本論文主要包括三種量子蒙地卡羅(QMC)方法的介紹及將其應用到不同的強關聯系統的結果。當中所涉及的強關聯系統主要是兩個不同的量子液體系統--自旋液體及玻色液體。 / 第二章將詳細介紹三個QMC方法，包括針對非零溫巨正則系統的行列式蒙地卡羅方法(DQMC)，針對零溫正則系絶並解決部分負值問題的限制線軌蒙地卡羅方法(CPMC)，及主要應用在非零溫雜質系統上的Hirsch-Fye蒙地卡羅方法(HFQMC)。 / 自發現高溫起導體以後，其奇異特性如具有非費米液體特性的贗能隙(Pseudogap)引起科學界爭論，由此提出很多不同的理論嘗試解釋。RVB是其中一個具代表性的理論，當中把高溫超導體理解成輕度摻雜的莫特絶緣體(Mott insulator)及引入自旋－電荷分離(charge-spin separation)把系統兩個自由度分開處理，具費米特性的自旋子(spinon)及具玻色特性的空穴子(holon)因而產生。這兩種準粒子的特性在解釋高溫超導的奇異性中最為關鍵。 / 第三章將應用DQMC及CPMC研究擁有各向及各自旋相異費米面的吸引勢赫伯德模型。模型的起源在於有理論[1]提出玻色子的基態有可能因阻挫作用而不發生愛因斯坦-玻色凝聚，這種非凝聚的基態稱為d-波玻色液體。在本研究所採用的模型中，將由庫柏電子對取代原先的正則玻色子。模型在準一准雙排梯子晶格的特性最近已被密度矩阵重整化群(DMRG)方法詳細研究[2]，而本研究將率先使用QMC方法研究模型在準一維雙排、四排梯子及二維正方晶格的特性。QMC有部分證據顯示電子對液體確實在二維存在，在本論文中會作出交代。 / 第四章將應用CPMC研究阻挫作用(frustration)下的排斥勢赫伯德模型，而其具體晶格情況為在正方格子上加上單向斜線躍遷項，稱為t-t'-TH模型。有證據提出在此模型中有可能存自旋液體的基態，並可有效解釋最近在實驗中所觀察到的有機超導體超低溫自旋無序的特性[3]。t-t'-TH模型的導帶半滿情況被曾各種方法詳細研究，本項研究將採用不同 的導帶填充情況及阻挫作用強度，用其比較以觀察阻挫作用對模型基態自旋作用的影響。研究發現阻挫作用將對不同的長程自旋序作出不同程度的影響。 / 第五章則會說明HFQMC的可能應用，在雜質系統如安德遜模型中，HFQMC是研究其非零溫特性的有效方法。此外，這章亦會交代未來在這方面可能進行的研究，而最後一章則會總結全文。 / In this thesis, three quantum Monte Carlo(QMC) algorithms would be reviewed, including determinant Quantum Monte Carlo (DQMC), constraint path Quantum Monte Carlo(CPMC) and Hirsch-Fye Quantum Monte Carlo (HFQMC). These QMC methods would be used to study strongly correlated system. In chapter 3 and 4, DQMC and CPMC methods would be used to study two kinds of quantum liquid, Bose liquid and spin liquid. In chapter 5, the possible application of HFQMC would be discussed. / After the discovery of high T{U+ABB1} cuprate, intensive effort has been paid to construct its theoretical explanation. One of the most puzzling features in cuprate is the pseudogap(strange-metal) phase with non-Fermi liquid behaviour. To search for an non-Fermi liquid to represent this phase, resonating valence bond(RVB) theory proposed a picture of lightly doped spin liquid. Fermionic spinon and bosonic holon arise from the spin-charge separation, and the behaviors of these quasi-particle are important for explanation for high T{U+ABB1} superconductivity. / In chapter 3, we study possible Bose liquid. Motrunich and Fisher [1] proposed a possible uncondensed bosonic phase d-wave Bose liquid(DBL) which will not undergo BEC at ground state. A prior studies[2] has shown that Cooper pairs can be used to replace bosons and N-leg ladder lattice could be used to approach behaviour of 2D lattice. Inspired by them, determinant quantum Monte Carlo(DQMC) and constraint path Monte Carlo(CPMC) techniques are used to study the fermionic attractive Hubbard Model with spin-independent anisotropic Fermi surface. The probable (Local) Cooper Pair Bose metal is detected in 2-leg, 4-leg ladder and 2D lattice. / In chapter 4, we study possible spin liquid. The Hubbard model on an anisotropic triangular lattice called t - t¹ - TH model has been proposed to possess a non-magnetic insulating(spin liquid) state, induced by geometrical frustration. The effect of filling and degree of frustration on magnetic property is investigated by CPMC in the studies. / Chapter 5 is devoted to introducing the usages and possible research projects related to HFQMC. HFQMC is a quantum Monte Carlo method based on path integral formalism, and it is an efficient way to study impurity model at low temperature. A physical background of impurity model is also reviewed. In the last chapter, we would summarize this thesis by comparing the QMC methods used and discussing the result obtained. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Tang, Ho Kin = 強關聯系統的量子蒙地卡羅方法研究 / 鄧皓鍵. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2012. / Includes bibliographical references (leaves 83-88). / Abstracts also in Chinese. / Tang, Ho Kin = Qiang guan lian xi tong de liang zi Mengdi Kaluo fang fa yan jiu / Deng Haojian. / Chapter 1 --- Introduction to Strongly Correlated System: High T{U+ABB1} superconductivity and Quantum Liquid --- p.1 / Chapter 1.1 --- Types of strongly correlated electron systems --- p.1 / Chapter 1.2 --- High T{U+ABB1} superconductivity --- p.3 / Chapter 1.2.1 --- Phase diagram --- p.4 / Chapter 1.2.2 --- Mott insulator and Anti-ferromagnetic(AFM) order --- p.6 / Chapter 1.2.3 --- Spin-glass --- p.7 / Chapter 1.2.4 --- Pseudogap --- p.7 / Chapter 1.2.5 --- Superconducting --- p.7 / Chapter 1.2.6 --- The complexity and related theory --- p.7 / Chapter 1.3 --- Importance of quantum liquids in high T{U+ABB1} superconductivity --- p.10 / Chapter 1.3.1 --- Spin liquid --- p.10 / Chapter 1.3.2 --- Bose Liquid --- p.11 / Chapter 2 --- Methods --- p.12 / Chapter 2.1 --- Introduction to Quantum Monte Carlo --- p.12 / Chapter 2.2 --- Determinant Quantum Monte Carlo(DQMC) --- p.13 / Chapter 2.2.1 --- Purpose of DQMC --- p.13 / Chapter 2.2.2 --- Overall information of DQMC --- p.14 / Chapter 2.2.3 --- Green function in DQMC --- p.20 / Chapter 2.2.4 --- Observable measurement --- p.21 / Chapter 2.2.5 --- Numerical Implementation --- p.24 / Chapter 2.2.6 --- Limitation --- p.26 / Chapter 2.3 --- Constraint Path Quantum Monte Carlo(CPMC) --- p.26 / Chapter 2.3.1 --- Purpose of CPMC --- p.26 / Chapter 2.3.2 --- Algorithm discussion --- p.28 / Chapter 2.3.3 --- Implementation Issues --- p.32 / Chapter 2.4 --- Hirsch-Fye Quantum Monte Carlo(HFQMC) --- p.35 / Chapter 2.4.1 --- Algorithm outline --- p.35 / Chapter 2.4.2 --- Program Structure --- p.38 / Chapter 3 --- A Possible Realization of Bose Liquid: Attractive Hubbard Model with Spin-dependent Anisotropic Hopping --- p.41 / Chapter 3.1 --- Idea of Bose metal --- p.41 / Chapter 3.2 --- Model Hamiltonian --- p.44 / Chapter 3.3 --- Phases and its detection --- p.45 / Chapter 3.3.1 --- Measurement --- p.45 / Chapter 3.3.2 --- Phases --- p.46 / Chapter 3.4 --- Multi-leg ladder Lattice --- p.47 / Chapter 3.4.1 --- Band structure --- p.47 / Chapter 3.4.2 --- Two-leg ladder: Cooper-pair Bose Metal Phase --- p.51 / Chapter 3.4.3 --- Four-leg ladder: Cooper-pair Bose Metal Phase --- p.55 / Chapter 3.5 --- 2D Lattice --- p.56 / Chapter 3.5.1 --- Band structure --- p.56 / Chapter 3.5.2 --- 2D Lattice: Local Cooper-pair Bose Metal(LCPBM) Phase --- p.60 / Chapter 3.6 --- Summary --- p.61 / Chapter 4 --- A Possible Realization of Spin Liquid: Square Lattice Hubbard Model with Geometrical Frustration --- p.65 / Chapter 4.1 --- Frustration and Spin Liquid --- p.65 / Chapter 4.1.1 --- Physical systems --- p.66 / Chapter 4.1.2 --- Recent developments of t-t’-TH model --- p.67 / Chapter 4.2 --- Model Hamiltonian --- p.67 / Chapter 4.3 --- Band structure --- p.68 / Chapter 4.4 --- Frustration Effect on Magnetism --- p.70 / Chapter 4.5 --- Summary --- p.73 / Chapter 5 --- Possible Application of HFQMC --- p.75 / Chapter 5.1 --- Anderson Model --- p.75 / Chapter 5.1.1 --- Physical Issues --- p.75 / Chapter 5.1.2 --- Model proposal and mean field result --- p.76 / Chapter 5.1.3 --- Properties of model with quantum degree of freedom --- p.77 / Chapter 5.2 --- The application cases --- p.78 / Chapter 6 --- Summary --- p.80 / Chapter 6.1 --- Three QMC methods --- p.80 / Chapter 6.2 --- Two practical models --- p.80 / Bibliography --- p.83

Summary in Chinese. / Thesis (M.B.A.)--Chinese University of Hong Kong. / Bibliography: leaves 65-67.

Mediante técnicas de simulación Montecarlo, prescindiendo de la aproximación de la onda rotante (RWA), se predice la aparición de efectos medibles en los llamados "estados atrapados", rasgo eminentemente cuántico del micromáser o máser monoatómico. / Tesis

Tsang Yuk Fung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 59-62). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Sequential Monte Carlo --- p.5 / Chapter 2.1 --- Recursive Bayesian estimation --- p.7 / Chapter 2.2 --- Bayesian sequential importance sampling --- p.8 / Chapter 2.3 --- Sclcction of iiiipoitance function --- p.10 / Chapter 2.4 --- Particle filter --- p.12 / Chapter 3 --- Target tracking and data association --- p.15 / Chapter 3.1 --- Target tracking and its applications --- p.16 / Chapter 3.2 --- Data association and JPDA method --- p.16 / Chapter 4 --- Particle filter using the acceptance-rejection method --- p.21 / Chapter 4.1 --- Particle Filter using the acceptance-rejection method --- p.22 / Chapter 4.2 --- Modified accoptance-rcjoction algorithm --- p.24 / Chapter 4.3 --- Examples --- p.26 / Chapter 4.3.1 --- Example 1: One dimensional non-linear case --- p.26 / Chapter 4.3.2 --- Example 2: Bearings-only tracking example --- p.27 / Chapter 4.3.3 --- Example 3: Single-target tracking --- p.31 / Chapter 4.3.4 --- Example 4: Multi-target tracking --- p.33 / Chapter 4.4 --- A new importance weight for bearings-only tracking problem --- p.34 / Chapter 5 --- Conclusion --- p.41

by Liang Fa Ming. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (p. 150-161). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

Lam Ho-Suen Joffee. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2003. / Includes bibliographical references (leaf 40). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- Review of Mplus --- p.3 / Chapter 3 --- Design of the Simulation Study --- p.6 / Chapter 3.1 --- Simulation Design --- p.6 / Chapter 3.2 --- Covariance Structure Analysis and Mplus Restriction --- p.10 / Chapter 3.3 --- Implementation --- p.10 / Chapter 4 --- Method of Evalution --- p.12 / Chapter 4.1 --- Accuracy of Parameter Estimates --- p.12 / Chapter 4.2 --- Distribution of the Goodness-of-fit Statistic --- p.13 / Chapter 4.3 --- Precision of Standard Errors --- p.14 / Chapter 4.4 --- Number of Replications --- p.15 / Chapter 5 --- Results of the Simulation Study --- p.17 / Chapter 5.1 --- Accuracy of the Parameter Estimates --- p.17 / Chapter 5.2 --- Distribution of the Goodness-of-fit Statistic --- p.18 / Chapter 5.3 --- Precision of the Standard Error --- p.19 / Chapter 5.4 --- Results when the Sample Size is Extremely Large --- p.20 / Chapter 5.5 --- Conclusion --- p.21 / Chapter 6 --- Additional Simulation Study --- p.27 / Chapter 6.1 --- Precision of Standard Error when the Model Consists of Only Con- tinuous and Only Ordinal Variables --- p.28 / Chapter 6.2 --- Comparison of the Simulation Results of Mplus and LISREL --- p.29 / Chapter 6.3 --- Conclusion --- p.31 / Chapter 7 --- Conclusion and Discussion --- p.33 / Chapter A --- Mplus Sample Program (Condition C1 S2 N=500) --- p.36 / Chapter B --- PRELIS Sample Program (Condition C1 S1 N=500) --- p.37

There are many tools to simulate physical phenomena. Generally, the simulation technique is defined by the size of the simulation area. Two well know techniques for simulating atom dynamics are kinetic Monte Carlo (kMC) and molecular dynamics (MD). In this work we simulate physical vapor deposition of binary metallic systems using the kMC technique. A sufficient quantity of atoms are deposited so that morphological features can be observed. Where kMC has fallen short we have used MD to supplement our results.

"February 2003" / Bibliography: p. 121-135. / xii, 135 p. : ill. ; 30 cm. / Title page, contents and abstract only. The complete thesis in print form is available from the University Library. / This thesis is a theoretical evaluation of the (single) first photon detection (FPD) technique as a limiting case of time-resolved transillumination (TI) for diagnostic purposes. / Thesis (Ph.D.)--University of Adelaide, Dept. of Physics and Mathematical Physics, 2003

<p>Algorithmica Research AB develops software application for the financial markets. One of their products is Quantlab that is a tool for quantitative analyses. An effective method to value several financial instruments is Monte Carlo simulation. Since it is a common method Algorithmica is interesting in investigating if it is possible to create a Monte Carlo framework.</p><p>A requirement from Algorithmica is that the framework is general and this is the main problem to solve. It is difficult to generate a generalized framework because financial derivatives have very different appearances. To simplify the framework the thesis will be delimitated to European style derivatives where the underlying asset is following a Geometric Brownian Motion.</p><p>The definition of the problem and delimitation were defined gradually, in parallel with the review of literature, this to be able to decide what purpose, and delimitations that is reasonable to treat. Standard Monte Carlo requires a large number of trials and is therefore slow. To speed up the process there exist different variance reduction techniques and also Quasi Monte Carlo simulation, where deterministic numbers (low discrepancy sequences) is used instead of random. The thesis investigated the variance reduction techniques; control variate technique, antithetic variate technique, and the low discrepancy sequences; Sobol, Faure and Halton.</p><p>Three test instruments were chosen to test the framework, an Asian option and a Barrier option where the purpose is to conclude which Monte Carle method that performs best, and also a structured product; Smart Start, that is more complex and the purpose is to test that the framework can handle it.</p><p>To increase the understanding of the theory the Halton, Faure and Sobol sequence were implemented in Quantlab in parallel with the review of literature. The Halton and Faure sequences also seemed to perform worse than Sobol so they were not further analyzed.</p><p>The developing of the framework was an iterative process. The chosen solution is to design a general framework by using five function pointers; the path generator, the payoff function, the stop criterion function and the volatility and interest rates. The user specifies these functions by him/her given some obligatory input and output values. It is not a problem-free solution to use function pointers and several conflicts and issues are defined, therefore it is not recommended to implement the framework as it is designed today.</p><p>In parallel with the developing of the framework several experiments on the Asian and Barrier options were performed with varying result and it is not possible to draw a conclusion on which method that is best. Often Sobol seems to converge better and fluctuates less than standard Monte Carlo. The literature indicates that it is important that the user has an understanding of the instrument that should be valued, the stochastic process it follows and the advantages and disadvantages of different Monte Carlo methods. It is recommended to evaluate the different method with experiments, before deciding which method to use when valuing a new derivative.</p>

Le rêve ultime du radiothérapeute a toujours été d’avoir à disposition des technologies capables de délivrer avec une parfaite précision des doses élevées aux volumes tumoraux sans irradier les tissus sains avoisinants. Ce rêve ne deviendra jamais réalité, mais tous les efforts des physiciens, médecins et industriels doivent être combinés pour que la réalité s’approche le plus possible de cette utopie. Depuis le début des années 60 et l’avènement des accélérateurs linéaires d’électrons montés sur des unités de traitement, la technologie en thérapie par photons a évolué énormément. Aujourd’hui, les traitements les plus à la pointe incluent la radiothérapie par modulation d’intensité (« Intensity-Modulated Radiation Therapy » ou IMRT) avec l’aide d’outils d’imagerie hautement sophistiqués. L’IMRT est une technique complexe qui requiert un excellent contrôle de la précision dans toutes les étapes du processus du traitement. Ces étapes peuvent être résumées en trois catégories qui sont 1) l’étalonnage et la stabilité de l’unité de traitement, 2) le positionnement et la qualité des données associées au patient et 3) la précision du calcul de dose effectué lors de la planification du traitement. Pour améliorer l’incertitude globale d’un traitement donné, des efforts de recherche sont nécessaires dans les trois catégories. Cette thèse se concentre sur le processus de calcul de dose. Durant les dernières décennies, la complexité et la précision des algorithmes de dose ont augmenté fortement grâce aux énormes progrès de l’informatique. Malgré cela, l’immense majorité des algorithmes utilisent des méthodes analytiques impliquant des approximations importantes au niveau de la physique de transport des particules. Il est cependant possible de concevoir des algorithmes qui évitent ces approximations en se basant sur des méthodes dites de Monte Carlo (MC) qui simulent fidèlement la réalité physique et qui sont considérées aujourd’hui comme les plus précises de calcul de la dose dans les tissus humains. Malheureusement, jusqu’à récemment, la vitesse des simulations MC était trop lente pour être compatible avec les contraintes de temps liées à la routine clinique. Mais les progrès continus en puissance de calcul combinés avec l’introduction de simplifications pertinentes dans les codes MC permettent d’envisager l’introduction d’algorithmes MC en routine clinique, ce qui est déjà le cas pour plusieurs systèmes de planification de traitement commerciaux. L’objectif de cette thèse était d’évaluer la valeur ajoutée du MC comparé à des algorithmes analytiques modernes pour des traitements IMRT complexes de tumeurs entourées de nombreuses inhomogénéités de densité. Ces évaluations ont été effectuées pour deux techniques de traitement IMRT : « step-and-shoot » et tomothérapie hélicoïdale. Pour l’IMRT « step-and-shoot » délivrée par une unité de traitement Elekta SL25, des simulations MC avec BEAMnrc ont été comparées avec un algorithme commercialisé récemment par la firme Varian appelé « Anisotropic Analytical Algorithm » (AAA). Pour la tomothérapie, une étude similaire a été accomplie mais pour le code utilisé dans le système fourni par « Tomotherapy Incorporated » et basé sur un algorithme de type convolution/superposition utilisant l’approximation « collapsed-cone ». Durant cette seconde étude, la modélisation MC au moyen du code MC PENELOPE était un aspect très important étant donné que c’est la première fois qu’un code MC complet pour la tomothérapie était construit avec tous les détails techniques de la machine fournis par le constructeur. De plus, le modèle MC, appelé TomoPen, a été conçu en vue d’une introduction future dans le système clinique. La vitesse de la simulation était donc une contrainte importante. La stratégie utilisée pour la simulation et adoptée dans TomoPen consiste principalement à simplifier drastiquement le transport des photons dans le collimateur multilames et permet de calculer des distributions de dose dans une tumeur bilatérale de la sphère tête et cou en à peu près 10 heures sur un processeur de 2 GHz, sans perte de précision significative. En utilisant le groupe d’ordinateurs fourni avec chaque unité de traitement de tomothérapie, ce temps de simulation peut être réduit d’un facteur 32, correspondant au nombre de processeurs. Durant cette thèse, la correspondance entre algorithmes analytiques et MC était en général satisfaisante pour la majorité des cas cliniques et expérimentaux étudiés. Cependant, des différences ont pu être observées pour des situations critiques, comme des petites tumeurs pulmonaires ou des tumeurs ethmoïdes. Même si ces déviations n’étaient pas « dramatiques », elles ont pu démontrer clairement le potentiel des algorithmes MC dans la pratique clinique afin d’améliorer la qualité globale et la précision des traitements.