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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62492完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 趙挺偉(Ting-Wai Chiu) | |
| dc.contributor.author | Yu-Chih Chen | en |
| dc.contributor.author | 陳昱至 | zh_TW |
| dc.date.accessioned | 2021-06-16T16:03:16Z | - |
| dc.date.available | 2018-07-08 | |
| dc.date.copyright | 2013-07-08 | |
| dc.date.issued | 2012 | |
| dc.date.submitted | 2013-07-02 | |
| dc.identifier.citation | Bibliography
[1] H. J. Rothe, Lattice gauge theories: An Introduction,' World Sci. Lect. Notes Phys. 82, 1 (2012). [2] C. Gattringer, C. B. Lang and , Quantum chromodynamics on the lattice,' Lect. Notes Phys. 788, 1 (2010). [3] K. G. Wilson, in New Phenomena in Subnuclear Physics, ed. A. Zinchichi (Plenum Press, New York, 1975), Part A, p.69. [4] H. B. Nielsen and M. Ninomiya, Phys. Lett. B 105, 219 (1981). [5] D. B. Kaplan, Phys. Lett. B 288, 342 (1992) [6] T. W. Chiu, Phys. Rev. Lett. 90, 071601 (2003) [7] T. W. Chiu, Phys. Lett. B 552, 97 (2003) [8] Y. C. Chen, T. W. Chiu [TWQCD Collaboration], Phys. Rev. D 86, 094508 (2012) [arXiv:1205.6151 [hep-lat]]. [9] R. Narayanan and H. Neuberger, Nucl. Phys. B 443, 305 (1995) [10] H. Neuberger, Phys. Lett. B 417, 141 (1998); Phys. Lett. B 427, 353 (1998) [11] N. I. Akhiezer, New York, 1992. 101 [12] T. W. Chiu, T. H. Hsieh, C. H. Huang and T. R. Huang, Phys. Rev. D 66, 114502 (2002). [13] T. W. Chiu, Phys. Lett. B 716, 461 (2012); Nucl. Phys. Proc. Suppl. 129, 135 (2004) [14] T. W. Chiu and S. V. Zenkin, Phys. Rev. D 59, 074501 (1999) [15] Y. Shamir, Nucl. Phys. B 406, 90 (1993) [16] A. Borici, Nucl. Phys. Proc. Suppl. 83, 771 (2000) [17] R. C. Brower, H. Ne and K. Orginos, Nucl. Phys. Proc. Suppl. 140, 686 (2005) [18] V. Furman and Y. Shamir, Nucl. Phys. B 439, 54 (1995) [19] P. H. Ginsparg and K. G. Wilson, Phys. Rev. D 25, 2649 (1982). [20] R. G. Edwards, B. Joo, A. D. Kennedy, K. Orginos and U. Wenger, PoS LAT 2005, 146 (2006) [21] D. J. Antonio et al. [RBC and UKQCD Collaborations], Phys. Rev. D 77, 014509 (2008) [22] R. C. Brower, H. Ne and K. Orginos, arXiv:1206.5214 [hep-lat]. [23] T. W. Chiu et al. [TWQCD Collaboration], Phys. Lett. B 717, 420 (2012) [24] T. W. Chiu, Simulation of Lattice QCD with Domain-Wall Fermions,' arXiv:1302.6918 [hep-lat]. [25] M. Creutz, Phys. Rev. D 21, 2308 (1980). 102 [26] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, A. H. Teller and E. Teller, J. Chem. Phys. 21, 1087 (1953). [27] M. A. Clark and A. D. Kennedy, Phys. Rev. Lett. 98, 051601 (2007) [heplat/ 0608015]. [28] Y. C. Chen and T. W. Chiu [TWQCD Collaboration], Exact pseudofermion action for hybrid Monte Carlo simulation of one quark avor in lattice QCD with domain-wall fermion', in preparation. [29] T. Takaishi and P. de Forcrand, Phys. Rev. E 73, 036706 (2006) [heplat/ 0505020]. [30] J. C. Sexton and D. H. Weingarten, Nucl. Phys. B 380, 665 (1992). [31] M. Hasenbusch, Phys. Lett. B 519, 177 (2001) [hep-lat/0107019]. [32] I. Sachs and A. Wipf, Helv. Phys. Acta 65, 652 (1992) [arXiv:1005.1822 [hepth]]. [33] M. Luscher, Comput. Phys. Commun. 165, 199 (2005) [hep-lat/0409106]. [34] N. Madras and A. D. Sokal, J. Statist. Phys. 50, 109 (1988). [35] U. Wol [ALPHA Collaboration], Comput. Phys. Commun. 156, 143 (2004) [Erratum-ibid. 176, 383 (2007)] [hep-lat/0306017]. [36] M. F. Atiyah and I. M. Singer, Annals Math. 87, 484 (1968). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62492 | - |
| dc.description.abstract | 量子色動力學(QCD)是研究夸克和膠子間交互作用的最根本理論。它不但可描述核子間的強交互作用力，更在研究早期宇宙的演進中(由夸克-膠子相位到強子相位)扮演重要的角色。要在四維時空的離散晶格點上完全地計算解答量子色動力學是相當困難的挑戰，因為它需要非常大尺度的數值模擬計算。此外，為了使無質量極限下的夸克在有限晶格區間上能保持確切的手則對稱，額外的第五維空間將被引入並定義夸克在第五維空間的邊界上，這就是所謂的domain-wall費米子。在這篇論文中，我們討論其擁有確切手則對稱的格點量子色動力學，並研究如何用蒙地卡羅演算法來做包含動態的u, d, s 和c 夸克的量子色動力學的數值模擬計算。我們推導了domain-wall 費米子在格點量子色動力學的軸向Ward 恆等式，並從中獲得“殘留質量”的數學式，其可以用來測量由於有限晶格點數的第五維空間所帶來的手則對稱破壞。更進一步，我們獲得格點量子色動力學上最佳手則對稱domain-wall費米子的 ”殘留質量”的數值上限。 | zh_TW |
| dc.description.abstract | Quantum Chromodynamics (QCD) is the fundamental theory for the interaction between quarks and gluons. It manifests as the short-range strong interaction inside the nucleus, and plays an important role in the evolution of the early universe, from the quark-gluon phase to the hadron phase. To solve QCD is a grand challenge, since it requires very large-scale numerical simulations of the discretized action of QCD on the 4-dimensional space-time lattice. Moreover, since quarks are relativistic fermions, the 5-th dimension is introduced such that massless quarks with exact chiral symmetry can be realized at finite lattice spacing, on the boundaries of the 5-th dimension, the so-called domain-wall fermion (DWF). In this thesis, we discuss the formulation of lattice QCD with exact chiral symmetry, and the algorithms to perform Monte Carlo simulation of QCD with dynamical u, d, s, and c quarks. We also derive the axial Ward identity for lattice QCD with domain-wall fermion, and from which we obtain a formula for the residual mass, that can be used to measure the chiral symmetry breaking due to the finite extension $ N_s $ in the fifth dimension. Furthermore, we obtain an upper bound for the residual mass in lattice QCD with the optimal domain-wall fermion. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T16:03:16Z (GMT). No. of bitstreams: 1 ntu-101-F95222027-1.pdf: 1266319 bytes, checksum: 78541e85fcc6b76de4959933cdd1b660 (MD5) Previous issue date: 2012 | en |
| dc.description.tableofcontents | Contents
1 Introduction of Lattice QCD 1 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Free Scalar Field on the Lattice . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Klein-Gordon Field in the Euclidean Space-Time . . . . . . . 3 1.2.2 Fourier Transformation with Discrete Space-Time . . . . . . . 4 1.2.3 Klein-Gordon Field on the Lattice . . . . . . . . . . . . . . . . 5 1.3 Gauge Field on the Lattice . . . . . . . . . . . . . . . . . . . . . . . . 6 2 Fermion Field on the Lattice 9 2.1 Naive Fermion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Wilson Fermion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Wilson Fermion . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.2 No-Go Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.3 Domain-Wall Fermion . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.3.1 Domain-Wall Fermion in Continuum . . . . . . . . . . . . . . 12 2.3.2 Domain-Wall Fermion on the Lattice . . . . . . . . . . . . . . 13 2.4 Overlap Dirac Operator . . . . . . . . . . . . . . . . . . . . . . . . . 15 3 Optimal Domain-Wall Fermion 16 iii 3.1 The Chiral Symmetry of Optimal Domain-Wall Fermion . . . . . . . 17 3.2 Axial Ward Identity . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.3 Generating Functional for n-Point Green's Function . . . . . . . . . . 24 3.4 A Formula for the Residual Mass . . . . . . . . . . . . . . . . . . . . 30 3.5 An Upper Bound for the Residual Mass . . . . . . . . . . . . . . . . . 33 3.6 Numerical Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 3.7 Estimation of Nthres s . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 4 Monte Carlo Simulation of Lattice QCD 48 4.1 Methods for Integration . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.1 Naive Approach . . . . . . . . . . . . . . . . . . . . . . . . . . 49 4.1.2 Simple Sampling . . . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.3 Importance Sampling . . . . . . . . . . . . . . . . . . . . . . . 50 4.1.4 Importance Sampling and Heat Bath Method . . . . . . . . . 51 4.1.5 Importance Sampling with Rejection Method . . . . . . . . . 52 4.2 The Metropolis Algorithm . . . . . . . . . . . . . . . . . . . . . . . . 52 4.2.1 Markov Chains . . . . . . . . . . . . . . . . . . . . . . . . . . 53 4.2.2 The Algorithm of Metropolis, Rosenbluth, Rosenbluth, Teller and Teller . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 4.3 Hybrid Monte Carlo Simulation of Lattice QCD . . . . . . . . . . . . 56 4.3.1 Algorithm of Hybrid Monte Carlo . . . . . . . . . . . . . . . . 56 4.3.2 The Gauge Force of the Plaquette Action . . . . . . . . . . . . 59 4.4 Dirac Operator of ODWF . . . . . . . . . . . . . . . . . . . . . . . . 59 4.5 Two Flavors Algorithm of ODWF . . . . . . . . . . . . . . . . . . . . 61 4.5.1 Pseudofermion Action . . . . . . . . . . . . . . . . . . . . . . 62 iv 4.5.2 Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.5.3 Fermion Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.6 RHMC Algorithm of ODWF . . . . . . . . . . . . . . . . . . . . . . . 64 4.6.1 Pseudofermion Action . . . . . . . . . . . . . . . . . . . . . . 64 4.6.2 Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.6.3 Fermion Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.7 One Flavor Algorithm of ODWF . . . . . . . . . . . . . . . . . . . . 67 4.7.1 Pseudofermion Action . . . . . . . . . . . . . . . . . . . . . . 68 4.7.2 Gaussian Noise . . . . . . . . . . . . . . . . . . . . . . . . . . 72 4.7.3 Fermion Force . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 4.7.4 Simulations of the Schwinger Model with One Flavor of Optimal Domain-Wall Fermion . . . . . . . . . . . . . . . . . . . . 75 4.7.5 One Flavor Algorithm and Mass Preconditioning . . . . . . . 81 4.8 Comparison of OFA and RHMC in the Schwinger Model . . . . . . . 84 4.8.1 Autocorrelation Time . . . . . . . . . . . . . . . . . . . . . . . 85 4.8.2 Gauge Force and Fermion Forces . . . . . . . . . . . . . . . . 85 4.8.3 H in Molecular Dynamics . . . . . . . . . . . . . . . . . . . 88 4.8.4 Topological Charge . . . . . . . . . . . . . . . . . . . . . . . . 90 4.8.5 The Cost of Simulation . . . . . . . . . . . . . . . . . . . . . . 91 4.9 Comparison of OFA and RHMC in the HMC simulation of QCD . . . 93 4.9.1 Memory Consumption . . . . . . . . . . . . . . . . . . . . . . 93 4.9.2 Force and Eciency . . . . . . . . . . . . . . . . . . . . . . . 94 5 Conclusions 97 5.1 Residual Mass of ODWF . . . . . . . . . . . . . . . . . . . . . . . . . 97 v 5.2 One Flavor Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . 99 5.2.1 Schwinger Model Simulations . . . . . . . . . . . . . . . . . . 99 5.2.2 4D QCD Simulations . . . . . . . . . . . . . . . . . . . . . . . 100 Bibliography 101 A Gaussian Noise of the One Flavor Algorithm 104 | |
| dc.language.iso | en | |
| dc.subject | 格點量子色動力學 | zh_TW |
| dc.subject | 夸克 | zh_TW |
| dc.subject | 膠子 | zh_TW |
| dc.subject | 強交互作用力 | zh_TW |
| dc.subject | domain-wall 費米子 | zh_TW |
| dc.subject | 手則對稱 | zh_TW |
| dc.subject | 蒙地卡羅模擬計算 | zh_TW |
| dc.subject | 殘留質量 | zh_TW |
| dc.subject | quark | en |
| dc.subject | residual mass | en |
| dc.subject | Monte Carlo simulation | en |
| dc.subject | chiral symmetry | en |
| dc.subject | domain-wall fermion | en |
| dc.subject | strong interaction | en |
| dc.subject | gluon | en |
| dc.subject | quark | en |
| dc.subject | lattice quantum chromodynamics | en |
| dc.subject | residual mass | en |
| dc.subject | Monte Carlo simulation | en |
| dc.subject | lattice quantum chromodynamics | en |
| dc.subject | chiral symmetry | en |
| dc.subject | domain-wall fermion | en |
| dc.subject | strong interaction | en |
| dc.subject | gluon | en |
| dc.title | 格點量子色動力學: Domain-Wall 夸克之探討 | zh_TW |
| dc.title | Lattice QCD with Domain-Wall Quarks | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 高涌泉(Yeong-Chuan Kao),賀培銘(Pei-Ming Ho),張志義(Chi-Yee Cheung),余海禮(Hoi-Lai Yu),朱創新(Chong-Sun Chu) | |
| dc.subject.keyword | 格點量子色動力學,夸克,膠子,強交互作用力,domain-wall 費米子,手則對稱,蒙地卡羅模擬計算,殘留質量, | zh_TW |
| dc.subject.keyword | lattice quantum chromodynamics,quark,gluon,strong interaction,domain-wall fermion,chiral symmetry,Monte Carlo simulation,residual mass, | en |
| dc.relation.page | 105 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-02 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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