The Effect of Spin-Orbit Coupling and Spin-Spin Coupling of Compact Binaries on Chaos

There are spin-orbit interaction and spin-spin interaction in a generic post-Newtonian Lagrangian formu-lation of comparable mass spinning compact binaries. The spin-orbit coupling or the spin-spin coupling plays a quite important role in changing the evolution of the system and may sometime cause chaotic behavior. How do the two types of couplings exert together any influences on chaos in this formulation? To answer it, we simply take the Lagrangian formulation of a special binary system, including the Newtonian term and the leading-order spin-orbit and spin-spin couplings. The key to this question can be found from a Hamiltonian formulation that is completely identical to the Lagrangian formulation. If the Lagrangian does not include the spin-spin coupling, its equivalent Hamiltonian has an additional term (i.e. the next-order spin-spin coupling) as well as those terms of the Lagrangian. The spin-spin coupling rather than the spin-orbit coupling makes the Hamiltonian typically nonintegrable and probably chaotic when two objects spin. When the leading-order spin-spin coupling is also added to the Lagrangian, it still appears in the Hamiltonian. In this sense, the total Hamiltonian contains the leading-order spin-spin coupling and the next-order spin-spin coupling, which have different signs. Therefore, the chaos resulting from the spin-spin interaction in the Legrangian formulations is somewhat weakened by the spin-orbit coupling.     

Effect of the Quadrupole–Monopole Interaction on Chaos in Compact Binaries

The dynamics of a post‐Newtonian Lagrangian of spinning compact binaries, including the Newtonian, post‐Newtonian, spin‐orbit, spin‐spin, and quadrupole–monopole interaction contributions are investigated herein. According to the Euler–Lagrangian equations, exact and approximate equations of motion can be written. Numerical computations show that the constants of motion can reach satisfactory accuracies in the exact equations but rather poor accuracies in the approximate equations. Similar to the spin–orbit coupling or the spin–spin coupling, the quadrupole–monopole interaction plays a role in some spin effects that lead to the precession of orbits. With the increase in quadrupole–monopole and extension of integration, the orbits precess strongly and the difference in the precession of orbits between the two sets of equations increases. The quadrupole–monopole interaction can also cause the chaoticity of spinning compact binaries. When it increases, chaos is strong under some circumstances in the exact equations but not in the approximate equations.     

Chaos in a Quantum Dot with Spin-Orbit Coupling

Level statistics and nodal point distribution in a rectangular semiconductor quantum dot are studied for different degrees of spin-orbit coupling. The chaotic features occurring from the spin-orbit coupling have no classical counterpart. Using experimental values for GaSb/InAs/GaSb semiconductor quantum wells we find that level repulsion can lead to the semi-Poisson distribution for nearest level separations. Nodal lines and nodal points are also investigated. Comparison is made with nodal point distributions for fully chaotic states.     

Fe-Ga磁致伸缩合金自旋轨道耦合效应研究

磁致伸缩和磁晶各向异性来源于自旋轨道耦合及晶体场效应,两种效应作用效果将对Fe-Ga大磁致伸缩合金研究方向将起指导作用.通过基于均匀梯度近似的线形缀加平面波法研究了Fe-Ga磁致伸缩合金中D03、B2-like、L12结构在施加自旋轨道耦合效应前后Fe原子3d轨道劈裂情况,轨道电子数及磁晶各向异性.结果表明,自旋轨道耦合效应可以进一步劈裂D03及L12立方结构晶体场,D03和L12结构中Fe原子3d轨道电子数,尤其是dxy和d(x2-y2)轨道下自旋电子数由于自旋轨道耦合作用发生改变;但自旋轨道耦合对B2-like结构作用微弱.Fe-Ga磁致伸缩合金中磁晶各向异性主要由晶体场效应决定.     

Correlation Renormalized and Induced Spin-Orbit Coupling

Interplay of spin-orbit coupling(SOC) and electron correlation generates a bunch of emergent quantum phases and transitions, especially topological insulators and topological transitions. We find that electron correlation will induce extra large SOC in multi-orbital systems under atomic SOC and change ground state topological properties. Using the Hartree–Fock mean field theory, phase diagrams of px/py orbital ionic Hubbard model on honeycomb lattice are well studied. In general, correction of s...     

The Two Dimensional Kondo Model with Rashba Spin-Orbit Coupling

We investigate the effect that Rashba spin-orbit coupling has on the low energy behaviour of a two dimensional magnetic impurity system. It is shown that the Kondo effect, the screening of the magnetic impurity at temperatures T<T _K , is robust against such spin-orbit coupling, despite the fact that the spin of the conduction electrons is no longer a conserved quantity. A proposal is made for how the spin-orbit coupling may change the value of the Kondo temperature T _K in such systems and the prospects of measuring this change are discussed. We conclude that many of the assumptions made in our analysis invalidate our results as applied to recent experiments in semi-conductor quantum dots but may apply to measurements made with magnetic atoms placed on metallic surfaces.     

Inverse Spin Hall Effect in Two-Terminal Device with Rashba Spin-Orbit Coupling

We report a theoretic study on the inverse spin-Hall effect （ISHE） in a two-terminal nano-device that consists of a two-dimensional electron gas （2DEG） with Rashba spin-orbit coupling （RSOC） and two ideal leads. Based on a two-site toy model and Keldysh Green＇s function method, we derive an analytic result of ISHE, which shows clearly that a nonzero transverse charge current stems from the combined effect of the RSOC, the spin bias, and its spin polarization direction in spin space. Our further numerical calculations in a larger system other than two-site lattice model demonstrate that the transverse charge current, dependent on the strength of the RSOC, the Fermi energy of the system, as well as the system size, can exhibit oscillating behavior and even reverse its sign due to Rashba spin precession. These properties may be helpful for eficient detection of the spin current （spin bias） by measuring the transverse charge current in a spin-orbital coupling system.     

Chaotic Cyclotron and Hall Trajectories Due to Spin-Orbit Coupling

It is demonstrated that the synergistic effect of a gauge field, Rashba spin-orbit coupling (SOC), and Zeeman splitting can generate chaotic cyclotron and Hall trajectories of particles. The physical origin of the chaotic behavior is that the SOC produces a spin-dependent (so-called anomalous) contribution to the particle velocity and the presence of Zeeman field reduces the number of integrals of motion. By using analytical and numerical arguments, the conditions of chaos emergence are studied and the dynamics both in the regular and chaotic regimes is reported. The critical dependence of the dynamic patterns (such as the chaotic regime onset) on small variations in the initial conditions and problem parameters, that is the SOC and/or Zeeman constants, is observed. The transition to chaotic regime is further verified by the analysis of phase portraits as well as Lyapunov exponents spectrum. The considered chaotic behavior can occur in solid state systems, weakly relativistic plasmas, and cold atomic gases with synthetic gauge fields and spin-related couplings.     

Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling

We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z2 topological indices. According to the Z2 topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states.     

The Gravitational Wave Background from Coalescing Compact Binaries: A New Method

Gravitational waves are perturbations in the space-time that propagate at the speed of light. The study of such phenomenon is interesting because many cosmological processes and astrophysical objects, such as binary systems, are potential sources of gravitational radiation and can have their emissions detected in the near future by the next generation of interferometric detectors. Concerning the astrophysical objects, an interesting case is when there are several sources emitting in such a way that there is a superposition of signals, resulting in a smooth spectrum which spans a wide range of frequencies, the so-called stochastic background. In this paper, we are concerned with the stochastic backgrounds generated by compact binaries (i.e., binary systems formed by neutron stars and black holes) in the coalescing phase. In particular, we obtain such backgrounds by employing a new method developed in our previous studies.     

Topological Insulators on the Ruby Lattice with Rashba Spin-Orbit Coupling

We investigate a tight-binding model of the ruby lattice with Rashba spin-orbit coupling. We calculate the band structure of the lattice and evaluate the Z₂ topological indices. According to the Z₂ topological indices and the band structure, we present the phase diagrams of the lattice with different filling fractions. We find that topological insulators occur in some range of parameters at 1/6, 1/3, 1/2, 2/3 and 5/6 filling fractions. We analyze and discuss the characteristics of these topological insulators and their edge states.     

Effect of Anisotropic Spin-Orbit Coupling on the Ground State of Bose-Einstein Condensate in an External Potential

Spin-orbit coupled Bosonic atoms confined in external potentials open up new avenues for quantumstate manipulation and will contribute to the design and exploration of novel quantum devices.Here we consider a quasi-two-dimensional spin-orbit coupled Bose-Einstein condensate confined in an external harmonic potential,with emphasis on the effects of anisotropic spin-orbit coupling on the equilibrium ground-state structure of such a system.For the cases with spin-orbit coupling solely in x- or y-axis direction,the ground-state structure can develop to the well-known standing wave phase,in which the two components always form an alternative density arrangement.For a two-dimensional anisotropic spin-orbit coupling,the separated lumps first become bend,then form two rows of stripe structure along y direction with further increasing the strength of spin-orbit coupling in x-direction.Furthermore,the distance between these two rows of stripe structure is also investigated in detail.     

Dynamics of High-Order Spin-Orbit Couplings about Linear Momenta in Compact Binary Systems

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.     

Perturbative Handling of the Renner-Teller Effect and Spin-Orbit Coupling in Δ Electronic States of Triatomic and Tetra-atomic Molecules

Second-order perturbative formulae for handling the Renner-Teller effect combined with the spin-orbit coupling in Δ electronic states of triatomic and symmetric (ABBA-type) tetra-atomic molecules with linear equilibrium geometry are derived via two schemes for partition of the model Hamiltonian. The formulae for triatomic molecules are employed to compute the spectrum of the X⁵Δ_g state of FeH₂. The parameters entering the model Hamiltonian are generated by means of ab initio calculations.     

Perturbative Handling of the Renner-Teller Effect and Spin-Orbit Coupling in Π Electronic States of Triatomic and Tetra-atomic Molecules

Second-order perturbative formulae for handling the Renner-Teller effect combined with the spin-orbit coupling in Π electronic states of triatomic and symmetric (ABBA-type) tetra-atomic molecules with linear equilibrium geometry are derived. Two schemes for partition of the model Hamiltonian are employed: In the first the spin-orbit coupling term is treated as a perturbation, in the second it is included in the zeroth-order Hamiltonian. It is demonstrated that both approaches lead to the same results when the spin-orbit coupling constant is small compared to the bending frequency, but much larger than the splitting of potential surfaces upon bending. The perturbative formulae derived for tetra-atomic molecules are used to compute the spectrum of the X²Π_u state of the acetylene ion, employing the parameters obtained in ab initio calculations. The results are compared with those generated in corresponding variational computations.     

相对论平均场理论中的张量项对自旋-轨道劈裂的影响

在相对论平均场理论中引入同位旋标量-矢量介子ω张量项, 以²⁰⁸Pb为例,研究了张量项对原子核平均势场、介子场、自旋-轨道耦合势、单粒子能级的自旋-轨道劈裂和原子核壳层结构等的影响.结果发现张量项对核子平均势的影响主要表现在原子核的表面.随着张量耦合强度的增加, 自旋-轨道耦合势增强,单粒子能级的自旋-轨道劈裂增大,从而导致原子核单粒子能级的壳层结构发生很大变化,传统幻数所对应的主壳消失, 新的主壳出现.     

Effects of Rashba Spin-Orbit Coupling on the Anisotropic Magneto Resistance in Domain Wall

The present paper, based on semi-classical Boltzmann equation, aims to investigate the effects of Rashba and Dresselhaus spin orbit interaction and impurities on domain wall anisotropic magneto resistance. It has been shown that the mentioned effects play a remarkable role in anisotropic magneto resistance of electron current in domain walls. It was also concluded that while an increase in Rashba coupling strength can effectively enhance anisotropic magneto resistance of the domain wall, an increase in the wave-vector and exchange interaction leads to their decrease.