Neste trabalho estudamos algumas propriedades supercondutoras de compostos hidratados de cobalto do tipo NaxCoO2 · yH2O. Estes compostos são formados por planos de CoO2, intercalados por planos de íons de Na e moléculas de H2O, formando uma rede triangular bidimensional pelos átomos de Co. Utilizando como modelo um hamiltoniano de Hubbard estendido, foram construídas as funções de Green normal e anômala no limite U → ¥ e na aproximação de campo médio. Nos restringimos ao caso paramagnético, e estudamos a supercondutividade do sistema considerando a possibilidade de diferentes simetrias para o parâmetro de ordem da fase supercondutora. Os resultados indicam a ocorrência de supercondutividade para determinadas regiões do número de partículas, em concordância qualitativa com os dados experimentais. / In this work we study some properties of hydrated cobalt oxide, NaxCoO2 · yH2O in the superconducting phase. This compound consists of CoO2 layers interlayered by Na ions and H2O molecules, resulting in a Co triangular lattice. Our theoretical model is the extended Hubbard Model and we obtain the normal and anomalous Green’s functions in the infinite U limit by using the mean field approximation. We consider the paramagnetic case and we analyse coupling between electrons with different symmetries, so obtaining the singlet and triplet superconducting order parameters. The superconducting phases showed in this work are in qualitative agreement with experimental results.

Neste trabalho estudamos algumas propriedades supercondutoras de compostos hidratados de cobalto do tipo NaxCoO2 · yH2O. Estes compostos são formados por planos de CoO2, intercalados por planos de íons de Na e moléculas de H2O, formando uma rede triangular bidimensional pelos átomos de Co. Utilizando como modelo um hamiltoniano de Hubbard estendido, foram construídas as funções de Green normal e anômala no limite U → ¥ e na aproximação de campo médio. Nos restringimos ao caso paramagnético, e estudamos a supercondutividade do sistema considerando a possibilidade de diferentes simetrias para o parâmetro de ordem da fase supercondutora. Os resultados indicam a ocorrência de supercondutividade para determinadas regiões do número de partículas, em concordância qualitativa com os dados experimentais. / In this work we study some properties of hydrated cobalt oxide, NaxCoO2 · yH2O in the superconducting phase. This compound consists of CoO2 layers interlayered by Na ions and H2O molecules, resulting in a Co triangular lattice. Our theoretical model is the extended Hubbard Model and we obtain the normal and anomalous Green’s functions in the infinite U limit by using the mean field approximation. We consider the paramagnetic case and we analyse coupling between electrons with different symmetries, so obtaining the singlet and triplet superconducting order parameters. The superconducting phases showed in this work are in qualitative agreement with experimental results.

Made available in DSpace on 2014-06-12T18:07:24Z (GMT). No. of bitstreams: 2 arquivo7883_1.pdf: 1570834 bytes, checksum: 8e9d28cb0086107b52e23e67bf307844 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2005 / Nesta dissertação estudamos o hamiltonianano estendido de Hubbard através do método de diagonalização exata de Lanczos, em condição de contorno periódica, com foco na caracterização das propriedades magnéticas e de condução do estado fundamental da cadeia quântica AB2, nos diferentes regimes (forte, intermediário, fraco) de repulsão coulombiana local U e intersítio V, em semi-preenchimento da banda. Seguindo o mesmo procedimento caracterizamos o estado fundamental para a cadeia linear, comparando nossos resultados testes com aqueles já reportados na literatura. A inclusão da interação V, não considerada em estudos anteriores na cadeia AB2, deu origem a um novo diagrama de fases no plano (U,V), o qual exibe uma similitude não trivial com o diagrama obtido para a cadeia linear. No regime de acoplamento coulombiano U~>5t e para V<~/4, nosso sistema está numa fase ferrimagnética (FERRI), com a carga homogeneamente distribuída em cada sub-rede, e magnetizações locais < SzA > =~ -0.25 e < SZB > =~ 0.75. Para V~>/4, o sistema se encontra em uma fase onda de densidade de carga com ordem ferromagnética (ODCF), tal que < SzA > =0 e < SZB>=0.5, exibindo um defeito na distribuição de carga. No regime de acoplamento coulombiano U~<5t, o sistema exibe uma fase intermediária com correlação magnética tipo Espiral. Neste regime o spin salta do valor 1/2 por célula unitária, na fase FERRI, para zero na fase Espiral, e de zero ao valor de 1/2 por célula unitária na fase ODCF. Nossa análise de escala de tamanho finito indica que as duas transições são de primeira ordem no campo de spin. Examinamos também a natureza das fases mencionadas com respeito às propriedades de condução, assim como a ocorrência de um ponto multicrítico na linha V&#8776;U /4 para U&#8776;5t

In order to explore a quantum version of a discrete nonlinear Schrödinger equation (DNLS), we quantize one nonlinear Schrödinger model, which is used to study different physical systems, e.g. coupled Bose-Einstein condensates. We will focus on small systems, like Dimer and Trimer.In our efforts to solve this quantum problem, we develop a Mathematica routine that implements the Number State Method and solves the corresponding Schrödinger equation. We calculate analytically and numerically the energy spectrum of the Dimer and Trimer systems. Those eigenenergies depend on the parameter set Q=Q1, Q2, Q3, Q4, Q5 and by adjusting this set Q, we can obtain the desired results and examine their effects. After the quantization of the extended DNLS we obtain a quantum DNLS, also known as an extended Bose-Hubbard (BH) model. The aim of this Master's thesis is to study the differences and similarities between the classical DNLS and the extended BH model, and what happens when we approach from the quantum regime to the classical one. Taking into account that the Hamiltonian has an important conserved quantity, the number operator, enables the total Hamiltonian to be block-diagonalized. This can be accomplished by taking advantage of additional symmetries, such as translational symmetry, which will simplify the analysis of the Hamiltonian matrix. In our results we discuss several effects that break the lattice symmetry, as the intersection between symmetric and antisymmetric states. We also compare our results with those obtained in previous works for the classical model, and we find some similarities, e.g. the transition of the highest-energy state from a one-site solution to a two-site solution depending on which Q parameters we vary, but also differences, as the appearance of a three-site solution, in a Trimer system.

by Lee Kai Cheung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1993. / Includes bibliographical references. / Acknowledgements --- p.II / Abstract --- p.III / Chapter Chapter 1 --- Introduction --- p.1 / Chapter Chapter 2 --- Theory --- p.7 / Chapter Chapter 3 --- Application of the Connected-Moments Expansion to the S=l/2 Heisenberg Antiferromagnet Paper I --- p.16 / Chapter Chapter 4 --- Application of the Connected-Moments Expansion to the Half-filled Hubbard Model Paper II --- p.18 / Chapter Chapter 5 --- Conclusion --- p.20 / Appendix I --- p.21 / Appendix II --- p.29 / References --- p.37

Many novel materials, such as the vanadates MgV 2O5, the cuprates SrCu 2O3, conducting polymers and organic salts which involve longer-range Coulomb interactions, can be modeled by the extended Hubbard model. In this thesis, we applied the strong-coupling perturbation theory to study a generalized extended Hubbard model characterized by the inter-chain electron hopping t' and the inter-chain nearest-neighbor interaction V' as well as the on-site interaction U, the intra-chain nearest-neighbor interaction V and the intra-chain electron hopping t at strong coupling limit for quarter and half band fillings. / The early strong coupling perturbation expansion was only up to the fourth order in t/U and t/V expansion, which is good for the large values of interaction, U/t > 10. However, for real physical systems, the reasonable range of U/t should be from 4 to 10. In order to investigate the physical systems more accurately, we worked out a perturbation expansion up to the sixth order, hence obtained an effective Hamiltonian in t/U, t/V, t/V', t'/U, t'/V and t'/V' expansion for the extended Hubbard model in half and quarter band filings. The effective Hamiltonian obtained only contains the spin-spin correlation terms. For the half-filled band, we calculated the four spin-spin correlation terms and applied the first and second nearest-neighbor correlation of the linear Heisenberg model obtained by Hulthen and Takahashi and the third nearest-neighbor correlation obtained by Kazumitsu Sakai's group to calculate the ground state energy for the 1-D extended Hubbard chain with the realistic Coulomb interactions, U/t ranges from 4 to 14 and V/t ranges from 0 to 2 respectively. For the quarter-filled case, we worked out the effective Hamiltonian for the 1-D and the 2-D cases and calculated the spin-spin correlation functions by the spin-wave theory. We calculated the ground state energy with the same ranges of the on-site interaction input in the half-filled case and the V/t ranges from 1.5 to 4.0 for the 1-D, the quasi 2-D (t > t', t'/V &sim; t/V) and the isotropic 2-D (t = t', V = V') case respectively. In order to check the validity of the perturbation expansion, we proceeded numerical calculations of the ground state energy by exact diagonalization for the same values of U, V, t, V' and t' for both the half-filled and the quarter-filled cases. / Lee Wing Fai = 強耦合擴展 Hubbard模型之微擾計算 / 李榮輝. / "August 2005." / Adviser: Lin Hai Qing. / Source: Dissertation Abstracts International, Volume: 67-01, Section: B, page: 0323. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (p. 157-160). / 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. / School code: 1307. / Lee Wing Fai = Qiang ou he kuo zhan Hubbard mo xing zhi wei rao ji suan / Li Ronghui.

Lau Wai Chuen. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 93-94). / Lau Wai Chuen. / Contents --- p.ii / List of Figures --- p.iv / List of Tables --- p.vi / Abstract --- p.ix / Acknowledgement --- p.x / Chapter Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Superconductivity --- p.1 / Chapter 1.2 --- The Hubbard model and the Extended Hubbard model --- p.3 / Chapter 1.3 --- Gap Equation --- p.6 / Chapter 1.3.1 --- One-dimensional solutions --- p.11 / Chapter 1.3.2 --- Two-dimensional solutions --- p.12 / Chapter Chapter 2. --- Solving BCS equation --- p.15 / Chapter 2.1 --- Zero value of the denominator of the BCS equations --- p.15 / Chapter 2.2 --- Discontinuity of the BCS equations --- p.16 / Chapter Chapter 3. --- Results of BCS equations for finite size clusters --- p.34 / Chapter 3.1 --- Method used to solve BCS equations --- p.34 / Chapter 3.2 --- Results for the one dimensional and two dimensional lattices --- p.34 / Chapter 3.2.1 --- Extended S-wave solution --- p.35 / Chapter 3.2.2 --- P-wave and D-wave solutions --- p.36 / Chapter Chapter 4. --- Results of BCS equations compare with exact solutions --- p.69 / Chapter 4.1 --- "An exact solution of D-wave, Ne=2" --- p.69 / Chapter 4.2 --- Comparison of the ground state energy with the results calculated by exact diagonalization --- p.73 / Chapter Chapter 5. --- The Phase Diagram of the superconducting state --- p.78 / Chapter Chapter 6. --- Conclusion --- p.91 / Bibliography --- p.93

Extr. de: Diss.--Physique--Aachen (Allemagne)--Technischen Hochschule, 2001. / Bibliogr. p. 193-197.

Thèses (M.Sc.)--Université de Sherbrooke (Canada), 1997. / Titre de l'écran-titre (visionné le 20 juin 2006). Publié aussi en version papier.

Made available in DSpace on 2014-06-12T18:03:00Z (GMT). No. of bitstreams: 2 arquivo7692_1.pdf: 156573 bytes, checksum: efbcda03282532417ac013b427e5ca96 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2000 / A versão de ALCANC infinito da hamiltoniana de Hubbard pode ser resolvida exatamente em qualquer dimensão. Em banda semi-cheia, o modelo apresenta uma transição metal-isolante (Mott) como função da interação quando seu valor é exatamente igual à largura da banda. Em nosso trabalho, estudamos este modelo em uma dimensão, onde o calculo exato da função de Green de 1- partícula permite obter a densidade de estudos modificada pela interação. Um diagrama de fase é então obtido. Obtemos também a função de correlação densidade-densidade e a susceptibilidade magnética do sistema. Em dimensão d>2, utilizamos uma densidade de estados parabólica e obtivemos numericamente várias das quantidades acima mencionadas. Nossos resultados evidenciaram diversas características microscópicas da transição Mott neste modelo