From multiple integrals to Fredholm determinants

We consider a multiple integral representation for the finite temperature density-density correlation functions of the one-dimensional Bose gas with delta function interaction in the limits of infinite and vanishing repulsion. In the former case a known Fredholm determinant is recovered. In the latter case a similar expression appears with permanents replacing determinants.Comment: 11 pages, section on the free Boson limit adde

On optimal head starts in all-pay auctions

We consider a two-player all-pay auction with symmetric independent private values that are uniformly distributed. The designer chooses the size of a head start that is given to one of the players. The designer’s objective is to maximize a convex combination of the expected highest effort and the expected aggregate effort. Unless the weight on the highest effort is one, small head starts are always worse than no head start. Moreover, the optimal head start is strictly positive if and only if the weight on the highest effort is large enough

Low temperature/short duration steaming as a sustainable method of soil disinfection

This report was presented at the UK Organic Research 2002 Conference. Soil samples containing resting structures of fungal crop pathogens (Verticillium dahliae, Sclerotinia sclerotiorum, Sclerotium cepivorum, Pythium ultimum), potato cyst nematodes (Globodera rostochiensis and Globodera pallida) and weeds (Chenopodium album and Agropyron repens) were treated with aerated steam in the laboratory at temperatures ranging from 50–80oC in a specially constructed apparatus. Steaming at 50 or 60oC for three minutes, followed by an eight-minute resting period in the steamed soil and immediate removal from the soil thereafter, resulted in 100% kill of all weeds, fungi and nematodes. Low temperature/ short duration soil steaming could become a sustainable alternative to chemical or high-temperature steam soil disinfestation

Continuous time contests with private information

This paper introduces a class of contest models in which each player decides when to stop a privately observed Brownian motion with drift and incurs costs depending on his stopping time. The player who stops his process at the highest value wins a prize. We prove existence and uniqueness of a Nash equilibrium outcome and derive the equilibrium distribution in closed form. As the variance tends to zero, the equilibrium outcome converges to the symmetric equilibrium of an all-pay auction. For two players and constant costs, each player’s equilibrium profit decreases if the drift increases, the variance decreases, or the costs decrease

Sub-dekahertz ultraviolet spectroscopy of 199Hg+

Using a laser that is frequency-locked to a Fabry-Perot etalon of high finesse and stability, we probe the 5d10 6s 2S_1/2 (F=0) - 5d9 6s 2D_5/2 (F=2) Delta-m_F = 0 electric-quadrupole transition of a single laser-cooled 199Hg+ ion stored in a cryogenic radio-frequency ion trap. We observe Fourier-transform limited linewidths as narrow as 6.7 Hz at 282 nm (1.06 X 10^15 Hz), yielding a line Q = 1.6 X 10^14. We perform a preliminary measurement of the 5d9 6s2 2D_5/2 electric-quadrupole shift due to interaction with the static fields of the trap, and discuss the implications for future trapped-ion optical frequency standards.Comment: 4 pages, 4 figures, submitted for publicatio

Modeling metallic island coalescence stress via adhesive contact between surfaces

Tensile stress generation associated with island coalescence is almost universally observed in thin films that grow via the Volmer-Weber mode. The commonly accepted mechanism for the origin of this tensile stress is a process driven by the reduction in surface energy at the expense of the strain energy associated with the deformation of coalescing islands during grain boundary formation. In the present work, we have performed molecular statics calculations using an embedded atom interatomic potential to obtain a functional form of the interfacial energy vs distance between two closely spaced free surfaces. The sum of interfacial energy plus strain energy provides a measure of the total system energy as a function of island separation. Depending on the initial separation between islands, we find that in cases where coalescence is thermodynamically favored, gap closure can occur either spontaneously or be kinetically limited due to an energetic barrier. Atomistic simulations of island coalescence using conjugate gradient energy minimization calculations agree well with the predicted stress as a function of island size from our model of spontaneous coalescence. Molecular dynamics simulations of island coalescence demonstrate that only modest barriers to coalescence can be overcome at room temperature. A comparison with thermally activated coalescence results at room temperature reveals that existing coalescence models significantly overestimate the magnitude of the stress resulting from island coalescence.Comment: 20 pages, 8 figures, 2 tables, submitted to PR

Optical cavity tests of Lorentz invariance for the electron

A hypothetical violation of Lorentz invariance in the electrons' equation of motion (expressed within the Lorentz-violating extension of the standard model) leads to a change of the geometry of crystals and thus shifts the resonance frequency of an electromagnetic cavity. This allows experimental tests of Lorentz invariance of the electron sector of the standard model. The material dependence of the effect allows to separate it from an additional shift caused by Lorentz violation in electrodynamics, and to place independent limits on both effects. From present experiments, upper limits on Lorentz violation in the electrons' kinetic energy term are deduced.Comment: 17 pages revte

Algebraic Bethe ansatz for the gl(1∣|2) generalized model II: the three gradings

The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe ansatz for all models with $9 \times 9$, rational, gl(1$|$2)-invariant $R$-matrix and all three possibilities of choosing the grading. Our Bethe ansatz solution applies, for instance, to the supersymmetric t-J model, the supersymmetric $U$ model and a number of interesting impurity models. It may be extended to obtain the quantum transfer matrix spectrum for this class of models. The properties of a specific model enter the Bethe ansatz solution (i.e. the expression for the transfer matrix eigenvalue and the Bethe ansatz equations) through the three pseudo vacuum eigenvalues of the diagonal elements of the monodromy matrix which in this context are called the parameters of the model.Comment: paragraph added in section 3, reference added, version to appear in J.Phys.