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

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

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

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

Branes, Quantum Nambu Brackets, and the Hydrogen Atom

The Nambu Bracket quantization of the Hydrogen atom is worked out as an illustration of the general method. The dynamics of topological open branes is controlled classically by Nambu Brackets. Such branes then may be quantized through the consistent quantization of the underlying Nambu brackets: properly defined, the Quantum Nambu Brackets comprise an associative structure, although the naive derivation property is mooted through operator entwinement. For superintegrable systems, such as the Hydrogen atom, the results coincide with those furnished by Hamiltonian quantization--but the method is not limited to Hamiltonian systems.Comment: 6 pages, LateX2e. Invited talk by CZ at the XIII International Colloquium on Integrable Systems and Quantum Groups, Prague, June 18, 200

Oviposition Decisions by Red Flour Beetle [Tribolium castaneum]

The red flour beetle [Tribolium castaneum] and the confused flour beetle [Tribolium confusum] are very important flour pest. We tested if the red flour beetle can discriminate between flour infested by the same species or congeneric species and lay different number of eggs. Results of the choice tests were inconclusive, because oviposition across all the treatments was very low. Future research will be needed manipulating the female age and the length of time in the arenas to be able to address the proposed question. With this future research, it will hopefully help us better understand how these beetles exploit flour patches and improve management in flour mills