Numerical Study of the Kneading Theory for the Lorenz Model

To a good approximation, the Lorenz attractor in the Poincark section may be viewed as a one-dimensional object. A family of maps proposed by Sparrow models the Lorenz system very well. Such maps are numerically constructed. Under the guide of the kneading theory for the maps a numerical study of the Lorenz system is conducted.     

TurboDisc MOCVD设备的理论和应用:流体动力学方法

报道了EMCORE公司的旋转盘反应器,或TurboDisc反应器,这是一种带有旋转盘的立式反应器.衬底片放置在高速旋转的盘上并被加热到合适的生长温度.反应物在初始阶段因高速旋转盘的牵引力被竖直向下地泵入,然后偏斜形成一个与衬底片托盘平行的流动区域.在"GaNzilla”,EMCORE公司的一种新型325mm的GaN生产反应器中外延生长了GaN材料.为在蓝宝石衬底上得到高质量的GaN,采用高的生长压力和高旋转速度,可以在这种旋转盘反应器中实现必要的生长条件.还对p-GaN,InGaN,InGaN多量子阱,以及LED器件进行了类似的实验,都能获得最佳的生长条件.     

Stochastic Perturbations to Dynamical Systems: A Response Theory Approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.     

The Theory of Equivalent Lagrangians Revisited: A Symplectic Approach

The existence of different Lagrangian functions for the same dynamical vector field is studied using the methods of symplectic mechanics. The concept of Lagrangeoid transformation is introduced and its relation with the theory of bi-Hamiltonian systems analyzed. The relation between equivalent (non-gauge equivalent) Lagrangian formulations in TQ and their associated Hamiltonian dynamical systems in T*Q is developed and, finally, the Noether theorem is considered.     

A Kinetic Theory Approach to Quantum Gravity

We describe a kinetic theory approach to quantum gravity by which we mean a theory of the microscopic structure of space-time, not a theory obtained by quantizing general relativity. A figurative conception of this program is like building a ladder with two knotty poles: quantum matter field on the right and space-time on the left. Each rung connecting the corresponding knots represents a distinct level of structure. The lowest rung is hydrodynamics and general relativity; the next rung is semiclassical gravity, with the expectation value of quantum fields acting as source in the semiclassical Einstein equation. We recall how ideas from the statistical mechanics of interacting quantum fields helped us identify the existence of noise in the matter field and its effect on metric fluctuations, leading to the establishment of the third rung: stochastic gravity, described by the Einstein–Langevin equation. Our pathway from stochastic to quantum gravity is via the correlation hierarchy of noise and induced metric fluctuations. Three essential tasks beckon: (1) deduce the correlations of metric fluctuations from correlation noise in the matter field; (2) reconstituting quantum coherence—this is the reverse of decoherence—from these correlation functions; and (3) use the Boltzmann–Langevin equations to identify distinct collective variables depicting recognizable metastable structures in the kinetic and hydrodynamic regimes of quantum matter fields and how they demand of their corresponding space-time counterparts. This will give us a hierarchy of generalized stochastic equations—call them the Boltzmann–Einstein hierarchy of quantum gravity—for each level of space-time structure, from the the macroscopic (general relativity) through the mesoscopic (stochastic gravity) to the microscopic (quantum gravity).     

A Unified Algebraic Approach to Quantum Theory

Conventional approaches to quantum mechanics are essentially dualistic. This is reflected in the fact that their mathematical formulation is based on two distinct mathematical structures: the algebra of dynamical variables (observables) and the vector space of state vectors. In contrast, coherent interpretations of quantum mechanics highlight the fact that quantum phenomena must be considered as undivided wholes. Here, we discuss a purely algebraic formulation of quantum mechanics. This formulation does not require the specification of a space of state vectors; rather, the required vector spaces can be identified as substructures in the algebra of dynamical variables (suitably extended for bosonic systems). This formulation of quantum mechanics captures the undivided wholeness characteristic of quantum phenomena, and provides insight into their characteristic nonseparability and nonlocality. The interpretation of the algebraic formulation in terms of quantum process is discussed.     

Functorial geometric quantization and Van Hove's theorem

A classical theorem of Van Hove in conjunction with a formalism developed by Weinstein is used to prove that a quantization functor does not exist. In the proof a category of exact transverse Lagrangian submanifolds is introduced which provides a functorial link between Schrödinger quantization and the prequantization/polarization theory of Kostant and Souriau.     

Towards a Kneading Theory for Lozi Mappings. II: Monotonicity of the Topological Entropy and Hausdorff Dimension of Attractors

We construct a kneading theory à la Milnor–Thurston for Lozi mappings (piecewise affine homeomorphisms of the plane). In the first article a two-dimensional analogue of the kneading sequence called the pruning pair is defined, and a topological model of a Lozi mapping is constructed in terms of the pruning pair only. As an application of this result, in the current paper we show the partial monotonicity of the topological entropy and of bifurcations for the Lozi family near horseshoes. Upper and lower bounds for the Hausdorff dimension of the Lozi attractor are also given in terms of parameters. Dédié au Professeur A. Douady pour son 60ème anniversaire Received: 1 September 1996 / Accepted: 16 April 1997     

Theory of Atom Optics: Feynman''s Path Integral Approach

The present theory of atom optics is established mainly on the Schr?dinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.     

Little-Group Approach to Gauge Theory

Factor representations of the nonsemisimpleE(2)-like little group for massless particles are usedto construct free gauge theories for arbitrary spin,which explicitly solves the dichotomy between the unitary requirement and the appearance of gaugedegrees of freedom. This conceptually new approach mayhelp us understand the deep relation between gaugetheory and space-time symmetry.     

Effective Mean-Field Theory Based on Cumulant Expansion: A New Approach Method Order by Order

We propose in this paper an effective mean-field theory, which makes the calculation for any observable being performed in a general form of cumulant expansion. The effective mean-field equation with reasonable physical annotation, which is obtained from the lower bound extreme value condition of free energy, can be applied to general statistic mechanics and Lagrangian quantum theory. By applying it to lattices, our theory, for various models containing nonuniform system and nonequilibrium phenomenon, can give a realistic scheme to study the nonperturbative effect order by order. As a testing example to two-dimensional Ising model, we obtain a result approaching the Onsager solution order by order.     

A Nonperturbative, Finite Particle Number Approach to Relativistic Scattering Theory

We present integral equations for the scattering amplitudes of three scalar particles, using the Faddeev channel decomposition, which can be readily extended to any finite number of particles of any helicity. The solution of these equations, which have been demonstrated to be calculable, provide a nonperturbative way of obtaining relativistic scattering amplitudes for any finite number of particles that are Lorentz invariant, unitary, cluster decomposable and reduce unambiguously in the nonrelativistic limit to the nonrelativistic Faddeev equations. The aim of this program is to develop equations which explicitly depend upon physically observable input variables, and do not require renormalization or dressing of these parameters to connect them to the boundary states. As a unitary, cluster decomposible, multichannel theory, physical systems whose constituents are confined can be readily described.     

Statistical Mechanics Approach to Coding Theory

We propose a method based on cluster expansion to study the optimal code with a given distance between codewords. Using this approach we find the Gilbert–Varshamov lower bound for the rate of largest code.     

Decoherence: A Closed-System Approach

The aim of this paper is to review a new perspective about decoherence, according to which formalisms originally devised to deal just with closed or open systems can be subsumed under a closed-system approach that generalizes the traditional account of the phenomenon. This new viewpoint dissolves certain conceptual difficulties of the orthodox open-system approach but, at the same time, shows that the openness of the quantum system is not the essential ingredient for decoherence, as commonly claimed. Moreover, when the behavior of a decoherent system is described from a closed-system perspective, the account of decoherence turns out to be more general than that supplied by the open-system approach, and the quantum-to-classical transition defines unequivocally the realm of classicality by identifying the observables with classical-like behavior.     

Theory of Atom Optics: Feynman’s Path Integral Approach

The present theory of atom optics is established mainly on the Schrödinger equations or the matrix mechanics equation. The authors present a new theoretical formulation of atom optics: Feynman’s path integral theory. Its advantage is that one can describe the diffraction and interference of atoms passing through slits (or grating), apertures, and standing wave laser field in Earth’s gravitational field by using a type of wave function and calculation is simple. For this reason, we derive the wave functions of particles in the following configurations: single slit (and slit with the van der Waals interaction), double slit, N slit, rectangular aperture, circular aperture, the Mach-Zehnder-type interferometer, the interferometer with the Raman beams, the Sagnac effect, the Aharonov-Casher effect, the Kapitza-Dirac diffraction effect, and the Aharonov-Bohm effect. The authors give a wave function of the state of particles on the screen in abovementioned configurations. Our formulas show good agreement with present experimental measurements.     

量子理论新方法研究光的双缝衍射

用量子理论新方法研究光的双缝衍射实验现象,首先用光的量子理论计算光在缝中双缝衍射的波函数,再由基尔霍夫定律计算光的衍射波函数,由衍射强度正比于衍射波函数模方,从而得到光双缝衍射强度的解析式,把量子理论计算结果和经典电磁理论计算结果以及与实验数据三者进行比较,发现量子理论结果与实验数据符合更好,而经典电磁理论计算结果与实验有一定偏差.从而说明量子理论更能精确解释光的衍射现象.该方法还可进一步研究光的单缝、多缝以及光栅衍射的实验现象.     

The Nonsymmetric Kaluza–Klein Theory and Modern Physics A Novel Approach

We consider in the paper the Nonsymmetric Kaluza–Klein Theory finding a condition for a color confinement in the theory. We consider also a Kerner–Wong–Kopczyński equation in this theory. The Nonsymmetric Kaluza–Klein Theory with a spontaneous symmetry breaking and Higgs' mechanism is examined. We find a mass spectrum for a broken gauge bosons and Higgs' particles. We derive a generalization of Kerner–Wong–Kopczyński equation in the presence of Higgs' field. A new term in the equation is a generalization of a Lorentz force term for a Higgs' field. We consider also a bosonic part of GSW (Glashow–Salam–Weinberg) model in our theory, getting masses for W, Z bosons and for a Higgs' boson agreed with an experiment. We consider Kerner–Wong–Kopczyński equation in GSW model obtaining some additional charges coupled to Higgs' field.