Price Formation under Small Numbers Competition: Evidence from Land Auctions in Singapore

This paper examines the price formation process under small numbers competition using data from Singapore land auctions. The theory predicts that bid prices are less than the zero-profit asset value in these first-price sealed-bid auctions. The model also shows that expected sales price increases with the number of bidders both because each bidder has an incentive to offer a higher price and because of a greater likelihood that a high-value bidder is present. The empirical estimates are consistent with auction theory and show that the standard land attributes are reflected in auction prices as expected. Working Paper No. 04-0

Intermodal entanglement in Raman processes

The operator solution of a completely quantum mechanical Hamiltonian of the Raman processes is used here to investigate the possibility of obtaining intermodal entanglement between different modes involved in the Raman processes (e.g. pump mode, Stokes mode, vibration (phonon) mode and anti-Stokes mode). Intermodal entanglement is reported between a) pump mode and anti-Stokes mode, b) pump mode and vibration (phonon) mode c) Stokes mode and vibration phonon mode, d) Stokes mode and anti-stokes mode in the stimulated Raman processes for the variation of the phase angle of complex eigenvalue $\alpha_{1}$ of pump mode $a$. Some incidents of intermodal entanglement in the spontaneous and the partially spontaneous Raman processes are also reported. Further it is shown that the specific choice of coupling constants may produce genuine entanglement among Stokes mode, anti-Stokes mode and vibration-phonon mode. It is also shown that the two mode entanglement not identified by Duan's criterion may be identified by Hillery-Zubairy criteria. It is further shown that intermodal entanglement, intermodal antibunching and intermodal squeezing are independent phenomena.Comment: 11 pages, 4 figure