An Almost—Poisson Structure for Autoparallels on Riemann—Cartan Spacetime

An almost-Poisson bracket is constructed for the regular Hamiltonian formulation of autoparallels on Riemann-Cartan spacetime, which is considered to be the motion trajectory of spinless particles in the space. This bracket satisfies the usual properties of a Poisson bracket except for the Jacobi identity. There does not exist a usual Poisson structure for the system although a special Lagrangian can be found for the case that the contracted torsion tensor is a gradient of a scalar field and the traceless part is zero. The almost-Poisson bracket is decomposed into a sum of the usual Poisson bracket and a “Lie-Poisson“ bracket, which is applied to obtain a formula for the Jacobiizer and to decompose a non-Hamiltonian dynamical vector field for the system. The almost-Poisson structure is also globally formulated by means of a pseudo-symplectic two-form on the cotangent bundle to the spacetime manifold.     

Calibration error analysis of electro-optical detection systems

We present detailed analysis of calibration process error for electro-optical detection systems, which can be simplified as the plane rotation around a non-orthogonal axis. By means of octonions it firstly proves that the plane rotation around a non-orthogonal axis can be decomposed into rotations around two perpendicular axes. The rotation is further divided into three steps, and the calibration error is hence discussed and obtained. The simulation and test results indicate that there are large calibration errors in calibration process. The pointing error can be effectively improved after separating error components, which provides a more accurate set data for further comDensation.     

Nonholonomic mapping theory of autoparallel motions in Riemann-Cartan space

The method of nonholonomic mapping is utilized to construct a Riemann-Cartan space embedded into a known Riemann-Cartan space,which includes two special cases that a Weitzenbck space and a Riemann-Cartan space are respectively embedded into a Euclidean space and a Riemann space.By means of this mapping theory,the nonholonomic corresponding relation between the autoparallels of two Riemman-Cartan spaces is investigated.In particular,an autoparallel in a Riemann-Cartan space can be mapped into a geodesic line in a Riemann space and an autoparallel in Weitzenbck space be mapped into a geodesic line in Euclidean space.Based on the Lagrange-d'Alembert principle,the equations of motion for dynamical systems in Riemman-Cartan space should be autoparallel equations of the space.As applications,the problem of autoparallel motion of spinless particles,Chaplygin's nonholonomic systems and a rigid body rotating with a fixed point are investigated in space with torsion.     

Fractional Fourier transform of apertured paraboloid refracting system

The limitation of paraxial condition of paraboloid refracting system in performing fractional Fourier trans-form acts like an aperture, which makes the system different from ideal systems. With aperture expanded as the sum of finite complex Gaussian terms, a more practical approximate analytical solution of frac-tional Fourier transform of Gaussian beam in an apertured paraboloid refracting system is obtained and also numerical investigation is presented. Complicated and practical fractional Fourier transform systems can be constructed by cascading several apertured paraboloid refracting systems which are the simplest and the most basic units for performing more precise transform.     

Symmetric and Anti-Symmetric Lamb Waves in a Two-Dimensional Phononic Crystal Plate

It is weft known that Lamb waves in a plate with a mirror plane can be separated into two uncoupled sets： symmetric and anti-symmetric modes. Based on this property, we present a revised plane wave expansion method （PWE） to calculate the band structure of a phononie crystal （PC） plate with a mirror plane. The developed PWE method can be used to calculate the band structure of symmetric and anti-symmetric modes separately, by which the depending relationship between the partial acoustic band gap （PABG）, which belongs to the symmetric and anti-symmetric modes alternatively, and the position of the scatterers can be determined. As an example of its application, the band structure of the Lamb modes in a two-dimensional PC plate with two layers of void circular inclusions is investigated. The results show that the band structure for the symmetric and anti-symmetric modes can be changed by the position of the scatterers drastically, and larger PABGs will be opened when the scatterers are inserted into the area of the plate, where the elastic potential energy is concentrated.     

Conductance in an Aharonov-Bohm Interferometer with Parallel-Coupled Double Dots

We present a theoretical study of the conductance in an Aharonov-Bohm interferometer containing two coupled quantum dots. The interdot tunneling divides the interferometer into two coupled subrings, where opposite magnetic fluxes are threaded separately while the net flux is kept zero. Using the Green function technique we derive the expression of the linear conductance. It is found that the Aharonov-Bohm effect still exists, and when the level of each dot is aligned, the exchange of the Fano and Breit-Wigner resonances in the conductance can be achieved by tuning the magnetic flux. When the two levels are mismatched the exchange may not happen. Further, for some specific asymmetric systems where the coupling strengths between the two dots and the leads are not equal, the flux can change the Fano resonance into an antiresonance, which is absent in symmetric systems.     

A Test of Two-photon Entanglement in Spatial Modes

Two schemes for unconditionally generating two-mode motional entanglement for two ions trapped in a cavity have been proposed. The first scheme is： the vibrational mode of the first ion is coupled to the cavity field via a linear-mixing interaction and the vibrational mode of the second ion is coupled to the cavity field via an effective parametric interaction respectively. The two ions can evolve into a steady-state two-mode entangled Gaussian state, which is a mixed state. The second scheme is. the two ions are trapped in a bimodal cavity, through choosing the frequency and intensity of the driven lasers, the two ions can evolve into a two-mode entangled state, which is a pure state.     

Multiplexing Chaotic Signals Generated by Colpitts Oscillator and Chua Circuit Using Dual Synchronization

We demonstrate multiplexing chaotic signals generated by two totally different dynamic systems (one is a Colpitts oscillator and the other is a Chua circuit) using dual synchronization and propose a method to select the proper coupling parameters. In the response systems, the cross coupling method is used, in which the voltage difference between the sum of two master oscillators and one slave oscillator is converted to current and then feed into the other slave oscillator. The result in this letter offers a potential multiuser coherent chaotic communication scheme where different chaotic oscillators can be used in one system.     

Two-Step Deterministic Remote Preparation of an Arbitrary Quantum State

We present a two-step deterministic remote state preparation protocol for an arbitrary qubit with the aid of a three-particle Greenberger-Horne-Zeilinger state. Generalization of this protocol for higher-dimensional Hilbert space systems among three parties is also given. We show that only single-particle yon Neumann measurements, local operations, and classical communication are necessary. Moreover, since the overall information of the quantum state can be divided into two different pieces, which may be at different locations, this protocol may be useful in the quantum information field.     

Quantifying quantum non-Markovianity via max-relative entropy

We investigate the non-Markovian behavior in open quantum systems from an information-theoretic perspective. Our main tool is the max-relative entropy, which quantifies the maximum probability with which a state ρ can appear in a convex decomposition of a state σ. This operational interpretation provides a new view for the non-Markovian process.We also find that max-relative entropy can be the witness and measure of non-Markovian processes. As applications, some examples are also given and compared with other measures in this paper.     

Singular reduction of implicit Hamiltonian systems

This paper develops the theory of singular reduction for implicit Hamiltonian systems admitting a symmetry Lie group. The reduction is performed at a singular value of the momentum map. This leads to a singular reduced topological space which is not a smooth manifold. A topological Dirac structure on this space is defined in terms of a generalized Poisson bracket and a vector space of derivations, both being defined on a set of smooth functions. A corresponding Hamiltonian formalism is described. It is shown that solutions of the original system descend to solutions of the reduced system. Finally, if the generalized Poisson bracket is nondegenerate, then the singular reduced space can be decomposed into a set of smooth manifolds called pieces. The singular reduced system restricts to a regular reduced implicit Hamiltonian system on each of these pieces. The results in this paper naturally extend the singular reduction theory as previously developed for symplectic or Poisson Hamiltonian systems.     

Hamiltonian systems on fibered manifolds

We offer a new geometric theory of Hamiltonian systems with an infinite number of degrees of freedom in which the Hamiltonian operators are nonlinear differential operators on fields. The Poisson bracket is carried into the vertical bracket by the mapping between functionals and Hamitonian operators which is established by a Hamiltonian structure.     

Gauge-free Hamiltonian structure of the spin Maxwell-Vlasov equations

We derive the gauge-free Hamiltonian structure of an extended kinetic theory, for which the intrinsic spin of the particles is taken into account. Such a semi-classical theory can be of interest for describing, e.g., strongly magnetized plasma systems. We find that it is possible to construct a generalized noncanonical Poisson bracket on the extended phase space, and discuss the implications of our findings, including stability of monotonic equilibria.     

Incomplete Dirac reduction of constrained Hamiltonian systems

First-class constraints constitute a potential obstacle to the computation of a Poisson bracket in Dirac’s theory of constrained Hamiltonian systems. Using the pseudoinverse instead of the inverse of the matrix defined by the Poisson brackets between the constraints, we show that a Dirac–Poisson bracket can be constructed, even if it corresponds to an incomplete reduction of the original Hamiltonian system. The uniqueness of Dirac brackets is discussed. The relevance of this procedure for infinite dimensional Hamiltonian systems is exemplified.     

完全可积的非线性方程建立哈密顿理论的一般方法和对SG方程应用

完全可积的非线性方程的单式矩阵的泊松括号已知可以表为对x的积分，指出被积函数一定 可以表为约斯特解对的直积的线性组合的微分，并可由直积矩阵相应元的对比确定组合系数 .从而解决了建立非线性方程哈密顿理论的一般方法.由于实验室系中的SG方程，相应的表述 异常复杂，所以以它为例来说明方法的实质.同时由于现有的相关工作违反了泊松括号同时 性的要求，给出了必要的改正. 关键词： 非线性方程 哈密顿理论 孤子     

The Lie-Poisson structure of integrable classical non-linear sigma models

The canonical structure of classical non-linear sigma models on Riemannian symmetric spaces, which constitute the most general class of classical non-linear sigma models known to be integrable, is shown to be governed by a fundamental Poisson bracket relation that fits into ther-s-matrix formalism for non-ultralocal integrable models first discussed by Maillet. The matricesr ands are computed explicitly and, being field dependent, satisfy fundamental Poisson bracket relations of their own, which can be expressed in terms of a new numerical matrixc. It is proposed that all these Poisson brackets taken together are, representation conditions for a new kind of algebra which, for this class of models, replaces the classical Yang-Baxter algebra governing the canonical structure of ultralocal models. The Poisson brackets for the transition matrices are also computed, and the notorious regularization problem associated with the definition of the Poisson brackets for the monodromy matrices is discussed.Suported by the Deutsche Forschungsgemeinschaft, Contract No. Ro 864/1-1Supported by the Studienstiftung des Deutschen Volkes     

Covariant description of Hamiltonian form for field dynamics

Hamiltonian form of field dynamics is developed on a space-like hypersurface in space-time. A covariant Poisson bracket on the space-like hypersurface is defined and it plays a key role to describe every algebraic relation into a covariant form. It is shown that the Poisson bracket has the same symplectic structure that was brought in the covariant symplectic approach. An identity invariant under the canonical transformations is obtained. The identity follows a canonical equation in which the interaction Hamiltonian density generates a deformation of the space-like hypersurface. The equation just corresponds to the Yang-Feldman equation in the Heisenberg pictures in quantum field theory. By converting the covariant Poisson bracket on the space-like hypersurface to four-dimensional commutator, we can pass over to quantum field theory in the Heisenberg picture without spoiling the explicit relativistic covariance. As an example the canonical QCD is displayed in a covariant way on a space-like hypersurface.     

On deformations of quasi-Miura transformations and the Dubrovin–Zhang bracket

In our recent paper, we proved the polynomiality of a Poisson bracket for a class of infinite-dimensional Hamiltonian systems of partial differential equations (PDEs) associated to semi-simple Frobenius structures. In the conformal (homogeneous) case, these systems are exactly the hierarchies of Dubrovin and Zhang, and the bracket is the first Poisson structure of their hierarchy.     

Permutation Representations Defined by G-Clusters with Application to Quasicrystals

Starting from each finite union of orbits (called G- cluster) of an R-irreducible orthogonal representation of a finite group G, we define a representation of G in a higher-dimensional space (called permutation representation), and we prove that it can be decomposed into an orthogonal sum of two representations such that one of them is equivalent to the initial representation. This decomposition allows us to use the strip projection method and to obtain some patterns useful in quasicrystal physics. We show that certain self-similarities of such a pattern can be obtained by using the decomposition into R-irreducible components of the corresponding permutation representation, and we present two examples.     

Geometric Constructions of Toda and Periodic Toda Chains

A geometrical and neat framework is established to derive both Toda and periodic Toda systems from the geodesics of symmetric spaces. The counterpart of the Iwasawa decomposition of a semisimple Cie group in the case of a loop group is also derived. By these, we get a Lie su balgebra with Lie bracket [,]R, and the corresponding Poisson bracket {,}R gives the Hamiltonian form of the periodic Toda chains.