There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.
Based on the critical unstable of both crystal and magnetic structure of Gd-intermetallic compound near the competition of two strongly independent subsystem （＂local 4f7＂ and ＂conduction electron concentration＂）...Based on the critical unstable of both crystal and magnetic structure of Gd-intermetallic compound near the competition of two strongly independent subsystem （＂local 4f7＂ and ＂conduction electron concentration＂）, a new QPT （quantum point transition） is predicted by calculation of： （1） The band structure and density of state by density functional theory where a strong narrowing fluidity of fermions around EF with shifted to negative value ＂-0.8 eV ＂is observable in the Gd-intermetalliccompound system while in the Y-case, it is not dominated. An antiferromagnetic state on the fluidity of conduction band can be investigated; （2） The internal magnetic field due to short range exchange interaction Jij between the nearest neighbor of local magnetic moment of stable s-state of Gd （L = 0） through the mean field approximation and of Eigenvalue-Eigenfunction ~.（k） are calculated. While a strong negative value of Jy is predicted, the eigenvalue L（k） of the system shows a strong antiferromagnetic phase in the reciprocal lattice direction 〈010〉, 〈001〉 in the correlation length 3.38 ~A. Although the antiferromagnetic state at Rc 〈_ 3.38 °A is a puzzle but it is completely dominated at Rc = 9 °A after passing through the competition between ）.λmin（O） and λmin（π） in the ranger of 3.2 °A 〈 Rc 〈 9 °A. Since both of the antiferromagnetic subsystems are sensitive to the predicted KF, the effect of decreasing of conduction electron is proposed to investigate, the change of the antiferromagnetic ordering state to the competition of ferromagnetic state （in direction 〈010〉） and antiferromagnetic state （in direction 〈001 〉 and 〈 100〉） resulted to paramagnetic state in the long range Rc = 9 °A.展开更多
We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris ...We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.展开更多
In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximati...In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pade approach. In this method, homotopy relations are constructed to link the original system with an ideal, solvable model. An artificial homotopy parameter is introduced to the homotopy relations as the normal perturbation parameter to generate the perturbation series, and is used to implement the Padd approximation. Meanwhile, some other auxiliary nonperturbative parameters, which are used to control the convergence of the perturbation series, are inserted to the approximants, and are fixed via the principle of minimal sensitivity. The method is used to study the eigenvalue problem of the quantum anharmonic oscillators. Highly accurate numerical results show its validity. Possible further studies on this method are also briefly discussed.展开更多
The refined Arnoldi method proposed by Jia is used for computing some eigen-pairs of large matrices. In contrast to the Arnoldi method, the fundamental dif-ference is that the refined method seeks certain refined Ritz...The refined Arnoldi method proposed by Jia is used for computing some eigen-pairs of large matrices. In contrast to the Arnoldi method, the fundamental dif-ference is that the refined method seeks certain refined Ritz vectors, which aredifferent from the Ritz vectors obtained by the Arnoldi method, from a projection space with minimal residuals to approximate the desired eigenvectors. In com-parison with the Ritz vectors, the refined Ritz vectors are guaranteed to converge theoretically and can converge much faster numerically. In this paper we propose to replace the Ritz values, obtained by the Arnoldi method with respect to a Krylovsubspace, by the ones obtained with respect to the subspace spanned by the refined Ritz vectors. We discuss how to compute these new approximations cheaply and reliably. Theoretical error bounds between the original Ritz values and the new Ritz values are established. Finally, we present a variant of the refined Arnoldi al-gorithm for an augmented Krylov subspace and discuss restarting issue. Numerical results confirm efficiency of the new algorithm.展开更多
文摘There are three non-integrable phases in literatures: Berry phase, Aharonov-Anandan phase, and Yang phase. This article discusses the definitions and relations between these three non-integrable phases.
文摘Based on the critical unstable of both crystal and magnetic structure of Gd-intermetallic compound near the competition of two strongly independent subsystem （＂local 4f7＂ and ＂conduction electron concentration＂）, a new QPT （quantum point transition） is predicted by calculation of： （1） The band structure and density of state by density functional theory where a strong narrowing fluidity of fermions around EF with shifted to negative value ＂-0.8 eV ＂is observable in the Gd-intermetalliccompound system while in the Y-case, it is not dominated. An antiferromagnetic state on the fluidity of conduction band can be investigated; （2） The internal magnetic field due to short range exchange interaction Jij between the nearest neighbor of local magnetic moment of stable s-state of Gd （L = 0） through the mean field approximation and of Eigenvalue-Eigenfunction ~.（k） are calculated. While a strong negative value of Jy is predicted, the eigenvalue L（k） of the system shows a strong antiferromagnetic phase in the reciprocal lattice direction 〈010〉, 〈001〉 in the correlation length 3.38 ~A. Although the antiferromagnetic state at Rc 〈_ 3.38 °A is a puzzle but it is completely dominated at Rc = 9 °A after passing through the competition between ）.λmin（O） and λmin（π） in the ranger of 3.2 °A 〈 Rc 〈 9 °A. Since both of the antiferromagnetic subsystems are sensitive to the predicted KF, the effect of decreasing of conduction electron is proposed to investigate, the change of the antiferromagnetic ordering state to the competition of ferromagnetic state （in direction 〈010〉） and antiferromagnetic state （in direction 〈001 〉 and 〈 100〉） resulted to paramagnetic state in the long range Rc = 9 °A.
文摘We study Duffin-Kemmer-Petiau(DKP) equation in the presence of the Woods-Saxon potential and obtain eigenvalues and corresponding eigenfunctions for any J state by using of the Nikiforov-Uvarov(NU) method.The Pekeris approximation is used to deal with centrifugal term.
基金Supported by the National Natural Science Foundations of China under Grant Nos.10735030,10475055,10675065 and 90503006National Basic Research Program of China (973 Program) under Grant No.2007CB814800+2 种基金Program for Changjiang Scholars and Innovative Research Team (IRT0734)the Research Fund of Postdoctoral of China under Grant No.20070410727Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20070248120
文摘In order to investigate a complicated physical system, it is convenient to consider a simple, easy to solve model, which is chosen to reflect as much physics as possible of the original system, as an ideal approximation. Motivated by this fundamental idea, we propose a novel asymptotic method, the nonsensitive homotopy-Pade approach. In this method, homotopy relations are constructed to link the original system with an ideal, solvable model. An artificial homotopy parameter is introduced to the homotopy relations as the normal perturbation parameter to generate the perturbation series, and is used to implement the Padd approximation. Meanwhile, some other auxiliary nonperturbative parameters, which are used to control the convergence of the perturbation series, are inserted to the approximants, and are fixed via the principle of minimal sensitivity. The method is used to study the eigenvalue problem of the quantum anharmonic oscillators. Highly accurate numerical results show its validity. Possible further studies on this method are also briefly discussed.
文摘The refined Arnoldi method proposed by Jia is used for computing some eigen-pairs of large matrices. In contrast to the Arnoldi method, the fundamental dif-ference is that the refined method seeks certain refined Ritz vectors, which aredifferent from the Ritz vectors obtained by the Arnoldi method, from a projection space with minimal residuals to approximate the desired eigenvectors. In com-parison with the Ritz vectors, the refined Ritz vectors are guaranteed to converge theoretically and can converge much faster numerically. In this paper we propose to replace the Ritz values, obtained by the Arnoldi method with respect to a Krylovsubspace, by the ones obtained with respect to the subspace spanned by the refined Ritz vectors. We discuss how to compute these new approximations cheaply and reliably. Theoretical error bounds between the original Ritz values and the new Ritz values are established. Finally, we present a variant of the refined Arnoldi al-gorithm for an augmented Krylov subspace and discuss restarting issue. Numerical results confirm efficiency of the new algorithm.
