Quantum Multibaker Maps: Extreme Quantum Regime
Daniel K. Wojcik, J. R. Dorfman

TL;DR
This paper introduces quantum multibaker maps as models for quantum random walks, analyzing their eigenstates, steady states, and relaxation properties in the deep quantum regime, with analytical and numerical results.
Contribution
It presents a new family of quantum multibaker maps, providing analytical solutions for uniform cases and exploring their quantum behavior in the deep quantum regime.
Findings
Eigenstates are extended in uniform QMB and localized in random QMB.
Analytical solutions for time-dependent states in the deep quantum regime.
Steady state properties and relaxation dynamics are analytically described.
Abstract
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…
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
