It is believed that in the long time limit, the limiting behavior of the discrete-time quantum random walk will cross from quantum to classical if we take into account of the decoherence. The computer simulation has already shown that for the discrete-time one-dimensional Hadamard quantum random walk with coin decoherence such that the measurement operators on the coin space are defined by A0 = Ic √1 − p, A1 = |R > < R| √p and A2 = |L > < L > < L| √p is diffusive when 0 < p ≤ 1 and it is ballistic when P = 0. In this thesis, we are going to let p to be dynamical depending on the step t, that is, we consider p = 1/tß, ß ≥ 0 and we found that it has sub-ballistic behavior for 0 < ß < 1. Furthermore, we study not only the coin decoherence, but the total decoherence, that means the measurement operators apply on the Hilbert space H = Hp ⊗ Hc instead of the coin space only. We find that the results are both sub-ballistic for the coin and total decoherence when 0 < ß < 1. Moreover, according to the model given in [T. A. Brun, H. A. Carteret, and A. Ambainis, Phys. Rev. A 67, 032304 (2003)], we know that if the walker has chance to hop to the second nearest neighbor lattice in one step, the long-time behavior is also sub-ballistic and it is similar to that the walker can hop to the third nearest neighbor lattice in one step. By the way, we also find that if we combine the classical part of the model given in [Jing Zhao and Peiqing Tong. One-dimensional quantum walks subject to next nearest neighbor hopping decoherence, Nanjing Normal University, preprint (2014)] with different step length, then this decoherence will also cross from quantum to classical. Finally, we define the quantum γ-stable walk and obtain the quantum γ-stable law with decoherence. By this decoherence, we can see that the limiting behavior of the quantum stable walk will also cross from quantum to classical and we shows that it spreads out faster than the classical stable walk. / Mathematics
| Identifer | oai:union.ndltd.org:TEMPLE/oai:scholarshare.temple.edu:20.500.12613/3033 |
| Date | January 2015 |
| Creators | HUANG, SHIH TING |
| Contributors | Yang, Wei-shih, 1954-, Szyld, Daniel, Shi, Justin Y. |
| Publisher | Temple University. Libraries |
| Source Sets | Temple University |
| Language | English |
| Detected Language | English |
| Type | Thesis/Dissertation, Text |
| Format | 67 pages |
| Rights | IN COPYRIGHT- This Rights Statement can be used for an Item that is in copyright. Using this statement implies that the organization making this Item available has determined that the Item is in copyright and either is the rights-holder, has obtained permission from the rights-holder(s) to make their Work(s) available, or makes the Item available under an exception or limitation to copyright (including Fair Use) that entitles it to make the Item available., http://rightsstatements.org/vocab/InC/1.0/ |
| Relation | http://dx.doi.org/10.34944/dspace/3015, Theses and Dissertations |
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