Cole-Hopf Like Transformation for Schr\"odinger Equations Containing Complex Nonlinearities

We consider systems, which conserve the particle number and are described by Schr\"odinger equations containing complex nonlinearities. In the case of canonical systems, we study their main symmetries and conservation laws. We introduce a Cole-Hopf like transformation both for canonical and noncanonical systems, which changes the evolution equation into another one containing purely real nonlinearities, and reduces the continuity equation to the standard form of the linear theory. This approach allows us to treat, in a unifying scheme, a wide variety of canonical and noncanonical nonlinear systems, some of them already known in the literature. pacs{PACS number(s): 02.30.Jr, 03.50.-z, 03.65.-w, 05.45.-a, 11.30.Na, 11.40.DwComment: 26 pages, no figures, to be appear in J. Phys. A: Math. Gen. (2002

Comment on ``the Klein-Gordon Oscillator''

The different ways of description of the $S=0$ particle with oscillator-like interaction are considered. The results are in conformity with the previous paper of S. Bruce and P. Minning.Comment: LaTeX file, 5p

The NuMI Neutrino Beam and Potential for an Off-Axis Experiment

The Neutrinos at the Main Injector (NuMI) facility at Fermilab is under construction and due to begin operations in late 2004. NuMI will deliver an intense $\nu_{\mu}$ beam of variable energy 2-20 GeV directed into the Earth at 58 mrad. Several aspects of the design are reviewed, and potential limitations to the ultimate neutrino flux are described. In addition, potential measurements of neutrino mixing properties are described.Comment: talk given at NuFact '02, Imperial College London, proceedings to appear in J. Phys. G, revised to add a referenc

Secondary Beam Monitors for the NuMI Facility at FNAL

The Neutrinos at the Main Injector (NuMI) facility is a conventional neutrino beam which produces muon neutrinos by focusing a beam of mesons into a long evacuated decay volume. We have built four arrays of ionization chambers to monitor the position and intensity of the hadron and muon beams associated with neutrino production at locations downstream of the decay volume. This article describes the chambers' construction, calibration, and commissioning in the beam.Comment: Accepted for publication in Nucl. Instr. Meth.

Some Variations on Maxwell's Equations

In the first sections of this article, we discuss two variations on Maxwell's equations that have been introduced in earlier work--a class of nonlinear Maxwell theories with well-defined Galilean limits (and correspondingly generalized Yang-Mills equations), and a linear modification motivated by the coupling of the electromagnetic potential with a certain nonlinear Schroedinger equation. In the final section, revisiting an old idea of Lorentz, we write Maxwell's equations for a theory in which the electrostatic force of repulsion between like charges differs fundamentally in magnitude from the electrostatic force of attraction between unlike charges. We elaborate on Lorentz' description by means of electric and magnetic field strengths, whose governing equations separate into two fully relativistic Maxwell systems--one describing ordinary electromagnetism, and the other describing a universally attractive or repulsive long-range force. If such a force cannot be ruled out {\it a priori} by known physical principles, its magnitude should be determined or bounded experimentally. Were it to exist, interesting possibilities go beyond Lorentz' early conjecture of a relation to (Newtonian) gravity.Comment: 26 pages, submitted to a volume in preparation to honor Gerard Emch v. 2: discussion revised, factors of 4\pi corrected in some equation

Machine-Related Backgrounds in the SiD Detector at ILC

With a multi-stage collimation system and magnetic iron spoilers in the tunnel, the background particle fluxes on the ILC detector can be substantially reduced. At the same time, beam-halo interactions with collimators and protective masks in the beam delivery system create fluxes of muons and other secondary particles which can still exceed the tolerable levels for some of the ILC sub-detectors. Results of modeling of such backgrounds in comparison to those from the e+ e- interactions are presented in this paper for the SiD detector.Comment: 29 pages, 34 figures, 7 table