FLUCTUATION PROPERTIES OF STRENGTH FUNCTIONS IN NONLINEAR SYSTEMS

非线性系统中强度函数的涨落特性

• 批准号: 07640400
• 负责人: SUZUKI Toru
• 金额: $ 0.9万
• 依托单位: TOKYO METROPOLITAN UNIVERSITY
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1995
• 资助国家: 日本
• 起止时间: 1995 至 1996
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-07640400/
• 关键词: Strength Function; Nonlinear System; Dissipation Mechanism; 応答関数; 非線形模型; 原子核反応

The purpose of the present investigation is to study fluctuation properties of the strength functions which appear when some parent state (s) is embedded in a vast number of background states. We studied several model systems and calculated various signatures which measure fluctuation of the strength function.We first considered a model which consists of a single parent state (supposedly a collective state) and a background states, the latter being taken as the two-dimensional anharmonic oscillator. The dynamical characteristics of this oscillator system is known to show regular as well as chaotic properties as a function of a single parameter. The coupling between the parent state and the background system has been taken to be a simple form so as to isolate the effects of the background system. We studied energy-moments, strength distribution, fractal dimensions and the survival probability (Fourier transform) for the strength function. It was found that the strength distribution and the survival probability are sensity to the dynamical character of the background system, while the energy moments are not much dependent on the latter being constrained by sum rules. The fractal dimension, too, is insensitive to the parameter of the background system. It takes, however, a different value from that obtained for a background system constructed from random matrix, and thus may be a signature of another character.We then considered a model where two parent states couple to the same backround system. Here it is possible to study (in) coherence of the two parent states as a result of the coupling. We calculated energies and strength functions as function of the energy difference between the parent states. It was shown that the behavior of the main strength is quite different for a regular or a chaotic background system. A further study is being performed from the standpoint of the level dyanmics.

本研究的目的是研究强度函数的波动特性，这些函数在某些母体状态嵌入大量背景状态中时会出现。我们研究了几个模型系统，并计算了各种签名，这些签名测量了强度函数的波动。我们首先考虑了由单亲状态（据说是集体状态）和背景状态组成的模型，后者被视为二维肛门振荡器。已知该振荡器系统的动力学特性显示出与单个参数的函数的规则和混沌性质。母体状态与背景系统之间的耦合已被视为一种简单的形式，以隔离背景系统的效果。我们研究了强度函数的能量矩，强度分布，分形维度和生存概率（傅立叶变换）。发现强度分布和生存概率对背景系统的动态特征有感觉，而能量矩并不依赖于后者受到总和规则的约束。分形维度也对背景系统的参数不敏感。但是，它具有与从随机矩阵构建的背景系统获得的值不同的值，因此可能是另一个字符的签名。然后，我们考虑了一个模型，其中两个父态夫妇夫妇到同一背景系统。在这里，可以研究两种母体状态的连贯性。我们将能量和强度功能计算为母体状态之间能量差的功能。结果表明，对于常规或混乱的背景系统，主要强度的行为是完全不同的。从水平染色体的角度进行了进一步的研究。

项目成果

H.Aiba, S.Mizutori and T.Suzuki: "Fluctuation Properties of Strength Function Phenomena : A Model Study" Phys. Rev. E. (to appear). (1997)

H.Aiba、S.Mizutori 和 T.Suzuki：“强度函数现象的波动特性：模型研究”Phys。

鈴木 徹: "核子準弾性散乱とスピン偏極量" 原子核研究. 41. 127-135 (1996)

铃木彻：“核子准弹性散射和自旋极化”核研究 41. 127-135 (1996)。

森田 彦、鈴木 徹: "Nuclear Correlation Effects in the Deep Inelastic Structure Function of 4He" Aust.J.Phys.50. 53-60 (1997)

Hiko Morita，Toru Suzuki：“4He 深层非弹性结构函数中的核相关效应”Aust.J.Phys.50 (1997)。

相場浩和,水島正二郎,鈴木徹: "Fluctuation Properties of Strength Function Phenomena:A Model Study" Phys.Rev.E. (to appear). (1997)

Hirokazu Aiba、Shojiro Mizushima、Toru Suzuki：“强度函数现象的波动特性：模型研究”Phys.Rev.E（待出版）。

T.Suzuki: "Quasielastic Nuclear Reactions and Spin Observables" Genshikaku-Kenkyu. 41. 127-135 (1996)

T.Suzuki：“准弹性核反应和自旋可观测”Genshikaku-Kenkyu。