In this paper we solve spin-weighted spheroidal wave equations through super-symmetric quantum mechanics with a different expression of the super-potential. We use the shape invariance property to compute the ＂excite...In this paper we solve spin-weighted spheroidal wave equations through super-symmetric quantum mechanics with a different expression of the super-potential. We use the shape invariance property to compute the ＂excited＂ eigenvalues and eigenfunctions. The results are beneficial to researchers for understanding the properties of the spin-weighted spheroidal wave more deeply, especially its integrability.展开更多
Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their an...Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.展开更多
Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far...Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 10875018)
文摘In this paper we solve spin-weighted spheroidal wave equations through super-symmetric quantum mechanics with a different expression of the super-potential. We use the shape invariance property to compute the ＂excited＂ eigenvalues and eigenfunctions. The results are beneficial to researchers for understanding the properties of the spin-weighted spheroidal wave more deeply, especially its integrability.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 10875018 and 10773002)
文摘Spin-weighted spheroidal wave functions play an important role in the study of the linear stability of rotating Kerr black holes and are studied by the perturbation method in supersymmetric quantum mechanics. Their analytic ground eigenvalues and eigenfunctions are obtained by means of a series in low frequency. The ground eigenvalue and eigenfunction for small complex frequencies are numerically determined.
文摘Entanglement in quantum theory is a peculiar concept to scientists. With this concept we are forced to re-consider the cluster property which means that one event is irrelevant to another event when they are fully far away. In the recent works we showed that the quasi-degenerate states induce the violation of cluster property in antiferromagnets when the continuous symmetry breaks spontaneously. We expect that the violation of cluster property will be observed in other materials too, because the spontaneous symmetry breaking is found in many systems such as the high temperature superconductors and the superfluidity. In order to examine the cluster property for these materials, we studied a quantum nonlinear sigma model with U(1) symmetry in the previous work. There we showed that the model does have quasi-degenerate states. In this paper we study the quantum nonlinear sigma model with SU(2) symmetry. In our approach we first define the quantum system on the lattice and then adopt the representation where the kinetic term is diagonalized. Since we have no definition on the conjugate variable to the angle variable, we use the angular momentum operators instead for the kinetic term. In this representation we introduce the states with the fixed quantum numbers and carry out numerical calculations using quantum Monte Carlo methods and other methods. Through analytical and numerical studies, we conclude that the energy of the quasi-degenerate state is proportional to the squared total angular momentum as well as to the inverse of the lattice size.
