Deformation theory of quantizable dynamical systems

Deformations of families of quantizable dynamical systems are introduced and the local extension problem for quantizable dynamical systems is solved. This research was supported in part by NSF GP-13375 and NSF GP-20856. Entrata in Redazione il 2 dicembre 1970.     

Examples of quantisable dynamical systems: The hydrogen atom and automorphism groups

The regularised energy surface of then-dimensional hydrogen atom is shown to be naturally the total space of a quantisable dynamical system. The automorphism groups of dynamical systems are studied; and the connected Riemannian dynamical systems with automorphism groups of maximal dimension are classified. Finally, the compact, connected and simply connected quantisable dynamical system with automorphism group of maximal dimension is shown to be the set of independent harmonic oscillators with equal periods.This research was supported in part by NSF GP-20856A, No. 1.     

Entropy of a fibered dynamical system

The entropy of the geodesic flow associated to a fibered dynamical system is shown to be zero; in particular the entropy of a quantizable dynamical system is zero. An ergodic dynamical system which defines a quantizable dynamical system is outlined.This research was supported in part by NSF GP-20856 A 1     

Autoresonant excitation of antiproton plasmas

We demonstrate controllable excitation of the center-of-mass longitudinal motion of a thermal antiproton plasma using a swept-frequency autoresonant drive. When the plasma is cold, dense, and highly collective in nature, we observe that the entire system behaves as a single-particle nonlinear oscillator, as predicted by a recent theory. In contrast, only a fraction of the antiprotons in a warm plasma can be similarly excited. Antihydrogen was produced and trapped by using this technique to drive antiprotons into a positron plasma, thereby initiating atomic recombination.     

Zeta Functions and Periodic Orbit Theory: A Review

The article reviews the interrelationship of periodic orbit theory and the Selberg trace formula. Examples from recent work on quantization of chaos are surveyed. The review emphasizes the development in terms of Lie group representation theory and differential geometry. Finally, the formal connections to string theory are discussed.     

Combinatorial chemistry: oh what a decade or two can do

This short commentary takes a stroll through the early days of the field of combinatorial chemistry and molecular diversity. It offers a high-level perspective on the field’s beginnings—and its future—as it relates to journals, books, pioneers, and advances.     

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Exponential Sums and Coding Theory: A Review

This article is a survey of several recent applications of methods from analytic number theory to research in coding theory, including results on Kloosterman codes, binary Goppa codes, and prime phase shift sequences. The mathematical methods focus on exponential sums, in particular Kloosterman sums. The interrelationships with the Weil–Carlitz–Uchiyama bound, results on Hecke operators, theorems of Bombieri and Deligne and the Eichler–Selberg trace formula are reviewed.