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1996•Physical Review LettersRequires access

Semiclassical Quantization of Nonseparable Systems without Periodic Orbits

Franz Josef Weiper, Joachim Ankerhold, Hermann Grabert, Eli Pollak

Open publisher page 6 citations

Abstract

We present a new method for the semiclassical quantization of classically integrable as well as nonintegrable systems. The method is based on the semiclassical approximation of the equilibrium density matrix, using classical trajectories on the upside down potential surface. Periodic orbits do not play any special role. Explicit results are given for the case of the classically chaotic potential ${\mathrm{kx}}^{2}{y}^{2}/2$.

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What this paper is about

We present a new method for the semiclassical quantization of classically integrable as well as nonintegrable systems. The method is based on the semiclassical approximation of the equilibrium density matrix, using classical trajectories on the upside down potential surface. Periodic orbits do not play any special role. Explicit results are given for the case of the classically chaotic potential ${\mathrm{kx}}^{2}{y}^{2}/2$.

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OpenAlex reports 6 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present a new method for the semiclassical quantization of classically integrable as well as nonintegrable systems. The method is based on the semiclassical approximation of the equilibrium density matrix, using classical trajectories on the upside down potential surface. Periodic orbits do not play any special role. Explicit results are given for the case of the classically chaotic potential ${\mathrm{kx}}^{2}{y}^{2}/2$.

Key concepts: Semiclassical physics, Integrable system, Quantization (signal processing), Periodic orbits, Chaotic, Physics, Chaotic systems, Mathematical physics

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