, no figure

Interferometric detection of a single vortex in a dilute Bose-Einstein condensate

Using two radio frequency pulses separated in time we perform an amplitude division interference experiment on a rubidium Bose-Einstein condensate. The presence of a quantized vortex, which is nucleated by stirring the condensate with a laser beam, is revealed by a dislocation in the fringe pattern.Comment: 4 pages, 4 figure

Jack superpolynomials with negative fractional parameter: clustering properties and super-Virasoro ideals

The Jack polynomials P_\lambda^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible partitions are known to span an ideal I^{(k,r)}_N of the space of symmetric functions in N variables. The ideal I^{(k,r)}_N is invariant under the action of certain differential operators which include half the Virasoro algebra. Moreover, the Jack polynomials in I^{(k,r)}_N admit clusters of size at most k: they vanish when k+1 of their variables are identified, and they do not vanish when only k of them are identified. We generalize most of these properties to superspace using orthogonal eigenfunctions of the supersymmetric extension of the trigonometric Calogero-Moser-Sutherland model known as Jack superpolynomials. In particular, we show that the Jack superpolynomials P_{\Lambda}^{(\alpha)} at \alpha=-(k+1)/(r-1) indexed by certain (k,r,N)-admissible superpartitions span an ideal {\mathcal I}^{(k,r)}_N of the space of symmetric polynomials in N commuting variables and N anticommuting variables. We prove that the ideal {\mathcal I}^{(k,r)}_N is stable with respect to the action of the negative-half of the super-Virasoro algebra. In addition, we show that the Jack superpolynomials in {\mathcal I}^{(k,r)}_N vanish when k+1 of their commuting variables are equal, and conjecture that they do not vanish when only k of them are identified. This allows us to conclude that the standard Jack polynomials with prescribed symmetry should satisfy similar clustering properties. Finally, we conjecture that the elements of {\mathcal I}^{(k,2)}_N provide a basis for the subspace of symmetric superpolynomials in N variables that vanish when k+1 commuting variables are set equal to each other.Comment: 36 pages; the main changes in v2 are : 1) in the introduction, we present exceptions to an often made statement concerning the clustering property of the ordinary Jack polynomials for (k,r,N)-admissible partitions (see Footnote 2); 2) Conjecture 14 is substantiated with the extensive computational evidence presented in the new appendix C; 3) the various tests supporting Conjecture 16 are reporte

Transport of short-lived halocarbons to the stratosphere over the Pacific Ocean

The effectiveness of transport of short-lived halocarbons to the upper troposphere and lower stratosphere remains an important uncertainty in quantifying the supply of ozone-depleting substances to the stratosphere. In early 2014, a major field campaign in Guam in the western Pacific, involving UK and US research aircraft, sampled the tropical troposphere and lower stratosphere. The resulting measurements of CH3I, CHBr3 and CH2Br2 are compared here with calculations from a Lagrangian model. This methodology benefits from an updated convection scheme that improves simulation of the effect of deep convective motions on particle distribution within the tropical troposphere. We find that the observed CH3I, CHBr3 and CH2Br2 mixing ratios in the tropical tropopause layer (TTL) are consistent with those in the boundary layer when the new convection scheme is used to account for convective transport. More specifically, comparisons between modelled estimates and observations of short-lived CH3I indicate that the updated convection scheme is realistic up to the lower TTL but is less good at reproducing the small number of extreme convective events in the upper TTL. This study consolidates our understanding of the transport of short-lived halocarbons to the upper troposphere and lower stratosphere by using improved model calculations to confirm consistency between observations in the boundary layer, observations in the TTL and atmospheric transport processes. Our results support recent estimates of the contribution of short-lived bromocarbons to the stratospheric bromine budget

More is the Same; Phase Transitions and Mean Field Theories

This paper looks at the early theory of phase transitions. It considers a group of related concepts derived from condensed matter and statistical physics. The key technical ideas here go under the names of "singularity", "order parameter", "mean field theory", and "variational method". In a less technical vein, the question here is how can matter, ordinary matter, support a diversity of forms. We see this diversity each time we observe ice in contact with liquid water or see water vapor, "steam", come up from a pot of heated water. Different phases can be qualitatively different in that walking on ice is well within human capacity, but walking on liquid water is proverbially forbidden to ordinary humans. These differences have been apparent to humankind for millennia, but only brought within the domain of scientific understanding since the 1880s. A phase transition is a change from one behavior to another. A first order phase transition involves a discontinuous jump in a some statistical variable of the system. The discontinuous property is called the order parameter. Each phase transitions has its own order parameter that range over a tremendous variety of physical properties. These properties include the density of a liquid gas transition, the magnetization in a ferromagnet, the size of a connected cluster in a percolation transition, and a condensate wave function in a superfluid or superconductor. A continuous transition occurs when that jump approaches zero. This note is about statistical mechanics and the development of mean field theory as a basis for a partial understanding of this phenomenon.Comment: 25 pages, 6 figure

Glueballs of Super Yang-Mills from Wrapped Branes

In this paper we study qualitative features of glueballs in N=1 SYM for models of wrapped branes in IIA and IIB backgrounds. The scalar mode, 0++ is found to be a mixture of the dilaton and the internal part of the metric. We carry out the numerical study of the IIB background. The potential found exhibits a mass gap and produces a discrete spectrum without any cut-off. We propose a regularization procedure needed to make these states normalizable.Comment: 22 pages plus a appendixes, 2 figure

Enhanced ozone loss by active inorganic bromine chemistry in the tropical troposphere

Abstract Bromine chemistry, particularly in the tropics, has been suggested to play an important role in tropospheric ozone loss (Theys et al., 2011) although a lack of measurements of active bromine species impedes a quantitative understanding of its impacts. Recent modelling and measurements of bromine monoxide (BrO) by Wang et al. (2015) have shown current models under predict BrO concentrations over the Pacific Ocean and allude to a missing source of BrO. Here, we present the first simultaneous aircraft measurements of atmospheric bromine monoxide, BrO (a radical that along with atomic Br catalytically destroys ozone) and the inorganic Br precursor compounds HOBr, BrCl and Br2 over the Western Pacific Ocean from 0.5 to 7 km. The presence of 0.17-€“1.64 pptv BrO and 3.6-8 pptv total inorganic Br from these four species throughout the troposphere causes 10-20% of total ozone loss, and confirms the importance of bromine chemistry in the tropical troposphere; contributing to a 6 ppb decrease in ozone levels due to halogen chemistry. Observations are compared with a global chemical transport model and find that the observed high levels of BrO, BrCl and HOBr can be reconciled by active multiphase oxidation of halide (Br- and Cl-ˆ’) by HOBr and ozone in cloud droplets and aerosols. Measurements indicate that 99% of the instantaneous free Br in the troposphere up to 8 km originates from inorganic halogen photolysis rather than from photolysis of organobromine species