In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials out...In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.展开更多
We study the dynamics of an electron spin state transfer along a half-filled two-band model(TBM).It is shown that this solvable and realistic medium has an energy gap between the ground and first-excited states in the...We study the dynamics of an electron spin state transfer along a half-filled two-band model(TBM).It is shown that this solvable and realistic medium has an energy gap between the ground and first-excited states in the half-filled case.By connecting two qubits to two sites of the TBM,the system can accomplish a high-fidelity and long-distance quantum state transfer(QST).Moreover,numerical simulations have been performed for a finite system.The results show that the numerical and analytical results of the effective coupling strength agree well with each other.Furthermore,the investigation shows that the reduced density matrix also has high fidelity beyond the range of perturbation.展开更多
In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that t...In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.展开更多
基金Project(2007CB714001) supported by the National Basic Research Program of China (973 Program)
文摘In contrast to the traditional interpretation of shear bands in sand as a bifurcation problem in continuum mechanics,shear bands in sand are considered as high-strain phase(plastic phase) of sand and the materials outside the bands are still in low-strain phase(elastic phase),namely,the two phases of sand can coexist under certain condition.As a one-dimensional example,the results show that,for materials with strain-softening behavior,the two-phase solution is a stable branch of solutions,but the method to find two-phase solutions is very different from the one for bifurcation analysis.The theory of multi-phase equilibrium and the slow plastic flow model are applied to predict the formation and patterns of shear bands in sand specimens,discontinuity of deformation gradient and stress across interfaces between shear bands and other regions is considered,the continuity of displacements and traction across interfaces is imposed,and the Maxwell relation is satisfied.The governing equations are deduced.The critical stress for the formation of a shear band,both the stresses and strains inside the band and outside the band,and the inclination angle of the band can all be predicted.The predicted results are consistent with experimental measurements.
基金supported by the National Natural Science Foundation of China (Grant Nos. 10874091,2006CB921205,and 108471507)Shandong Provincial Natural Science Foundation,China (Grant No.ZR2009AM026)
文摘We study the dynamics of an electron spin state transfer along a half-filled two-band model(TBM).It is shown that this solvable and realistic medium has an energy gap between the ground and first-excited states in the half-filled case.By connecting two qubits to two sites of the TBM,the system can accomplish a high-fidelity and long-distance quantum state transfer(QST).Moreover,numerical simulations have been performed for a finite system.The results show that the numerical and analytical results of the effective coupling strength agree well with each other.Furthermore,the investigation shows that the reduced density matrix also has high fidelity beyond the range of perturbation.
基金Supported by National Natural Science Foundation of China under Grant No.11374017
文摘In the present paper, we investigate the existence of ferromagnetism in a two-band Hubbard model, by applying a recently-introduced method by us to study ferromagnetism in metallic clusters. We prove rigorously that the ground state of this model is ferromagnetic if the intra-orbital Coulomb repulsion between electrons is infinitely strong and only one hole exists in the system. Our theorem improves a previous result. Furthermore, our method can also be applied to deal with the case of multiple holes.
基金Supportedin part bythe National Natural Science Foundations of China (Grant No.10274007 and 90103027) a grant of the ChinaAcademy of Engineering and Physics
