静电分析器非线性轨迹的Lie代数分析

介绍了Lie代数的方法，用Lie代数方法分析了静电分析器对束流传输过程的非线性影响，其计算结果分析到三级近似. 首先给出了静电分析器的哈密顿函数，然后将哈密顿函数展开为齐次多项式的和，再求Lie映射，最后得到粒子轨迹各级近似解.     

Fractional standard map

Properties of the phase space of the standard map with memory are investigated. This map was obtained from a kicked fractional differential equation. Depending on the value of the map parameter and the fractional order of the derivative in the original differential equation, this nonlinear dynamical system demonstrates attractors (fixed points, stable periodic trajectories, slow converging and slow diverging trajectories, ballistic trajectories, and fractal-like structures) and/or chaotic trajectories. At least one type of fractal-like sticky attractors in the chaotic sea was observed.     

A Very Smooth Ride in a Rough Sea

It has been known for some time that a 3D incompressible Euler flow that has initially a barely smooth velocity field nonetheless has Lagrangian fluid particle trajectories that are analytic in time for at least a finite time Serfati (C. R. Acad. Sci. Paris Série I 320:175–180, 1995), Shnirelman (Glob. Stoch. Anal., http://arxiv.org/abs/1205.5837v1, 2012). Here an elementary derivation is given, based on Cauchy’s form of the Euler equations in Lagrangian coordinates. This form implies simple recurrence relations among the time-Taylor coefficients of the Lagrangian map, used here to derive bounds for the C ^1,γ Hölder norms of the coefficients and infer temporal analyticity of Lagrangian trajectories when the initial velocity is C ^1,γ.     

Supercritical ordered trajectories with quadratically irrational winding number

The dynamics of the circle map is studied in the supercritical regime where the map is not invertible and thus the trajectory elements are clustered on the circle. Existence of a simple ordering structure is established for trajectories with arbitrary irrational winding number. A previously developed formalism is then generalized to predict the trajectories when the winding number is quadratically irrational. Explicit results are given for a simple case.     

Towards a general framework for fast and feasible k-space trajectories for MRI based on projection methods

The design of feasible trajectories to traverse the k-space for sampling in magnetic resonance imaging (MRI) is important while considering ways to reduce the scan time. Over the recent years, non-Cartesian trajectories have been observed to result in benign artifacts and being less sensitive to motion. In this paper, we propose a generalized framework that encompasses projection-based methods to generate feasible non-Cartesian k-space trajectories. This framework allows to construct feasible trajectories from both random or structured initial trajectories, e.g., based on the traveling salesman problem (TSP). We evaluate the performance of the proposed methods by simulating the reconstruction of 128 × 128 and 256 × 256 phantom and brain MRI images in terms of structural similarity (SSIM) index and peak signal-to-noise ratio (PSNR) using compressed sensing techniques. It is observed that the TSP-based trajectories from the proposed projection method with constant acceleration parameterization (CAP) result in better reconstruction compared to the projection method with constant velocity parameterization (CVP) and this for a similar read-out time. Further, random-like trajectories are observed to be better than TSP-based trajectories as they reduce the read-out time while providing better reconstruction quality. A reduction in read-out time by upto 67% is achieved using the proposed projection with permutation (PP) method.     

Baryon trajectories revisited

Various properties of baryon trajectories are re-examined in the light of the latest data: in particular we study trajectory assignments of the 1982 baryon resonance data and evaluate effective trajectories for backward πN scattering incorporating FNAL data. We find that all of the information is consistent with trajectories linear inu, withF/D ratios constant along the trajectories and parity doublets absent. We find that exchange degeneracy (EXD) is good for Λ and Σ trajectories and residues and shed some qualitative light on the systematics of EXD breaking.     

Bipolarons and polarons in the Holstein-Hubbard model: analogies and differences

We consider a simple model of spring-mass block placed over a constant velocity v rolling plate. The map of the dynamic is presented in the (v,r) space where r accounts for the possible variation of the periodic shape profile of the rolling carpet. In order to characterize each type of motion, we found that evaluating the area of the phase space trajectories is more relevant than attempting on one hand, to solve analytically the asymptotic behavior, or on the other hand, to obtain an equivalent of the entropy and the free energy. First-order transition reveals to be the characteristic route from one type of motion to another. Later, we investigate the influence of the classical TMD¹ and TLCD² on the dynamic of this mass. Moreover, we numerically study the effects of a modified TMD. Reduced order parameter provides a quick overview of the whole system than phase space representations and bifurcation diagrams. Comparison of performances in the (v,r) space is made. It reveals the efficiency of the modified TMD. It comes out that the new TMD we designed stabilizes the system better than the two above control systems.     

Spectroscopy and Regge trajectories of heavy quarkonia in the relativistic quark model

The mass spectra of charmonia and bottomonia are calculated in the framework of the relativistic quark model up to high orbital and radial excitations. The Regge trajectories of heavy quarkonia are constructed both in the (J,M ²) and (n _r ,M ²) planes, where J is the total angular momentum and nr is the radial quantum number. All daughter trajectories turn out to be almost linear and parallel, while parent trajectories exhibit some nonlinearity. Such nonlinearity occurs only in the vicinity of ground states and few lowest excitations and is more pronounced for bottomonia, while it is only marginal for charmonia. The obtained results are compared with available experimental data, and a possible interpretation of the new charmonium-like states above open charm production threshold is discussed.     

Singularities of zero trajectories of scattering amplitudes

We discuss the possible types of singularities of zero trajectories of scattering amplitudes and give examples from πN scattering. Special emphasis is placed on the branch points of the zero trajectories that lie close to the physical region. Their appearance is related to small but typical deviations from the zero pattern predicted by dual models. We show how a study of the behaviour of the zero trajectories in the neighbourhood of such points can be used to reduce the reflection ambiguity of phase shift analysis.     

Possible phenomenological implications of the new trajectories on the pion trajectory

We discuss possible phenomenological consequences of the new Regge trajectories recently discovered in the conventional dual model (CDM) and the Neveu-Schwarz model (NSM). The contributions of the new trajectories to the scattering amplitude dominate at large enough momentum transfers in the multi-Regge limit and it is shown that the β_π trajectory of the NSM should be the most easy to detect experimentally.     

Off lattice simulations of cluster-cluster aggregation in dimensions 2–6

Cluster-cluster aggregation has been simulated in dimensions two to six using both linear and brownian cluster trajectories. Relatively efficient off lattice algorithms have allowed large clusters to be generated and values for the fractal dimensionalities of the aggregates have been obtained without finite concentration effects. The values for the fractal dimensionality are in good aggreement with lattice model simulations for euclidean dimensionalities 2–4. The effective dimensionality (D_β) obtained from the dependence of the radius of gyration on cluster size increases with increasing cluster size for all of our models (particularly for d ≥ 4). For clusters in the accessible size range (up to 10³-10⁴) D_β is slightly larger for cluster-cluster aggregation via linear trajectories than for brownian trajectories. For cluster-cluster aggregation via brownian trajectories, the limiting (large cluster size) fractal dimensionality is estimated to be 1.46 ± 0.04 for d=2,1.82 ± 0.10 for d = 3, 2.10 ± 0.15 for d = 4, 2.35 ± 0.15 for d = 4, 2.65 ± 0.25 for d = 6. For cluster- cluster aggregation via linear trajectories, the limiting fractal dimensionality is estimated to be 1.55 ± 0.04 for d = 2, 1.91 ± 0.10 for d = 3≥ 2.5 ± 0.06 for d = 5 and ≥2.64 ± 0.05 for d = 6.     

Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems

For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories, as well as the extremal trajectories themselves. Upper bounds on time averages can be proved a priori using auxiliary functions, the optimal choice of which is a convex optimization problem. We prove that the problems of finding maximal trajectories and minimal auxiliary functions are strongly dual. Thus, auxiliary functions provide arbitrarily sharp upper bounds on time averages. Moreover, any nearly minimal auxiliary function provides phase space volumes in which all nearly maximal trajectories are guaranteed to lie. For polynomial equations, auxiliary functions can be constructed by semidefinite programming, which we illustrate using the Lorenz system.     

Quantum particle trajectories and geometric phase

Particle trajectories are defined as integrable dx _μ dp ^μ=0 paths in projective space. Quantum states evolving on such trajectories, open or closed, do not delocalize in (x, p) projection, the phase associated with the trajectories related to the geometric (Berry) phase and the classical mechanics action. Properties at high energies of the states evolving on particle trajectories are discussed.     

Traffic noise and the hyperbolic plane

We consider the problem of sound propagation in a wind. We note that the rays, as in the absence of a wind, are given by Fermat’s principle and show how to map them to the trajectories of a charged particle moving in a magnetic field on a curved space. For the specific case of sound propagating in a stratified atmosphere with a small wind speed, we show that the corresponding particle moves in a constant magnetic field on the hyperbolic plane. In this way, we give a simple ‘straightedge and compass’ method to estimate the intensity of sound upwind and downwind. We construct Mach envelopes for moving sources. Finally, we relate the problem to that of finding null geodesics in a squashed anti-de Sitter spacetime and discuss the SO(3,1)×R symmetry of the problem from this point of view.     

Flavouring the Gribov process

The exchange of flavour carrying trajectories is studied in the non-covariant parton interpretation of reggeon field theory. While pomeron exchange is described by wee partondensities, i.e. diagonal elements of the density matrix of a fast hadron, meson exchange is described by density matrix elements which are diagonal in parton number but off-diagonal in flavour. The reggeon field theory “hamiltonian” describes a markoffian evolution of this block-diagonal density matrix during a boost. This interpretation is possible both if there are two distinctf and ? trajectories and in case of ? identity. The meson trajectories are superpositions of odd and even signature trajectories.     

From Open Quantum Systems to Open Quantum Maps

For a class of quantized open chaotic systems satisfying a natural dynamical assumption we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is of finite dimensional operators obtained by quantizing the Poincaré map associated with the flow near the set of trapped trajectories.     

Symbolic Dynamics and Topological Entropy of Henon Map

By using the method with which the trajectories of dissipative maps can be derived from the Hamiltonian, we study the symbolic dynamics of Henon map and its relation with the symbolic dynamics of unimodal map, and compute the topological entropy as a function of the parameter a and b. Finally, the boundary of the region where the topological entropy exists on the parameter plane is given.     

Quantum transport in lattices of coupled electronic billiards

A new system with dynamic chaos—2D lattice of single Sinai billiards coupled through quantum dots—is studied experimentally. Localization in such a system was found to be substantially suppressed, because the characteristic size of the billiard for g≤1 (g is conductance measured in e ₂/h units) is the localization length rather than the de Broglie wavelength of an electron, as in the usual 2D electron system. Lattice ballistic effects (commensurate peaks in the magnetoresistance) for g?1, as well as extremely large magnetoresistance caused by the interference in chaotic electron trajectories, were found. Thus, this system is shown to be characterized by simultaneous existence of effects that are inherent in order (commensurate peaks of magnetoresistance), disorder (percolation charge transport), and chaos (weak localization in chaotic electron trajectories).     

Reverberation in a trapezoidal room

The problem of sound decay in a trapezoidal room with a nonuniform distribution of wall absorption is considered. It is shown that the sound energy decay may be either anomalously slow, obeying the law ～1/t, or fast, obeying an exponential law. It is found that the type of the decay law depends on the presence of stable ray trajectories in the room. Manifestations of stable ray trajectories in both laboratory and field experiments are demonstrated.