中国物理B ›› 1995, Vol. 4 ›› Issue (9): 641-648.doi: 10.1088/1004-423X/4/9/001

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SENSITIVITY TO PERTURBATION IN QUANTUM CHAOTIC SYSTEM

揭泉林1, 徐躬耦2   

  1. (1)Department of Physics, Nanjing University, Nanjing 210008 , China; (2)Department of physics, Nanjing University, Nanjing 210008 , China; Department of Modern Physics, Lanzhou University, Lanzhou 730000, China
  • 收稿日期:1994-11-11 出版日期:1995-09-20 发布日期:1995-09-20
  • 基金资助:
    Project supported by the National Basic Research Project "Nonlinear Science" of China and by the National Natural Science Foundation of China.

SENSITIVITY TO PERTURBATION IN QUANTUM CHAOTIC SYSTEM

JIE QUAN-LIN (揭泉林)a, XU GONG-OU (徐躬耦)b   

  1. a Department of Physics, Nanjing University, Nanjing 210008 , China; b Department of physics, Nanjing University, Nanjing 210008 , China; Department of Modern Physics, Lanzhou University, Lanzhou 730000, China
  • Received:1994-11-11 Online:1995-09-20 Published:1995-09-20
  • Supported by:
    Project supported by the National Basic Research Project "Nonlinear Science" of China and by the National Natural Science Foundation of China.

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摘要： Numerical results show that, for quantum autonomous chaotic system, the evolution of initially coherent states are sensitive to perturbation. The overlap of a perturbed state with the unperturbed one decays exponentially, which is followed by fluctuation around N-1, N being the dimension of the Hilbert space. The matrix elements of the evolution operator in interaction picture tend to be a random distribution after sufficiently long time, where the interaction is the perturbation, even when the perturbation is very weak. The difference between a regular system and the chaotic one is shown clearly. In a regular system, the overlap shows strong revival. The distribution of the evolution matrix has only a few dominant terms.

Abstract: Numerical results show that, for quantum autonomous chaotic system, the evolution of initially coherent states are sensitive to perturbation. The overlap of a perturbed state with the unperturbed one decays exponentially, which is followed by fluctuation around N-1, N being the dimension of the Hilbert space. The matrix elements of the evolution operator in interaction picture tend to be a random distribution after sufficiently long time, where the interaction is the perturbation, even when the perturbation is very weak. The difference between a regular system and the chaotic one is shown clearly. In a regular system, the overlap shows strong revival. The distribution of the evolution matrix has only a few dominant terms.

中图分类号:  (Quantum chaos; semiclassical methods)

  • 05.45.Mt
03.65.Fd (Algebraic methods) 03.65.Vf (Phases: geometric; dynamic or topological) 05.45.Pq (Numerical simulations of chaotic systems) 05.40.-a (Fluctuation phenomena, random processes, noise, and Brownian motion)