The third part of this thesis is on one hole problem of asymmetric T and T -- Jz model, which we found can be turned into a single body problem and is solvable. We get the spectrum of the model and calculate as a result the mass of the hole. This model may be related to the two species fermion coexisting system which may be realized in the optical lattice. / This thesis project is mainly inspired by the newly discovered superconductor NaxCoO2 · yH 2O. It has a layered structure with an almost separated single band out of the inner band electrons. It becomes the theoretical focus because it is the first layered strongly correlated system that shows superconductivity besides the cuprate superconductors. It may help people to understand the superconductivity in the cuprate system. In this thesis we mainly focus our attention on the strongly correlated models on triangular lattice. These models are expected to provide a theoretical background for the Nax CoO2 · yH2O system. We investigate the magnetic and superconductivity properties of these models on the triangular lattice. By the mean field calculation of different magnetic orders we got a phase diagram of the triangular lattice Hubbard model for different magnetic orders in the Hubbard model in the triangular lattice. To further investigate the superconductivity pairing symmetry of the triangular lattice, we use the standard variational Monte Carlo method to find which kind of pairing symmetry is stabilized in the triangular lattice T -- J -- V model. Our finding is that the extended- f wave pairing is most stable in the lattice. / To further understand the properties of the related model in the electron interacting system in the triangular lattice, we also solve the few particle problem in the triangular lattice. For two particles with the T -- U -- J -- V model in the triangular lattice, we got the exact solutions. For four particles of the Hubbard model in the triangular lattice we got the asymptotic solutions. We discuss the existing of the bound states in these solutions and the pairing symmetry of these bound states. For system with two-hole and one down-spin away from the all up spin background we also get a solution utilizing a large U expansion. We discussed the relation of this solution with the Nagaoka states. / Fan, Rui = 三角格子上磁性與超導的研究 / 樊睿. / "September 2007." / Adviser: Lin Hai Qing. / Source: Dissertation Abstracts International, Volume: 70-03, Section: B, page: 1719. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 83-87). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Fan, Rui = San jiao ge zi shang ci xing yu chao dao de yan jiu / Fan Rui.

線性丢番圖方程系統（LDEs）連同其子類--子集和問題--在現實世界有大量且重要的應用。可是當線性番圖方程系統的整數解集被限定在一個有界的多面體中，則此系統屬于NP類問題。同理其子類--子集和問題--也同屬于NP類問題。另一方面，密度（density）接近或等于一的子集和問題已在文獻中被證實爲最難的一類子集和問題，並且現有的針對此最難子集和問題的所有解決方案都不能達到令人滿意的成功率。因此，在這篇論文中，我們旨在提出有效的算法來求解線性番圖方程系統以及其子類問題--密度爲一的子集和問題。 / 我們在此論文中的研究包括：1）基于格理論和LLL算法的性質，采用並改良針對LDEs的格表達式（lattice formulations）；2）提出針對子集和問題的分解（disaggregation）技術；3）創造性地將分解技術與格表達式整合在一起，從而提高求解密度爲一的子集和問題的成功率。 / 數值實驗顯示，我們提出的新整合算法對提高密度爲一的子集和問題的成功率有著顯著的效果。比如，針對維數分別爲20,30和40的密度爲一的子集和問題，對各個維數隨機産生的100個問題，我們的新整合算法均可將成功率提高到100%。同時，針對新整合算法的理論分析顯示，能將短且非0-1的整數解切割掉的分解在達到新整合算法的顯著實驗效果中起到了關鍵作用。 / While systems of linear Diophantine equations (LDEs) with bounded feasible set, including subset sum problem as its special subclass, find wide, and often significant, real-world applications, they unfortunately belong to the NP class in general. Furthermore, the literature has revealed that subset sum problems with their density close to one constitute the hardest subclass of subset sum problems and all the existing solution methods do not perform to a satisfactory level (with low success ratio) even when the problem size is only medium. / We take the challenge in this thesis to investigate lattice formulations for systems of LDEs in which LLL basis reduction algorithm (LLL algorithm) is utilized, propose disaggregation techniques for subset sum problems, and develop a powerful integration of disaggregation techniques with lattice formulations in solving feasible subset sum problems. / More specifically, the contributions in this thesis can be classified into three parts: i) we propose two revised lattice formulations of Aardal et al. (2000) for systems of LDEs to enhance further the computational capability of the LLL algorithm; ii) we study properties related to disaggregation of a single LDE and investigate thoroughly disaggregation schemes based on modular transformations; and iii) we develop a novel version of LLL algorithm by integrating modular disaggregation into the solution process. Promising numerical results have been achieved when applying our newly proposed LLL algorithm in tackling hard subset sum problems with density close to one. For instance, the success ratio can be raised to 100% for 100 randomly generated hard subset sum problems with dimensions 20, 30, and 40, respectively. We carry out theoretical study for possible driving force behind the success of our new algorithm, including dimension reduction of the solution space, information recovering of LDEs, and mechanism in cutting off short non-binary integer solutions when attaching disaggregation with LLL algorithm. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Detailed summary in vernacular field only. / Lu, Bojun. / Thesis (Ph.D.) Chinese University of Hong Kong, 2014. / Includes bibliographical references (leaves 143-153). / Abstracts also in Chinese.

Chu Lam Long. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaf 81). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 2 --- One-dimensional Open-ended Lattice --- p.3 / Chapter 2.1 --- Propagation rules --- p.3 / Chapter 2.2 --- Propagation velocity --- p.6 / Chapter 2.3 --- Propagation direction --- p.7 / Chapter 2.4 --- Number of visits --- p.11 / Chapter 2.5 --- Lattice pattern --- p.13 / Chapter 3 --- Statistical Behaviour of One-dimensional Open-ended Lattice --- p.15 / Chapter 3.1 --- Probability function of first visit --- p.15 / Chapter 3.2 --- Long-time large-distance behaviour of first visit probability func- tion --- p.22 / Chapter 3.3 --- Total probability function --- p.24 / Chapter 4 --- Simulation Results of One-dimensional Open-ended Lattice --- p.26 / Chapter 4.1 --- Number of visits --- p.26 / Chapter 4.2 --- Average propagation velocity --- p.29 / Chapter 4.3 --- Probability function of first visit --- p.32 / Chapter 4.4 --- Total probability function --- p.35 / Chapter 5 --- One-dimensional Periodic Lattice --- p.40 / Chapter 5.1 --- Periodic Boundary Condition --- p.41 / Chapter 5.2 --- Propagation direction --- p.42 / Chapter 5.3 --- Cycle of the particle --- p.42 / Chapter 5.4 --- Lattice pattern --- p.44 / Chapter 5.4.1 --- One cycle --- p.44 / Chapter 5.4.2 --- Two cycles --- p.51 / Chapter 5.5 --- Period of the system --- p.51 / Chapter 5.5.1 --- General case --- p.51 / Chapter 5.5.2 --- Lattices of alternating spin up and spin down --- p.52 / Chapter 5.6 --- Period of the particle --- p.53 / Chapter 5.7 --- Propagation velocity --- p.56 / Chapter 6 --- Statistical Behaviour of One-dimensional Periodic Lattice --- p.57 / Chapter 6.1 --- Average propagation velocity --- p.57 / Chapter 6.2 --- Probability function --- p.58 / Chapter 7 --- Simulation Results of One-dimensional Periodic Lattice --- p.63 / Chapter 7.1 --- Trajectory of the particle --- p.63 / Chapter 7.1.1 --- General case --- p.63 / Chapter 7.1.2 --- Lattices of alternating spin up and spin down --- p.64 / Chapter 7.2 --- Average propagation velocity --- p.67 / Chapter 7.3 --- Probability function of circular lattice --- p.69 / Chapter 7.4 --- Probability function of corresponding one-dimensional lattice --- p.71 / Chapter 8 --- Conclusion --- p.75 / Chapter A --- Generating function --- p.77 / Chapter B --- Discrete and integral transform --- p.78 / Chapter C --- Normal Distribution --- p.80 / Bibliography --- p.81

No description available.

Quantum Chromo - Dynamics ( QCD ) is the part of the Standard Model which describes the interaction of the strong nuclear force with matter. QCD is asymptotically free, so at high energies perturbation expansions in the coupling can be used to calculate expectation values. Away from this limit, however, perturbation expansions in the coupling do not converge. Lattice QCD ( LQCD ) is a non - perturbative approach to calculations in QCD. LQCD first performs a Wick rotation t → - it [subscript E], and then discretises spacetime into a regular lattice with some lattice spacing a. QCD is then expressed in terms of parallel transport operators of the gauge field between grid points, and fermion fields which are defined at the grid points. Operators are evaluated in terms of these quantities, and the lattice spacing is then taken to zero to recover continuum values. We perform computer simulations of Lattice QCD in order to extract a variety of meson observables. In particular, we perform a comprehensive survey of the light and strange meson octets, obtain for the first time exotic meson results consistent with experiment, calculate the charge form - factor of the light and strange pseudoscalar mesons, and determine ( for the first time in Lattice QCD ) all three form - factors of the vector meson. / Thesis (Ph.D.)--University of Adelaide, School of Chemistry and Physics, Discipline of Physics, Centre for the Subatomic Structure of Matter, 2007.

No description available.

We study the four-quark interaction as a first step in understanding the QCD origin of the nuclear force in nature. We simulate QCD on a 20 x 20 x 20 x 32 space-time lattice with the simplifying quenched and static approximations, and with the SU(2) gauge group. Recent four-quark simulations reveal interesting tetrahedral geometry and planar four-quark flux distributions that cannot be explained by existing models. We simulate the flux distribution for the still-unexplored next higher level of geometrical complexity, namely four quarks on the corners of a tetrahedron. In order to complete the simulation within the allotted computing time, we have improved the approach used to simulate the flux distribution. Compared to previous approaches, the new approach nearly eliminates the bottleneck of the computing time, provides more than a 100-time speedup in our project, and also provides a better strategy for improving signal-noise ratio and suppressing signal distortion from the lattice structure. As the result of this improved approach, we have observed the long diagonal flux tube structure, repeated the Helsinki group's 1998 results for the flux distribution of a square geometry, and, for the first time, simulated the flux distribution of a tetrahedron geometry. In this thesis, we also explore some fundamental questions of lattice QCD related to computability theory and complexity theory. / Graduation date: 2001

We consider a communication system where two transmitters wish to exchange information through a central relay. The data is assumed to be transmitted over synchronized, average power constrained additive white Gaussian noise channels with a real input with signal-to-noise ratio (SNR) of snr. It has been shown that using lattice codes and lattice decoding, a rate of 1/2 log_2(1/2 plus snr) can be obtained asymptotically, which is essentially optimal at high SNR. However, there has been a lack of practical encoding/decoding schemes for the above mentioned system. We address this issue in this thesis by developing encoding/decoding strategies for the bidirectional relaying system using low-dimensional lattice codes. Our efforts are aimed at developing coding schemes which possess low computational complexity while at the same time providing good performance. We demonstrate two schemes using low-dimensional lattice codes. Both these schemes have their own advantages and are suitable for different classes of lattice codes. The two schemes are tested with different lattices and their performance is compared to that of other schemes for bidirectional relays. The first scheme is termed as demodulate and forward and it essentially consists of performing optimal estimation at the relay. It is primarily implemented with lattice codes of low rate and possesses low decoding complexity. When used with a two-dimensional hexagonal lattice, it achieves a gain of around 3.5 dB in comparison to other schemes like Analog network coding. The second scheme is the sphere decoding scheme which has been implemented with high-rate lattice codes. The sphere decoder is a low-complexity decoder which is used for decoding to a lattice point at the relay. We observe that as the dimensionality of the lattice code is increased, the performance of the sphere decoder for the bidirectional relay gets consistently better. The sphere decoder is also used at high SNR for those instances in which the low density lattice code(LDLC) decoder makes an error and it is found that the sphere decoder can correct around 90 percent of these errors at an SNR of 9.75 dB.

NTRU is a public key cryptosystem, which was first introduced in 1996. It is a ring-based cryptosystem and its security relies on the complexity of a well-known lattice problem, i.e. shortest vector problem (SVP). There is no efficient algorithm known to solve SVP exactly in arbitrary high dimensional lattices. However, approximate solutions to SVP can be found by lattice reduction algorithms. LLL is the first polynomial time algorithm that finds reasonable short vectors of a lattice. The best known attacks on the NTRU cryptosystem are lattice attacks. In these attacks, the lattice constructed by the public key of the system is used to find the private key. The target vector, which includes private key of the system is one of the short vectors of the NTRU lattice. In this thesis, we study NTRU cryptosystem and lattice attacks on NTRU. Also, we applied an attack to a small dimensional NTRU lattice.

We intend to study the properties of two dimensional electron-hole systems in superlattice of ¢»-¢½ semiconductors at ultra-low temperature and high magnetic field by SdH measurement and QHE measurement and to explore the electron¡¦s oscillation varied with the external magnetic field. Considering the sample 2749,the electron densities of the first subband is 2.42¡Ñ1010cm-2,respectively,of which is 2.42¡Ñ1010cm-2 after low temperature¡¦s illumination. Considering the sample 2758,the electron densities of the first subband is 1.236¡Ñ1010cm-2,respectively,of which is 1.236¡Ñ1010cm-2 after low temperature¡¦s illumination. Data are the same, which may be concerned with the quality of the sample.