06-40 Maurice de Gosson

Symplectic Non-Squeezing Theorems, Quantization of Integrable Systems, and Quantum Uncertainty (239K, pdf) Feb 26, 06

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Abstract. The ground energy level of an oscillator cannot be zero because of Heisenberg's uncertainty principle. We use methods from symplectic topology (Gromov's non-squeezing theorem, and the existence of symplectic capacities) to analyze and extend this heuristic observation to Liouville-integrable systems, and to propose a topological quantization scheme for such systems, thus extending previous results of ours.

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