Exact Time Evolution of a Quantum Harmonic-Oscillator Chain : General Matter and Statistical Physics

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概要

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• We generalize the classical time evolution problem of a harmonic-oscillator chain with periodic and fixed-end boundary conditions to the quantum mechanical case. It is shown explicitly that the high-temperature limits of our quantum mechanical treatment give the known classical results. We also show that the finite diffusion constant for the periodic chain arises from the zero-frequency normal mode which represents the rotational mode of the periodic chain, and the diffusion constant vanishes as temperature approaches zero. The zero-frequency normal mode is also responsible for the divergence of the mean square displacement of a tagged oscillator. On the other hand, the absence of the zero-frequency normal mode in a fixed-end chain gives rise to zero diffusion constant and finite mean square displacement. The finiteness of diffusion constant and the divergence of mean square displacement in this model are responsible for the symmetry of the system.

• 理論物理学刊行会の論文
• 1989-08-25

著者

• HONG J.

  Department of Orthopaedic Surgery, Medical College of Wisconsin

• Hong J

  Samsung Electronics Co. Ltd. Gyungki‐do Kor

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