Statistical Theory of the Many-Body Nuclear System

A recently proposed statistical theory of the mean fields associated with the ground and excited collective states of a generic many-body system is extended by increasing the dimensions of the P-space. In applying the new framework to nuclear matter, in addition to the mean field energies we obtain their fluctuations as well, together with those of the wavefunctions, in first order of the expansion in the complexity of the Q-space states. The physics described by the latter is assumed to be random. To extract numerical predictions from our scheme we develop a schematic version of the approach, which, while much simplified, yields results of significance on the size of the error affecting the mean fields, on the magnitude of the residual effective interaction, on the ground state spectroscopic factor, and on the mixing occurring between the vectors spanning the P-space.     

Theory of electrodynamic levitation with a continuous sheet track — Part I

Exact analytical expressions for forces on moving rectangular current-carrying coils above and below an infinite conducting sheet track of arbitrary thickness are developed. These general expressions for the lift and drag forces acting on the excitation coils as functions of speed are investigated for normal flux, null flux and brake flux systems and discussed with the aid of numerical calculations. A concise parameter study is also made. The system velocity characteristics with constant load (technologically more relevant) are given for the first time for normal and null flux systems.     

Reduction of the Many-Body Problem and the Unified Theory for Nuclear Reaction

We reduce the many-body problem to a multi-channel few-body problem by the AGS method. The channels may be chosen according to the problem under consideration and the reduction is formally exact. For the nuclear reaction we may choose some one-body channels to represent compound nucleus and choose some two- or more-body channels to represent open reaction channels. We then apply formal collision theory to this multi-channel system. Direct reaction, resonant reaction and their interference emerge. There are also distortions of ingoing and outgoing waves in compound nucleus formation and decay respectively. The omission of all but one open channel leads to the optical model, and an incomplete consideration of the open channels may lead to a multi-channel generalization of the optical model. Nonnucleon degrees of freedom as well as relativity may be included in principle. The reaction induced by particles other than nuclei may be considered on the same footing.     

The Relativistic Many-Body Perturbation Treatment of the Long Range Part of the Nuclear Force

Based on the many-body perturbation theory and cloudy bag model, the long range part of the nuclbar force is discussed. The results show that it agrees with one-pion exchange-potential in respect of both the radial dependence and the strength.     

Chalcogenide glasses as a medium for controlling ultrashort IR pulses: Part I

Chalcogenide glasses are ideal materials for developing fiber lasers and amplifiers, remote sensors, high-speed switches, and other devices that operate in the IR range of 1–10 μm. The nonlinear refractive index of chalcogenide glasses may exceed that of quartz glass by a factor of 100–1200 or even more. The data on the dispersion properties of some chalcogenide glass compositions in the IR range are presented. The possibility of forming waveguide structures with specified dispersion properties (in particular with a fixed wavelength at which the group velocity dispersion is zero) from these glasses is numerically investigated. It is shown by the example of completely glassy periodic waveguide structures with planar geometry that the use of photonic band gap modes makes it possible the change the position of zero dispersion in a wide wavelength range. In the calculations the contrast of waveguide structures was varied using parameters of glasses of different composition.     

Massive Yang-Mills Field Theory with Conformal (Weyl) Invariance

A massive Yang-Mills field theory with the conformal (Weyl) invariance^[1] and gauge invariance is proposed. It involves the gravitational and various gauge interactions, in which all the mass terms appear as the uniform interactional form m(x) = KΦ(x). When the conformal and gauge symmetries are broken spontaneously, the Einstein gravitation emerges and all the fields obtain masses, this theory is renormalizable and unitary with the gravitation ignored. Finally we give a relation between the theory and the Higgs mechanism.     

Towards a Theory of Transition Paths

We construct a statistical theory of reactive trajectories between two pre-specified sets A and B, i.e. the portionsof the path of a Markov process during which the path makes a transition from A to B. This problem is relevant e.g. in the context of metastability, in which case the two sets A and B are metastable sets, though the formalism we propose is independent of any such assumptions on A and B. We show that various probability distributions on the reactive trajectories can be expressed in terms of the equilibrium distribution of the process and the so-called committor functions which give the probability that the process reaches first B before reaching A, either backward or forward in time. Using these objects, we obtain (i) the distribution of reactive trajectories, which gives the proportion of time reactive trajectories spend in sets outside of A and B; (ii) the hitting point distribution of the reactive trajectories on a surface, which measures where the reactive trajectories hit the surface when they cross it; (iii) the last hitting point distribution of the reactive trajectories on the surface; (iv) the probability current of reactive trajectories, the integral of which on a surface gives the net average flux of reactive trajectories across this surface; (v) the average frequency of reactive trajectories, which gives the average number of transitions between A and B per unit of time; and (vi) the traffic distribution of reactive trajectories, which gives some information about the regions the reactive trajectories visit regardless of the time they spend in these regions.     

Towards a Theory of Conservative Computing

We extend the notion of conservativeness, given by Fredkin and Toffoli in 1982, to generic gates whose input and output lines may assume a finite number d of truth values. A physical interpretation of conservativeness in terms of conservation of the energy associated to the data used during the computation is given. Moreover, we define conservative computations, and we show that they naturally induce a new NP-complete decision problem. Finally, we present a framework that can be used to explicit the movement of energy occurring during a computation, and we provide a quantum implementation of the primitives of such framework using creation and annihilation operators on the Hilbert space ℂ^d, where d is the number of energy levels considered in the framework.     

Towards a Local Hidden Variable Theory

A local hidden variable theory of quantum mechanics is formulated by adapting Gell-Mann and Hartle’s many-histories formulation. The resulting theory solves the measurement problem by exploiting the independence loophole in Bell’s theorem; it violates the independence of hidden variable values and measuring device settings. Although the theory is problematic in some respects, it provides a concrete example via which the tenability of this approach can be better evaluated.     

Parameter Invariance in Field Theory and the Hamiltonian Formalism

The deparametrization problem for parameter‐invariant Lagrangian densities defined over J¹(N, F), is solved in terms of a projection onto a suitable jet bundle. The Hamilton‐Cartan formalism for such Lagrangians is then introduced and the pre‐symplectic structure of such variational problems is proved to be projectable through the aforementioned projection. Specific examples with physical meaning are also analyzed. 1998 PACS codes. 02.20.Tw Infinite‐dimensional Lie groups, 02.30.Wd Calculus of variations and optimal control, 02.40.Ky Riemannian geometries, 02.40.Ma Global differential geometry, 02.40.Vh Global analysis and analysis on manifolds, 04.20.Fy Canonical formalism, Lagrangians, and variational principles, 11.10.Ef Lagrangian and Hamiltonian approach, 11.10.Kk Field theories in dimensions other than four, 11.25.Sq Nonperturbative techniques; string field theory. 1991 Mathematics Subject Classification. Primary: 58E30 Variational principles; Secondary: 53B20 Local Riemannian geometry, 58A20 Jets, 58E12 Applications to minimal surfaces (problems in two independent variables), 58G35 Invariance and symmetry properties, 81S10 Geometric quantization, symplectic methods, 83E30 String and superstring theories.     

One-Particle Distribution Functions and Thermodynamics of Crystals with Many-Body Forces. III. Perturbation Theory

The theory of crystalline state described in preceding papers is considered as a zeroth-order approximation. Statistical perturbation theory is used for the purpose of improving this approximation. The second-order corrections to the Helmholtz free energy and thermodynamic properties of strongly anharmonic crystals are derived. The properties of solid Ar, Kr, and Xe are calculated using various pair-potential functions in conjunction with the AXILROD -TELLER -MUTO three-body potential. The first quantum corrections are taken into account in the quasi-classical approximation. The result of computations are compared with the experimental data.     

On a condition characterizing the Lorentz and Galilei groups

We prove by topological and Lie group theoretical methods that, in the class of the subgroups of $\text{GL}\text{(n,}\text{R}\text{)(n ≥ 3)}$, the n-dimensional Lorentz and Galilei groups are characterized by a condition which is the n-dimensional generalization of an “isotropy of space axiom” previously introduced. The inclusion of the n = 3 case implies a complete solution for the hitherto unsolved problem of determining the subgroups of GL(3, R) compatible with the three-dimensional isotropy condition.     

单壁碳纳米管中暗激子变亮的多体格林函数理论研究

本文发现了吸附在碳纳米管外壁和管内的有机分子可以调控碳纳米管的光学性质. 本文以手性为(7,0)的单壁碳纳米管与有机分子方酸菁和聚噻吩组成的复合物为例,利用从头算多体格林函数理论研究了物理吸附的有机分子对碳纳米管光激发性质的影响. 碳纳米管的E₁₁和E₂₂吸收峰红移了几十个毫电子伏特. 重要的是,碳纳米管与分子之间的弱相互作用使得(7,0)管原来能量低于E₁₁峰的暗激子获得一定的振子强度,成为亮激子,从而在低能量处产生一个较弱的卫星吸收峰. 吸附分子的类型影响该卫星峰的能量. 这些发现可为调控碳纳米管的发光波长和发光效率提供有价值的信息.     

Femtosecond filamentation in air at low pressures: Part I: Theory and numerical simulations

We investigate numerically the influence of the pressure on femtosecond filamentation in air. We show that femtosecond filamentation occurs at low pressure and compute the features of the plasma channel generated in the wake of the pulse. We discuss the influence of the pulse duration, chirp and input beam shape on the length of the plasma channels. These calculations constitute a prerequisite for laboratory experiments over short distances as well as for vertical femtosecond filamentation at high altitude on which light detection and ranging techniques or lightning protection rely.     

Electrodynamics of Superconductors as a Consequence of Local Gauge Invariance

The electromagnetic properties of superconductors are studied in the framework of a quantum gauge-invariant theory. The formulation is developed in the generalized pair approximation which preserves the Ward-Takahashi identities. The macroscopic equations which regulate current and electromagnetic fields are derived by means of the boson transformation method. Comparison with previous works is reported.     

Random fields as solutions of the inhomogeneous quaternionic Cauchy-Riemann equation. I. Invariance and analytic continuation

We consider random fieldsA satisfying the quaternionic Cauchy-Riemann equationA=F, whereF is white noise. Under appropriate conditions onF, A is invariant under the proper Euclidean group in four dimensions, but in general not under time reflection. The Schwinger functions can be analytically continued to Wightman functions satisfying the relativistic postulates on invariance, specrral property and locality.     

Towards a nonperturbative foundation of the dipole picture: I. Functional methods

This is the first of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. We classify different contributions to this process and identify the leading contributions at high energies. We then study the renormalisation of the photon-quark-antiquark vertex that occurs in the leading contributions. We find something like the dipole picture in one of these contributions but also find two correction terms which can potentially become large at small photon virtualities. In the second paper we will discuss the additional approximations and assumptions that are necessary to obtain the dipole model of high energy scattering from the results found here.