Quantum Multibaker Maps: Extreme Quantum Regime

We introduce a family of models for quantum mechanical, one-dimensional random walks, called quantum multibaker maps (QMB). These are Weyl quantizations of the classical multibaker models previously considered by Gaspard, Tasaki and others. Depending on the properties of the phases parametrizing the quantization, we consider only two classes of the QMB maps: uniform and random. Uniform QMB maps are characterized by phases which are the same in every unit cell of the multibaker chain. Random QMB maps have phases that vary randomly from unit cell to unit cell. The eigenstates in the former case are extended while in the latter they are localized. In the uniform case and for large $\hbar$, analytic solutions can be obtained for the time dependent quantum states for periodic chains and for open chains with absorbing boundary conditions. Steady state solutions and the properties of the relaxation to a steady state for a uniform QMB chain in contact with ``particle'' reservoirs can also be described analytically. The analytical results are consistent with, and confirmed by, results obtained from numerical methods. We report here results for the deep quantum regime (large $\hbar$) of the uniform QMB, as well as some results for the random QMB. We leave the moderate and small $\hbar$ results as well as further consideration of the other versions of the QMB for further publications.Comment: 17 pages, referee's and editor's comments addresse

Is Hedging a Habit? Hedging Ratio Determination of Cotton Producers

We examine the role that habit plays when producers determine their hedge ratio. Data were collected from U.S. cotton growers in which they indicated their hedging position in 2001 and 2002 as well as their perceived profitability, land ownership structure, and income. To account for heterogeneity, a generalized mixture regres-sion model is used to identify the influence of the determinants of the hedge ratio. Our results identified two segments. In the smaller segment, consisting of 35% of the producers, habit did not affect the hedge ratio; instead, land ownership and perceived profitability were most influential. In the larger segment, consisting of 65% of the producers, the hedge ratio was solely driven by habit. The results show the important role of habit formation in understanding producers’ employed hedge ratio, confirm the importance of heterogeneity, and strengthen the relation-ship between financial structure and market-risk mitigating behavior