13 research outputs found
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 , 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 ) of
the uniform QMB, as well as some results for the random QMB. We leave the
moderate and small 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)
A NEW DETERMINATION OF N-A
The Avogadro constant was determined by measurements of the (220) lattice spacing, density, and molar mass of silicon crystals. The measured value is N-A = (6.0221379 +/- 0.0000025) x 10(23) mol(-1)