Quantization of Chaos : h^^--Expansion Theory

概要

論文の詳細を見る
We present and review several results on the semiclassical quantization of classically chaotic systems. Using Feynman path integrals and the stationary phase method, we develop a semiclassical theory for quantum trace formulas which are expanded in asymptotic series of powers of the Planck constant around the equilibrium points and the periodic orbits. The coefficients of these series are expressed in terms of diagrams. The transition between effective separability and nonseparability is discussed in relation with the importance of periodic orbits in the quantization. The theory is developed for smooth Hamiltonians, quantum maps, and billiards where several illustrations are given of the role of the h^^-- expansion. We briefly review several applications of the semiclassical theory to the determination of scattering resonances in the hydrogen negative ion, in unimolecular dissociation processes, and in nanometric semiconducting devices.
理論物理学刊行会の論文
1994-08-12