This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit coup...This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian(3 PN),4 PN, 5 PN, 6 PN and 7 PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically.展开更多
We study the Kondo screening of a spin-1/2 magnetic impurity coupled to a superconductor,which is fabricated by combination of an s-wave superconductor,a ferromagnet and a semiconductor with Rashba spin-orbit coupling...We study the Kondo screening of a spin-1/2 magnetic impurity coupled to a superconductor,which is fabricated by combination of an s-wave superconductor,a ferromagnet and a semiconductor with Rashba spin-orbit coupling(RSOC).The proximity induced superconducting states include the s-wave and p-wave pairing components with the aids of RSOC,and the ferromagnet induces a Zeeman field which removes the spin degeneracy of the quasiparticles in the triplet states.Thus,the Kondo screening of magnetic impurity involves the orbital degrees of freedom,and is also affected by the Zeeman field.Using the variational method,we calculate the binding energy and the spin-spin correlation between the magnetic impurity and the electrons in the coexisting s-wave and p-wave pairing states.We find that Kondo singlet forms more easily with stronger RSOC,but Zeeman field in general decreases the binding energy.The spin-spin correlation decays fast in the vicinity of the magnetic impurity.Due to the RSOC,the spatial spin-spin correlation becomes highly anisotropic,and the Zeeman field can induce extra asymmetry to the off-diagonal components of the spin-spin correlation.Our study can offer some insights into the studies of extrinsic topological superconductors fabricated from the hybrid structures containing chains of magnetic impurities.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos.11533004,11663005the Natural Science Foundation of Jiangxi Province under Grant Nos.20153BCB22001 and 20171BAB211005
文摘This paper relates to the post-Newtonian Hamiltonian dynamics of spinning compact binaries, consisting of the Newtonian Kepler problem and the leading, next-to-leading and next-to-next-to-leading order spin-orbit couplings as linear functions of spins and momenta. When this Hamiltonian form is transformed to a Lagrangian form, besides the terms corresponding to the same order terms in the Hamiltonian, several additional terms, third post-Newtonian(3 PN),4 PN, 5 PN, 6 PN and 7 PN order spin-spin coupling terms, yield in the Lagrangian. That means that the Hamiltonian is nonequivalent to the Lagrangian at the same PN order but is exactly equivalent to the full Lagrangian without any truncations. The full Lagrangian without the spin-spin couplings truncated is integrable and regular. Whereas it is non-integrable and becomes possibly chaotic when any one of the spin-spin terms is dropped. These results are also supported numerically.
基金Project supported by the Zhejiang Provincial Natural Science Foundation of China(Grant No.LY19A040003)。
文摘We study the Kondo screening of a spin-1/2 magnetic impurity coupled to a superconductor,which is fabricated by combination of an s-wave superconductor,a ferromagnet and a semiconductor with Rashba spin-orbit coupling(RSOC).The proximity induced superconducting states include the s-wave and p-wave pairing components with the aids of RSOC,and the ferromagnet induces a Zeeman field which removes the spin degeneracy of the quasiparticles in the triplet states.Thus,the Kondo screening of magnetic impurity involves the orbital degrees of freedom,and is also affected by the Zeeman field.Using the variational method,we calculate the binding energy and the spin-spin correlation between the magnetic impurity and the electrons in the coexisting s-wave and p-wave pairing states.We find that Kondo singlet forms more easily with stronger RSOC,but Zeeman field in general decreases the binding energy.The spin-spin correlation decays fast in the vicinity of the magnetic impurity.Due to the RSOC,the spatial spin-spin correlation becomes highly anisotropic,and the Zeeman field can induce extra asymmetry to the off-diagonal components of the spin-spin correlation.Our study can offer some insights into the studies of extrinsic topological superconductors fabricated from the hybrid structures containing chains of magnetic impurities.
