Classical and Quantum Chaos of the Mixmaster Universe

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概要

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• We first review the main results of the theory of chaos in classical Hamiltonian dynamical systems and recent progress in understanding the quantum chaos which is expected in the quantized version of classical chaotic system. In cosmological dynamical system there exists a classical chaotic system known as the Mixmaster universe which is a homogeneous and anisotropic solution to the Einstein equation. The classical Mixmaster model is expounded in detail and it is shown that the dynamical system has a very strong stochasticity, so-called local instability. In the main part of this thesis we have shown that in the quantized Mixmaster system there exist some features of quantum chaos, i.e. the quantum mixing property proposed by Peres and the disordered distribution of probability density. In order to show these features we investigate the time evolution of a wave packet starting from a certain initial condition on 61×61 lattice by numerically integrating the Wheeler-DeWitt equation. As a result it is shown that the expectation values of anisotropic variables go into a small region around the isotropic point and the size of the region is about 0.12. (quantum mixing) And moreover the random distribution of probability density is demonstrated in the configuration space of anisotropic variables. These results strongly suggest the existence of quantum chaos in the quantized version of the Mixmaster universe.

• 素粒子論グループ 素粒子研究編集部の論文
• 1986-06-20

著者

• 古沢 豊明

  阪大・理

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