We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using stand...We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using standing-wave expansion method, we present symmetric andasymmetric ground state solutions of nonlinear Schroedinger equation (NLSE) with a symmetric doublesquare well potential for attractive nonlinearity. In particular, we study the ground state wavefunction's properties by changing the depth of potential and atomic interactions (here we restrictourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal aphase transition of BECs trapped in one-dimensional optical lattice potential.展开更多
Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively...Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure; symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian.展开更多
Insecurity and asymmetry in all their ramifications are ideological. They are also inherently communicative processes that are largely constructed and enacted through language in various institutional discourses. In U...Insecurity and asymmetry in all their ramifications are ideological. They are also inherently communicative processes that are largely constructed and enacted through language in various institutional discourses. In Urhobo, sex proverbs copiously couch the ideological conceptualizations of the male-female biological asymmetry. Studies on Urhobo proverbs dwell largely on functional applications and documentations of the proverbs, thereby overlooking their ideological underpinnings. Therefore, in this paper, efforts are geared toward investigating and unravelling ideologies that have been habitualized in the semantic and pragmatic structures of the Urhobo sex proverbs. The intention is to throw open the patterns of relationship between the male and female participants in the society in relation to sex matters and power. Twenty-six Urhobo indigenes （six males and 20 females）, who are competent in the socioculture and language were successfully interviewed to elicit Urhobo sex proverbs. Proverbs that contain the following lexical items： penis, virgina, to make love, or to have sex are purposively selected and subjected to CDA （critical discourse analysis）. The main assumption of CDA is that language is both the site and the stake in the struggle for power and domination. Findings show that in the Urhobo sex proverbs, there is asymmetry in access to sexual relations between the male and female. Although the sex proverbs do not always refer to copulation, they are often employed as powerful instruments to dominate and instil fear in the female participant. Consequently, patriarchal discourses are further entrenched in the society展开更多
A complete classification of static space times with maximal symmetric transverse spaces is provided, according to their Ricci collineations. The classification is made when one component of Ricci collineation vector ...A complete classification of static space times with maximal symmetric transverse spaces is provided, according to their Ricci collineations. The classification is made when one component of Ricci collineation vector field V is non-zero （cases 1 - 4）, two components of V are non-zero （cases 5 - 10）, and three components of V are non-zero （cases 11 - 14）, respectlvily. Both non-degenerate （detRab ≠ 0） as well as the degenerate （det Rab = 0） cases are discussed and some new metrics are found.展开更多
Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation r...Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.展开更多
We consider the question of characterizing compact quotients of the complex 2-ball by curvature conditions, which improve the known results. Moreover, we also give curvature conditions such that a compact Kaehler-Eins...We consider the question of characterizing compact quotients of the complex 2-ball by curvature conditions, which improve the known results. Moreover, we also give curvature conditions such that a compact Kaehler-Einstein surface is bi-holomorphic to a locally symmetric space.展开更多
In this paper,a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized（third order） Landau-Lifshitz equation. On the other hand it could be thought of a...In this paper,a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized（third order） Landau-Lifshitz equation. On the other hand it could be thought of as a special case of the Schroodinger-Airy flow when the target manifold is a Koahler manifold with constant holomorphic sectional curvature. We show the local existence of the new flow on a complete Riemannian manifold with some assumptions on Ricci tensor. Moreover,if the target manifolds are Einstein or some certain type of locally symmetric spaces,the global results are obtained.展开更多
文摘We investigate the phenomena of symmetry breaking and phase transition in theground state of Bose-Einstein condensates (BECs) trapped in a double square well and in an opticallattice well, respectively. By using standing-wave expansion method, we present symmetric andasymmetric ground state solutions of nonlinear Schroedinger equation (NLSE) with a symmetric doublesquare well potential for attractive nonlinearity. In particular, we study the ground state wavefunction's properties by changing the depth of potential and atomic interactions (here we restrictourselves to the attractive regime). By using the Fourier grid Hamiltonian method, we also reveal aphase transition of BECs trapped in one-dimensional optical lattice potential.
文摘Gravity and electromagnetism are two sides of the same coin, which is the clue of this unification. Gravity and electromagnetism are represented by two mathematical structures, symmetric and antisymmetric respectively. Einstein gravitational field equation is the symmetric mathematical structure. Electrodynamics Lagrangian is three parts, for electromagnetic field, Dirac field and interaction term. The definition of canonical energy momentum tensor was used for each term in Electrodynamics Lagrangian to construct the antisymmetric mathematical structure; symmetric and antisymmetric gravitational field equations are two sides of the same Lagrangian.
文摘Insecurity and asymmetry in all their ramifications are ideological. They are also inherently communicative processes that are largely constructed and enacted through language in various institutional discourses. In Urhobo, sex proverbs copiously couch the ideological conceptualizations of the male-female biological asymmetry. Studies on Urhobo proverbs dwell largely on functional applications and documentations of the proverbs, thereby overlooking their ideological underpinnings. Therefore, in this paper, efforts are geared toward investigating and unravelling ideologies that have been habitualized in the semantic and pragmatic structures of the Urhobo sex proverbs. The intention is to throw open the patterns of relationship between the male and female participants in the society in relation to sex matters and power. Twenty-six Urhobo indigenes （six males and 20 females）, who are competent in the socioculture and language were successfully interviewed to elicit Urhobo sex proverbs. Proverbs that contain the following lexical items： penis, virgina, to make love, or to have sex are purposively selected and subjected to CDA （critical discourse analysis）. The main assumption of CDA is that language is both the site and the stake in the struggle for power and domination. Findings show that in the Urhobo sex proverbs, there is asymmetry in access to sexual relations between the male and female. Although the sex proverbs do not always refer to copulation, they are often employed as powerful instruments to dominate and instil fear in the female participant. Consequently, patriarchal discourses are further entrenched in the society
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10325525 and 90403029, and Ministry of Science and Technology of China under Grant No. TG1999075401
文摘A complete classification of static space times with maximal symmetric transverse spaces is provided, according to their Ricci collineations. The classification is made when one component of Ricci collineation vector field V is non-zero （cases 1 - 4）, two components of V are non-zero （cases 5 - 10）, and three components of V are non-zero （cases 11 - 14）, respectlvily. Both non-degenerate （detRab ≠ 0） as well as the degenerate （det Rab = 0） cases are discussed and some new metrics are found.
文摘Adding a U（1） symmetry breaking term √V（λ1a0 ＋ λ1＊a0） ＋ √V（λ2b0 ＋ λ2＊b0） to Bogoliubov＇s truncated Hamiltonian HB for a weakly interacting coupled Bose system, by using the mean-field approximation rather than the c-number approximation, we And that, via a Feshbach resonance at zero temperature, the states of the coupled Bose system are generalized SU（1,1） SU（1,1） coherent states. The Bose-Einstein condensation occurs in response to the spontaneous U（1） symmetry breaking.
基金supported by National Natural Science Foundation of China (Grant No.1131008)partially by National Science Foundation of USA
文摘We consider the question of characterizing compact quotients of the complex 2-ball by curvature conditions, which improve the known results. Moreover, we also give curvature conditions such that a compact Kaehler-Einstein surface is bi-holomorphic to a locally symmetric space.
基金supported by National Natural Science Foundation of China(Grant Nos.11226082,11301557 and 10990013)
文摘In this paper,a class of new geometric flows on a complete Riemannian manifold is defined. The new flow is related to the generalized（third order） Landau-Lifshitz equation. On the other hand it could be thought of as a special case of the Schroodinger-Airy flow when the target manifold is a Koahler manifold with constant holomorphic sectional curvature. We show the local existence of the new flow on a complete Riemannian manifold with some assumptions on Ricci tensor. Moreover,if the target manifolds are Einstein or some certain type of locally symmetric spaces,the global results are obtained.
