T Duality Between Perturbative Characters of E8⊗E8E_8\otimes E_8 and SO(32) Heterotic Strings Compactified On A Circle

Characters of $E_8\otimes E_8$ and SO(32) heterotic strings involving the full internal symmetry Cartan subalgebra generators are defined after circle compactification so that they are T dual. The novel point, as compared with an earlier study of the type II case (hep-th/9707107), is the appearence of Wilson lines. Using SO(17,1) transformations between the weight lattices reveals the existence of an intermediate theory where T duality transformations are disentangled from the internal symmetry. This intermediate theory corresponds to a sort of twisted compactification of a novel type. Its modular invariance follows from an interesting interplay between three representations of the modular group.Comment: 17 pages LateX 2E, 2 figures (eps

Negative Probability and Uncertainty Relations

A concise derivation of all uncertainty relations is given entirely within the context of phase-space quantization, without recourse to operator methods, to the direct use of Weyl's correspondence, or to marginal distributions of x and p.Comment: RevTeX, 4 page

Logistic Map Potentials

We develop and illustrate methods to compute all single particle potentials that underlie the logistic map, x --> sx(1-x) for 0<s<=4. We show that the switchback potentials can be obtained from the primary potential through functional transformations. We are thereby able to produce the various branches of the corresponding analytic potential functions, which have an infinite number of branch points for generic s>2. We illustrate the methods numerically for the cases s=5/2 and s=10/3

Potentials Unbounded Below

Continuous interpolates are described for classical dynamical systems defined by discrete time-steps. Functional conjugation methods play a central role in obtaining the interpolations. The interpolates correspond to particle motion in an underlying potential, $V$. Typically, $V$ has no lower bound and can exhibit switchbacks wherein $V$ changes form when turning points are encountered by the particle. The Beverton-Holt and Skellam models of population dynamics, and particular cases of the logistic map are used to illustrate these features.Comment: Based on a talk given 29 July 2010, at the workshop on Supersymmetric Quantum Mechanics and Spectral Design, Centro de Ciencias de Benasque Pedro Pascual. This version incorporates modifications to conform to the published paper: Additional references and discussion; New section 3.2 on the Skellam exponential model; Appendix change

Areal Theory

New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given, and some conjectures are made about chaos in such field theories.Comment: December 2001 "Coral Gables" conference contribution; Scientific Workplace Late

T Duality of Perturbative Characters for Closed Bosonic and Type II String Theories

The duality properties of perturbative string characters associated with the transverse space-time rotations are studied. T duality is achieved by suitably integrating over the total momentum, contrary to earlier discussions. The O(8) triality properties of the characters for critical superstrings, are derived. This shows the existence of a third formulation (unnoticed so far to our knowledge) equivalent to, but different from the ones of Neveu-Schwarz-Ramond, and Green-Schwarz. Projectors in the NS and R sectors are defined in the GS formalism. The consequences of supersymmetry are neatly derived at once for all massive states by factorising the character of the long SUSY multiplet.Comment: 44 pages LateX 2E, 2 figures (eps

A history and analysis of hydrogen maser reliability

Hydrogen masers an integral part of the Deep Space Network, provide extremely accurate navigation about the outer planets, as well as precise location of tracking stations. Reliability of equipment over extended periods of time was considered. The Deep Space Network has a number of hydrogen masers deployed and in the test cycle, which enabled an analysis of reliability of several generations and breeds of construction. A history and analysis of hydrogen maser reliability over a three-year period was compiled several types of masers