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

On the Contraction of the Discrete-series of Su (1,1)

It is shown that ma non-zero mass, positive energy representation of the Poincare group P1,1 = SO(1, 1) x(s) R2 can be obtained via contraction from the discrete series of representations of SU(1, 1)

Sr–Nd–Pb–Hf isotope systematics of the Hugo Dummett Cu–Au porphyry deposit (Oyu Tolgoi, Mongolia)

Major and trace element geochemistry including Sr–Nd–Pb–Hf isotopic data are presented for a representative sample suite of Late Devonian to Early Carboniferous plutonic and volcanic rocks from the Hugo Dummett deposit of the giant Oyu Tolgoi porphyry Cu–Au district in South Gobi, Mongolia. Sr and Nd isotopes (whole-rock) show restricted ranges of initial compositions, with positive εNdt mainly between + 3.4 and + 7.4 and (87Sr/86Sr)t predominantly between 0.7037 and 0.7045 reflecting magma generation from a relatively uniform juvenile lithophile-element depleted source. Previously dated zircons from the plutonic rocks exhibit a sample-averaged range of εHft values of + 11.6 to + 14.5. Depleted-mantle model ages of 420–830 (Nd) and 320–730 Ma (zircon Hf) limit the involvement of pre-Neoproterozoic crust in the petrogenesis of the intermediate to felsic calc-alkaline magmas to, at most, a minor role. Pb isotopes (whole-rock) show a narrow range of unradiogenic initial compositions: 206Pb/204Pb 17.40–17.94, 207Pb/204Pb 15.43–15.49 and 208Pb/204Pb 37.25–37.64, in agreement with Sr–Nd–Hf isotopes indicating the dominance of a mantle component. All four isotopic systems suggest that the magmas from which the large Oyu Tolgoi porphyry system was generated originated predominantly from juvenile material within the subduction-related setting of the Gurvansayhan terrane