Geometric phases in a scattering process

The study of geometric phase in quantum mechanics has so far be confined to discrete (or continuous) spectra and trace preserving evolutions. Consider only the transmission channel, a scattering process with internal degrees of freedom is neither a discrete spectrum problem nor a trace preserving process. We explore the geometric phase in a scattering process taking only the transmission process into account. We find that the geometric phase can be calculated by the some method as in an unitary evolution. The interference visibility depends on the transmission amplitude. The dependence of the geometric phase on the barrier strength and the spin-spin coupling constant is also presented and discussed.Comment: 4 pages, 5 figure

OPTIMAL POST-HARVEST GRAINS STORAGE BY RISK AVERSE FARMERS

Most previous research on post-harvest grain storage by farmers has assumed risk-neutral behavior and/or made restrictive assumptions about underlying price probability distributions. In this study we solve the optimal post-harvest storage problem for a risk averse farmer under more general assumptions about underlying price distributions. The resulting model is applied to Michigan corn farmers and results show that, contrary to the sell all-or-nothing risk-neutral rule, risk averse farmers will spread sales out over the storage season. The optimal pattern for sales by Michigan corn farmers is to sell approximately 50% of corn at harvest in November (a risk-reduction strategy) and approximately 40% in May (a return-enhancing strategy).Crop Production/Industries,

The dynamics of market structure and market size in two health services industries

The relationship between the size of a market and the competitiveness of the market has been of long-standing interest to IO economists. Empirical studies have used the relationship between the size of the geographic market and both the number of firms in the market and the average sales of the firms to draw inferences about the degree of competition in the market. This paper extends this framework to incorporate the analysis of entry and exit flows. A key implication of recent entry and exit models is that current market structure will likely depend upon the history of past participation. The paper explores these issues empirically by examining producer dynamics for two health service industries, dentistry and chiropractic services.Markets ; Industrial organization ; Service industries

Anatomy of Zero-norm States in String Theory

We calculate and identify the counterparts of zero-norm states in the old covariant first quantised (OCFQ) spectrum of open bosonic string in two other quantization schemes of string theory, namely the light-cone DDF zero-norm states and the off-shell BRST zero-norm states (with ghost) in the Witten string field theory (WSFT). In particular, special attention is paid to the inter-particle zero-norm states in all quantization schemes. For the case of the off-shell BRST zero-norm states, we impose the no ghost conditions and recover exactly two types of on-shell zero-norm states in the OCFQ string spectrum for the first few low-lying mass levels. We then show that off-shell gauge transformations of WSFT are identical to the on-shell stringy gauge symmetries generated by two types of zero-norm states in the generalized massive sigma-model approach of string theory. The high energy limit of these stringy gauge symmetries was recently used to calculate the proportionality constants, conjectured by Gross, among high energy scattering amplitudes of different string states. Based on these zero-norm state calculations, we have thus related gauge symmetry of WSFT to the high-energy stringy symmetry of Gross.Comment: 30 page

Evaluation of ECMWF medium-range ensemble forecasts of precipitation for river basins

Providing probabilistic forecasts using Ensemble Prediction Systems has become increasingly popular in both the meteorological and hydrological communities. Compared to conventional deterministic forecasts, probabilistic forecasts may provide more reliable forecasts of a few hours to a number of days ahead, and hence are regarded as better tools for taking uncertainties into consideration and hedging against weather risks. It is essential to evaluate performance of raw ensemble forecasts and their potential values in forecasting extreme hydro-meteorological events. This study evaluates ECMWF's medium-range ensemble forecasts of precipitation over the period 1 January 2008 to 30 September 2012 on a selected midlatitude large-scale river basin, the Huai river basin (ca. 270 000 km2) in central-east China. The evaluation unit is sub-basin in order to consider forecast performance in a hydrologically relevant way. The study finds that forecast performance varies with sub-basin properties, between flooding and non-flooding seasons, and with the forecast properties of aggregated time steps and lead times. Although the study does not evaluate any hydrological applications of the ensemble precipitation forecasts, its results have direct implications in hydrological forecasts should these ensemble precipitation forecasts be employed in hydrology

Fermi gas in harmonic oscillator potentials

Assuming the validity of grand canonical statistics, we study the properties of a spin-polarized Fermi gas in harmonic traps. Universal forms of Fermi temperature $T_F$, internal energy $U$ and the specific heat per particle of the trapped Fermi gas are calculated as a {\it function} of particle number, and the results compared with those of infinite number particles.Comment: 8 pages, 1 figure, LATE