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題名 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貢獻者 林瑜琤
Lin, Yu Cheng
蘇柏銘
Su, Bo Ming關鍵詞 量子動力學
擴散
展透圖
無序效應
quantum dynamics
diffusion
percolation
disorder effects日期 2013 上傳時間 2-Jan-2014 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 資料類型 thesis dc.contributor.advisor 林瑜琤 zh_TW dc.contributor.advisor Lin, Yu Cheng en_US dc.contributor.author (Authors) 蘇柏銘 zh_TW dc.contributor.author (Authors) Su, Bo Ming en_US dc.creator (作者) 蘇柏銘 zh_TW dc.creator (作者) Su, Bo Ming en_US dc.date (日期) 2013 en_US dc.date.accessioned 2-Jan-2014 13:29:35 (UTC+8) - dc.date.available 2-Jan-2014 13:29:35 (UTC+8) - dc.date.issued (上傳時間) 2-Jan-2014 13:29:35 (UTC+8) - dc.identifier (Other Identifiers) G1007550081 en_US dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/63174 - dc.description (描述) 碩士 zh_TW dc.description (描述) 國立政治大學 zh_TW dc.description (描述) 應用物理研究所 zh_TW dc.description (描述) 100755008 zh_TW dc.description (描述) 102 zh_TW dc.description.abstract (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。 zh_TW dc.description.abstract (摘要) 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. en_US dc.description.tableofcontents 謝誌 i中文摘要 ii英文摘要 iii1 導論 12 擴散與主方程式 4 2.1 馬可夫過程與主方程式 42.2 主方程式求解 8 2.3 一維隨機運動 103 量子傳播 144 展透模型裏的古典與量子傳播 224.1 晶格展透模型 224.2 展透模型中的傳播 265 能量頻譜對於量子擴散的影響 346 總結 38 zh_TW dc.format.extent 8876971 bytes - dc.format.mimetype application/pdf - dc.language.iso en_US - dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G1007550081 en_US dc.subject (關鍵詞) 量子動力學 zh_TW dc.subject (關鍵詞) 擴散 zh_TW dc.subject (關鍵詞) 展透圖 zh_TW dc.subject (關鍵詞) 無序效應 zh_TW dc.subject (關鍵詞) quantum dynamics en_US dc.subject (關鍵詞) diffusion en_US dc.subject (關鍵詞) percolation en_US dc.subject (關鍵詞) disorder effects en_US dc.title (題名) 迷宮中的螞蟻:展透圖裏的擴散和量子傳播 zh_TW dc.title (題名) The ant in the labyrinth: classical diffusion and quantum propagation on percolation clusters en_US dc.type (資料類型) thesis en dc.relation.reference (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). zh_TW
