The Impacts of Retail Promotions on the Demand for Orange Juice: A Study of a Retail Chain

This study examined the impacts of retail promotions on the demand for five brands of orange juices for a retail chain (referred to as Retailer X) and its competitors using the Rotterdam model. Results show that the combination of feature ads and displays had the largest impacts on retail revenue among the four promotional tactics considered, while temporary price reductions had no additional advertising impacts other than price impacts on retail revenues. Results also show that when Retailer X promotes an OJ brand using any of the tactics studied, a larger portion of the increased demand for the promoted brand came from reduced demand for other brands of OJ in the same store and a smaller portion came from the decreased demand in competing stores in the same trading area.Demand and Price Analysis, Marketing,

Preparing and probing atomic number states with an atom interferometer

We describe the controlled loading and measurement of number-squeezed states and Poisson states of atoms in individual sites of a double well optical lattice. These states are input to an atom interferometer that is realized by symmetrically splitting individual lattice sites into double wells, allowing atoms in individual sites to evolve independently. The two paths then interfere, creating a matter-wave double-slit diffraction pattern. The time evolution of the double-slit diffraction pattern is used to measure the number statistics of the input state. The flexibility of our double well lattice provides a means to detect the presence of empty lattice sites, an important and so far unmeasured factor in determining the purity of a Mott state

Is there still a strong CP problem?

The role of a chiral U(1) phase in the quark mass in QCD is analysed from first principles. In operator formulation, there is a parity symmetry and the phase can be removed by a change in the representation of the Dirac gamma matrices. Moreover, these properties are also realized in a Pauli-Villars regularized version of the theory. In the functional integral scenario, attempts to remove the chiral phase by a chiral transformation are thought to be obstructed by a nontrivial Jacobian arising from the fermion measure and the chiral phase may therefore seem to break parity. But if one starts from the regularized action with the chiral phase also present in the regulator mass term, the Jacobian for a combined chiral rotation of quarks and regulators is seen to be trivial and the phase can be removed by a combined chiral rotation. This amounts to a taming of the strong CP problem.Comment: 6 pages, REVTeX; brief discussion available at http://theory.saha.ernet.in/~mitra/scp.htm

Positivity of Entropy in the Semi-Classical Theory of Black Holes and Radiation

Quantum stress-energy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $\Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {\it all} regular renormalized stress-energy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $\Delta S$ has a local minimum there. Explicit calculation shows that indeed $\Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stress-energy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the back-reaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $\Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The back-reaction, no matter how "small",Comment: 19 pages, RevTe

Dynamical Decoupling in Optical Fibers: Preserving Polarization Qubits from Birefringent Dephasing

One of the major challenges in quantum computation has been to preserve the coherence of a quantum system against dephasing effects of the environment. The information stored in photon polarization, for example, is quickly lost due to such dephasing, and it is crucial to preserve the input states when one tries to transmit quantum information encoded in the photons through a communication channel. We propose a dynamical decoupling sequence to protect photonic qubits from dephasing by integrating wave plates into optical fiber at prescribed locations. We simulate random birefringent noise along realistic lengths of optical fiber and study preservation of polarization qubits through such fibers enhanced with Carr-Purcell-Meiboom-Gill (CPMG) dynamical decoupling. This technique can maintain photonic qubit coherence at high fidelity, making a step towards achieving scalable and useful quantum communication with photonic qubits.Comment: 8 pages, 5 figure