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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 Chengen_US
dc.contributor.author (Authors) 蘇柏銘zh_TW
dc.contributor.author (Authors) Su, Bo Mingen_US
dc.creator (作者) 蘇柏銘zh_TW
dc.creator (作者) Su, Bo Mingen_US
dc.date (日期) 2013en_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) G1007550081en_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) 100755008zh_TW
dc.description (描述) 102zh_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 iii
1 導論 1
2 擴散與主方程式 4
2.1 馬可夫過程與主方程式 4
2.2 主方程式求解 8
2.3 一維隨機運動 10
3 量子傳播 14
4 展透模型裏的古典與量子傳播 22
4.1 晶格展透模型 22
4.2 展透模型中的傳播 26
5 能量頻譜對於量子擴散的影響 34
6 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/#G1007550081en_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 dynamicsen_US
dc.subject (關鍵詞) diffusionen_US
dc.subject (關鍵詞) percolationen_US
dc.subject (關鍵詞) disorder effectsen_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 clustersen_US
dc.type (資料類型) thesisen
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