政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/63174

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/63174

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题名:	迷宮中的螞蟻:展透圖裏的擴散和量子傳播 The ant in the labyrinth: classical diffusion and quantum propagation on percolation clusters
作者:	蘇柏銘 Su, Bo Ming
贡献者:	林瑜琤 Lin, Yu Cheng 蘇柏銘 Su, Bo Ming
关键词:	量子動力學擴散展透圖無序效應 quantum dynamics diffusion percolation disorder effects
日期:	2013
上传时间:	2014-01-02 13:29:35 (UTC+8)
摘要:	複雜的系統可以由大量相互作用的單元所構成；有關複雜系統的資料往往可建構成圖（graphs）或網絡系統的型式。複雜網路系統上經過連結及節點的傳播行為可描述例如資訊或能量的傳遞，此方向的研究已成跨各科學領域重要且熱門的課題。在凝態物理中，電子或準粒子在晶格與非晶格裡的傳播可描述許多性質，如導電性和導熱性等；在生物系統中細胞間的運輸亦可視為上述的網路傳播行為。本論文探討在幾種典型的離散晶格及滲透模型中的古典馬可夫擴散和量子傳播。藉此我們示範：（一）量子傳播可遠比古典傳播更快地，甚至達指數倍快地散佈至網路各節點;（二）在無序環境中，雜質對量子傳播的干擾影響較對古典擴散更顯著。在論文最後，我們討論能譜結構和傳播性質的關係。 Complex systems can be distilled into a large number of interacting components; data about complex systems often are schematized as graphs or networks. The study of the dynamics across the links and nodes in networks, which can describe e.g. information or energy flows, has become a popular and important topic in many scientific disciplines. For example, in condensed matter physics, many properties, such as electrical conductivity and thermal conductivity, can be understood in terms of dynamics of electrons and elementary excitations in crystals or in some non-crystalline structures. Another example is intracellular transport in biological systems. In this thesis we study classical Markovian-diffusion and quantum transport on several types of discrete lattices and percolation clusters. We demonstrate that (i) quantum spreading can transverse a network exponentially faster than its classical counterpart; (ii) slowdown by static disorder is more pronounced for quantum transport than for classical diffusion. Finally, connections between spectral properties and dynamical properties are discussed.
參考文獻:	[1] E. Bullmore and O. Sporns, Nat Rev Neurosci 10, 186 (2009). [2] E. Farhi and S. Gutmann, Phys. Rev. A 58, 915 (1998). [3] E. Collini et al., Nature 463, 644 (2010). [4] S. L. Masoud Mohseni, Patrick Rebentrost and A. Aspuru-Guzik, Journal of Chemical Physics 129 (2008). [5] Y. G. Sinai, Theory Probab. Appl. 27, 256–268 (1982). [6] M. Fratini et al., Nature 466, 841 (2010). [7] N. Poccia et al., Nat Mater 10, 733 (2011). [8] S. R. Broadbent and J. M. Hammersley, Proc. Cam. Phil. Soc. 53, 629 (1957). [9] D. Stauffer and A. Aharony, Introduction to Percolation Theory, CRC Press, Oxford, 1992. [10] J. Hoshen and R. Kopelman, Phys. Rev. B 14, 3438 (1976). [11] P. L. Leath, Phys. Rev. B 14, 5046 (1976). [12] Z. Alexandrowicz, Physics Letters A 80, 284 (1980). [13] M. E. J. Newman and R. M. Ziff, Phys. Rev. E 64, 016706 (2001). [14] P. G. de Gennes, La Recherche 7, 919 (1976). [15] S. Alexander and R. Orbach, J. Physique Lett. 43, L625 (1982). [16] R. Rammal and G. Toulouse, J. Physique Lett. 44, 13 (1983). [17] K. C. Chang, On quantum simulation: Quantum random walks and quantum adiabatic optimization, Master’s thesis, National Chengchi University, Taipei, Taiwan, 2012. [18] D. J. Thouless, Phys. Rev. Lett. 39, 1167–1169 (1977). [19] J. T. Edwards and D. J. Thouless, J. Phys. C 5, 807 (1972). [20] F. Pi ́echon, Phys. Rev. Lett. 76, 4372–4375 (1996). [21] A. P. Young and H. Rieger, Phys. Rev. B 53, 8486 (1996). [22] H. Rieger and A. P. Young, Phys. Rev. B 53, 3328 (1996).
描述:	碩士國立政治大學應用物理研究所 100755008 102
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G1007550081
数据类型:	thesis
显示于类别:	[應用物理研究所 ] 學位論文

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