Natural Density of Rectangular Unimodular Integer Matrices

In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers. As a corollary, we find the density of rectangular matrices with Hermite normal form [O Id]. Connections with Cesaro's Theorem on the density of coprime integers and Quillen-Suslin's Theorem are also presented.Comment: 8 page

Finite Width Effects and Gauge Invariance in Radiative WW Production and Decay

The naive implementation of finite width effects in processes involving unstable particles can violate gauge invariance. For the example of radiative $W$ production and decay, $q\bar q' \to \ell\nu\gamma$, at tree level, it is demonstrated how gauge invariance is restored by including the imaginary part of triangle graphs in addition to resumming the imaginary contributions to the $W$ vacuum polarization. Monte Carlo results are presented for the Fermilab Tevatron.Comment: 10 pages, Revtex, 3 figures submitted separately as uuencoded tarred postscript files, the complete paper is available at ftp://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-878.ps.Z or http://phenom.physics.wisc.edu/pub/preprints/1995/madph-95-878.ps.

Effect of Poisson ratio on cellular structure formation

Mechanically active cells in soft media act as force dipoles. The resulting elastic interactions are long-ranged and favor the formation of strings. We show analytically that due to screening, the effective interaction between strings decays exponentially, with a decay length determined only by geometry. Both for disordered and ordered arrangements of cells, we predict novel phase transitions from paraelastic to ferroelastic and anti-ferroelastic phases as a function of Poisson ratio.Comment: 4 pages, Revtex, 4 Postscript figures include

1.9 K Heat Inleak and Resistive Heating Measurements on LHC Cryomagnets

The superconducting magnets of the Large Hadron Collider (LHC) distributed over eight sectors of 3.3-km long are cooled at 1.9 K in pressurized superfluid helium. During the commissioning campaign of the sectors in 2008, cold standby periods at nominal operating temperature have allowed to measure the overall static heat inleaks reaching the magnet cold masses at 1.9 K by enthalpy balance in steady-state operation. In addition, during electrical powering of the different magnet circuits, helium II calorimetry based on precision thermometry has been implemented to assess with an accuracy of 100 mW/m the additional heat loads due to resistive heating and to detect possible abnormal heat dissipation during powering. This paper describes the method applied to perform these measurements, compares the results with the expected specified values and discusses the impact of the measured values on cryo-plant tuning and operational margins

Cooldown and Warmup Studies for the Large Hadron Collider

The Large Hadron Collider (LHC), currently under construction at CERN, will make use of superconducting magnets operating in superfluid helium below 2 K. The LHC ring is divided in 8 sectors, each of them cooled by a refrigerator of 18 kW at 4.5 K equivalent cooling power. For the cooldown and warmup of a 3.3 km long LHC sector, the flow available above 80 K per refrigerator is 770 g/s and the cor responding capacity is 600 kW. This paper presents the results of cooldown and warmup simulations, as concerns time delays, temperature difference across magnets, available power and flow-rates, and estimates of energy and liquid nitrogen consumption

Charge transfer and coherence dynamics of tunnelling system coupled to a harmonic oscillator

We study the transition probability and coherence of a two-site system, interacting with an oscillator. Both properties depend on the initial preparation. The oscillator is prepared in a thermal state and, even though it cannot be considered as an extended bath, it produces decoherence because of the large number of states involved in the dynamics. In the case in which the oscillator is intially displaced a coherent dynamics of change entangled with oscillator modes takes place. Coherency is however degraded as far as the oscillator mass increases producing a increasingly large recoherence time. Calculations are carried on by exact diagonalization and compared with two semiclassical approximations. The role of the quantum effects are highlighted in the long-time dynamics, where semiclassical approaches give rise to a dissipative behaviour. Moreover, we find that the oscillator dynamics has to be taken into account, even in a semiclassical approximation, in order to reproduce a thermally activated enhancement of the transition probability

Detection statistics in the micromaser

We present a general method for the derivation of various statistical quantities describing the detection of a beam of atoms emerging from a micromaser. The user of non-normalized conditioned density operators and a linear master equation for the dynamics between detection events is discussed as are the counting statistics, sequence statistics, and waiting time statistics. In particular, we derive expressions for the mean number of successive detections of atoms in one of any two orthogonal states of the two-level atom. We also derive expressions for the mean waiting times between detections. We show that the mean waiting times between de- tections of atoms in like states are equivalent to the mean waiting times calculated from the uncorrelated steady state detection rates, though like atoms are indeed correlated. The mean waiting times between detections of atoms in unlike states exhibit correlations. We evaluate the expressions for various detector efficiencies using numerical integration, reporting re- sults for the standard micromaser arrangement in which the cavity is pumped by excited atoms and the excitation levels of the emerging atoms are measured. In addition, the atomic inversion and the Fano-Mandel function for the detection of de-excited atoms is calculated for compari- son to the recent experimental results of Weidinger et al. [1], which reports the first observation of trapping states.Comment: 26 pages, 11 figure