Quantum Multibaker Maps: Extreme Quantum Regime

Details Quantum Multibaker Maps: Extreme Quantum Regime Quantum Multibaker Maps: Extreme Quantum Regime

2002-03-24

arxiv.org/abs/cond-mat/0203494v2

Phys. Rev. E 66, 036110 (2002)

Physics

Condensed Matter

Statistical Mechanics

17 pages, referee's and editor's comments addressed

Scientific paper

10.1103/PhysRevE.66.036110

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.

Affiliated with

Also associated with

No associations

Rating

Quantum Multibaker Maps: Extreme Quantum Regime does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Multibaker Maps: Extreme Quantum Regime, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Multibaker Maps: Extreme Quantum Regime will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-264510