In electronic transport through mesoscopic systems, the various resonances in quantities such as conductance and scattering cross sections are characterized by the universal Fano formula. Does a similar formula exist for spin transport? We provide an affirmative answer by deriving a Fano formula to characterize the resonances associated with two fundamental quantities underlying spin transport: spin-resolved transmission and spin polarization vector. In particular, we generalize the conventional Green's function formalism to spin transport and use the Fisher-Lee relation to obtain the spin resolved transmission matrix, which enables the spin polarization vector to be calculated, leading to a universal Fano formula for spin resonances. Particularly, the theoretically obtained resonance width depends on the nature of the classical dynamics as determined by the geometric shape of the dot. We explicitly demonstrate this fact and argue that it can be exploited to smooth out or even eliminate Fano spin resonances by manipulating the classical dynamics, which can be realized by applying or withdrawing a properly designed local gate potential. Likewise, modulating the classical dynamics in a different way can enhance the resonance. This is of particular importance in the design of electronic switches that can control spin orientation of the electrons associated with the output current through weakening or enhancement of a Fano resonance, which are a key component in spintronics.

The role of classical dynamics in spin transport is an intriguing problem from the point of view of classical-quantum correspondence, as spin is a purely relativistic quantum mechanical variable with no classical counterpart. Nevertheless, due to spin-orbit coupling (generally referred to as the relativistic interaction of a particle's spin with its motion inside a potential) and because the orbital motion does have a classical correspondence, the nature of the classical dynamics can affect spin. A basic transport structure is quantum dots, whose geometrical shape can be chosen to lead to characteristically distinct classical behaviors ranging from integrable dynamics to chaos. Whether and how classical chaos can affect spin transport and if the effect can be exploited for applications in spintronics are thus issues of both fundamental and practical interest. Here we report results from systematic, full quantum computations of spin transport through quantum dots hosting different types of classical dynamics. Our main finding is that chaos can play orthogonal roles in affecting spin polarization, depending on the relative strength of the spin-orbit coupling. For weak coupling with the characteristic interaction length much larger than the system size, chaos can be beneficial to preserving spin polarization. In the strong coupling regime where the interaction length is smaller than the system dimension, chaos typically destroys spin polarization. We develop a semiclassical theory to understand these phenomena and point out their implications and potential applications in developing spintronic devices.

For a quantum system with multiple degrees of freedom or subspaces, loss of coherence in a certain subspace is intimately related to the enhancement of entanglement between this subspace and another one. We investigate intra-particle entanglement in two-dimensional mesoscopic systems, where an electron has both spin and orbital degrees of freedom and the interaction between them is enabled by Rashba type of spin–orbit coupling. The geometric shape of the scattering region can be adjusted to produce a continuous spectrum of classical dynamics with different degree of chaos. Focusing on the spin degree of freedom in the weak spin–orbit coupling regime, we find that classical chaos can significantly enhance spin–orbit entanglement at the expense of spin coherence. Our finding that classical chaos can be beneficial to intra-particle entanglement may have potential applications such as enhancing the bandwidth of quantum communications.

For an industrial robots with unknown parameters, on the basis of preliminary measurement and data of the Cartesian and joints coordinates which are shown on the FlexPendant, the kinematic parameters is identified by using genetic algorithms and accurate kinematics modeling of the robot is established. Experimental data could prove the validity of this method.

Based on the characteristic that the change of the space posture will be a great influence on the error in the operating end when the articulated robot is used for cutting,in the case of the robot structure and the the cutting load in the operating end certain, based on the stiffness model of the robot system ,the paper makes the deformation of the operating end of the robot as the objective function with the genetic algorithms to optimize the space position of the operational mission of the robot, finally verify it with examples.