Dynamical mapping method in nonrelativistic models of quantum field theory

The solutions of Heisenberg equations and two-particles eigenvalue problems for nonrelativistic models of current-current fermion interaction and $N, \Theta$ model are obtained in the frameworks of dynamical mapping method. The equivalence of different types of dynamical mapping is shown. The connection between renormalization procedure and theory of selfadjoint extensions is elucidated.Comment: 14 page

The Free Quon Gas Suffers Gibbs' Paradox

We consider the Statistical Mechanics of systems of particles satisfying the $q$-commutation relations recently proposed by Greenberg and others. We show that although the commutation relations approach Bose (resp.\ Fermi) relations for $q\to1$ (resp.\ $q\to-1$), the partition functions of free gases are independent of $q$ in the range $-1<q<1$. The partition functions exhibit Gibbs' Paradox in the same way as a classical gas without a correction factor $1/N!$ for the statistical weight of the $N$-particle phase space, i.e.\ the Statistical Mechanics does not describe a material for which entropy, free energy, and particle number are extensive thermodynamical quantities.Comment: number-of-pages, LaTeX with REVTE

Superfield Realizations of Lorentz and CPT Violation

Superfield realizations of Lorentz-violating extensions of the Wess-Zumino model are presented. These models retain supersymmetry but include terms that explicitly break the Lorentz symmetry. The models can be understood as arising from superspace transformations that are modifications of the familiar one in the Lorentz-symmetric case.Comment: 10 page

Space construction system analysis. Part 2: Platform definition

The top level system requirements are summarized and the accompanying conceptual design for an engineering and technology verification platform (ETVP) system is presented. An encompassing statement of the system objectives which drive the system requirements is presented and the major mission and subsystem requirements are described with emphasis on the advanced communications technology mission payload. The platform design is defined and used as a reference configuration for an end to space construction analyses. The preferred construction methods and processes, the important interactions between the platform design and the construction system design and operation, and the technology development efforts required to support the design and space construction of the ETVP are outlined

Spacelike Ricci Inheritance Vectors in a Model of String Cloud and String Fluid Stress Tensor

We study the consequences of the existence of spacelike Ricci inheritance vectors (SpRIVs) parallel to $x^a$ for model of string cloud and string fluid stress tensor in the context of general relativity. Necessary and sufficient conditions are derived for a spacetime with a model of string cloud and string fluid stress tensor to admit a SpRIV and a SpRIV which is also a spacelike conformal Killing vector (SpCKV). Also, some results are obtained.Comment: 11 page

All-Optical Switching with Transverse Optical Patterns

We demonstrate an all-optical switch that operates at ultra-low-light levels and exhibits several features necessary for use in optical switching networks. An input switching beam, wavelength $\lambda$, with an energy density of $10^{-2}$ photons per optical cross section [$\sigma=\lambda^2/(2\pi)$] changes the orientation of a two-spot pattern generated via parametric instability in warm rubidium vapor. The instability is induced with less than 1 mW of total pump power and generates several $\mu$Ws of output light. The switch is cascadable: the device output is capable of driving multiple inputs, and exhibits transistor-like signal-level restoration with both saturated and intermediate response regimes. Additionally, the system requires an input power proportional to the inverse of the response time, which suggests thermal dissipation does not necessarily limit the practicality of optical logic devices

Phase Transition of XY Model in Heptagonal Lattice

We numerically investigate the nature of the phase transition of the XY model in the heptagonal lattice with the negative curvature, in comparison to other interaction structures such as a flat two-dimensional (2D) square lattice and a small-world network. Although the heptagonal lattice has a very short characteristic path length like the small-world network structure, it is revealed via calculation of the Binder's cumulant that the former exhibits a zero-temperature phase transition while the latter has the finite-temperature transition of the mean-field nature. Through the computation of the vortex density as well as the correlation function in the low-temperature approximation, we show that the absence of the phase transition originates from the strong spinwave-type fluctuation, which is discussed in relation to the usual 2D XY model.Comment: 5 pages, 6 figures, to be published in Europhys. Let

Planet Formation in the Outer Solar System

This paper reviews coagulation models for planet formation in the Kuiper Belt, emphasizing links to recent observations of our and other solar systems. At heliocentric distances of 35-50 AU, single annulus and multiannulus planetesimal accretion calculations produce several 1000 km or larger planets and many 50-500 km objects on timescales of 10-30 Myr in a Minimum Mass Solar Nebula. Planets form more rapidly in more massive nebulae. All models yield two power law cumulative size distributions, N_C propto r^{-q} with q = 3.0-3.5 for radii larger than 10 km and N_C propto r^{-2.5} for radii less than 1 km. These size distributions are consistent with observations of Kuiper Belt objects acquired during the past decade. Once large objects form at 35-50 AU, gravitational stirring leads to a collisional cascade where 0.1-10 km objects are ground to dust. The collisional cascade removes 80% to 90% of the initial mass in the nebula in roughly 1 Gyr. This dust production rate is comparable to rates inferred for alpha Lyr, beta Pic, and other extrasolar debris disk systems.Comment: invited review for PASP, March 2002. 33 pages of text and 12 figure

Surfaces, depths and hypercubes: Meyerholdian scenography and the fourth dimension

An appreciation of Meyerhold’s engagement with theatrical space is fundamental to understanding his directorial and pedagogic practice. This article begins by establishing Meyerhold’s theoretical and practical engagement with theatre as a fundamentally scenographic process, arguing for a reconceptualisation of the director as ‘director-scenographer’. Focusing on the construction of depth and surface in Meyerholdian theatre, the article goes on to identify trends in the director’s approach to space, with an emphasis on the de-naturalisation of depth on stage. This denaturalisation is seen as taking three forms: the rejection of depth as a prerequisite in theatrical space, the acknowledgement of the two-dimensional surface as surface, and the restructuring of depth space into a series of restricted planes. The combination of these trends indicates a consistent and systematic process of experimentation in Meyerhold’s work. In addition, this emphasis on depth and surface, and the interaction between the two, also highlights the contextualisation of Meyerhold’s practice within the visual, philosophical and scientific culture of the early twentieth century, echoing the innovations in n-dimensional geometry and particularly, the model of the fourth spatial dimension seen in the work of Russian philosopher P. D. Ouspensky