Scanning tunnelling spectroscopy of electron resonators

The electronic structure of artificial Mn atom arrays on Ag(111) is characterized in detail with scanning tunnelling spectroscopy and spectroscopic imaging at low temperature. We demonstrate the degree to which variations in geometry may be used to control spatial and spectral distributions of surface state electrons confined within the arrays, how these are influenced by atoms placed within the structure and how the ability to induce spectral features at specific energies may be exploited through lineshape analyses to deduce quasiparticle lifetimes near the Fermi level. Through extensive comparison of $dI/dV$ maps and spectra we demonstrate the utility of a model based upon two-dimensional s-wave scatterers for describing and predicting the characteristics of specific resonators

Phase coherence length and quantum interference patterns at step edges

The accepted approximation used to describe quantum interference patterns at steps is shown to be incorrect. As a result, electron lifetimes determined using it are in error by a factor 2.Comment: 3 pages, 1 figur

q-Newton binomial: from Euler to Gauss

A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter

Uncovering Ramanujan's "Lost" Notebook: An Oral History

Here we weave together interviews conducted by the author with three prominent figures in the world of Ramanujan's mathematics, George Andrews, Bruce Berndt and Ken Ono. The article describes Andrews's discovery of the "lost" notebook, Andrews and Berndt's effort of proving and editing Ramanujan's notes, and recent breakthroughs by Ono and others carrying certain important aspects of the Indian mathematician's work into the future. Also presented are historical details related to Ramanujan and his mathematics, perspectives on the impact of his work in contemporary mathematics, and a number of interesting personal anecdotes from Andrews, Berndt and Ono

Consumption Externalities and Diffusion in Pharmaceutical Markets: Antiulcer Drugs

We examine the role of consumption externalities in the demand for pharmaceuticals at both the brand level and over a therapeutic class of drugs. These effects emerge when use of a drug by others affects its value, and/or conveys information abut efficacy and safety to patients and physicians. This can affect that rate of market diffusion for a new entrant, and can lead to herb behavior whereby a particular drug can dominate the market despite the availability of close substitutes. We use data for H2-antagonist antiulcer drugs to estimate a dynamic demand model and quantify these effects. The model has three components: an hedonic price equation that measures how the aggregate usage of a drug, as well as conventional attributes, affect brand valuation; equations relating equilibrium market shares to quality-adjusted prices and marketing levels; and diffusion equations describing the dynamic adjustment process. We find that consumption externalities influence both valuations and rates of diffusion, but that they operate at the brand and not the therapeutic class level.

Theoretical analysis of STM-derived lifetimes of excitations in the Shockley surface state band of Ag(111)

We present a quantitative many-body analysis using the GW approximation of the decay rate $\Gamma$ due to electron-electron scattering of excitations in the Shockley surface state band of Ag(111), as measured using the scanning tunnelling microscope (STM). The calculations include the perturbing influence of the STM, which causes a Stark-shift of the surface state energy $E$ and concomitant increase in $\Gamma$. We find $\Gamma$ varies more rapidly with $E$ than recently found for image potential states, where the STM has been shown to significantly affect measured lifetimes. For the Shockley states, the Stark-shifts that occur under normal tunnelling conditions are relatively small and previous STM-derived lifetimes need not be corrected.Comment: 4 pages, 3 figure