联想笔记本蓝屏
考研励志语录量子混沌声弹性波的实验模拟研究
摘要
野山菌火锅
二十世纪下半叶以来，混沌学的研究获得了迅猛的发展，已经成为了一门重要的前沿交叉科学，它在物理、生物等各个传统科学领域都得到了广泛的应用。量子混沌则是混沌学在微观的量子力学领域的应用，它的目标是要弄明白，在经典世界存在的极为普遍的混沌现象，在量子世界里会有什么样的表现。科学家们在这个领域的研究成果，已经大大的扩展了我们对量子世界的认识。
在研究量子世界中混沌现象的过程中，为了更好的解释各种与经典混沌相关的特征，科学家们建立起了半经典理论。它现在已经成为人们研究量子世界中混沌现象的主要理论工具。近些年来，量子混沌科学研究中出现了另一种研究方法--实验模拟方法。该方法对混沌理论的贡献在于，它是集实验、理论和模拟于一身。由于它将观察和分析两种研究方法的特点综合在一起，并且其它方法相比，有着简便易行的优点，该研究方法正在被越来越多的科学家所采用，并取得了一系列的研究成果。
在本研究课题中即采用了实验模拟方法中的一种—声弹性波的实验模拟。本文介绍了混沌学、量子混沌学及半经典理论的相关知识，然后介绍了声弹性波实验模拟方法的原理及实验装置等相关知识，最后利用该方法观察、统计并分析了实验中所构造的量子台球体系中的一系列混沌特征。论文的主要的研究内容如下：
1.研究了信号处理中所采用的两种分析方法，一种是快速傅立叶变换，另一种则是过滤对角化方法。文中根据两种方法的原理，研究分析了两种方法各自的优缺点，并根据两种方法对本实验中随机抽取的一个信号的处理结果，选定了对本文模拟实验中的信号进行处理时所采用的方法—过滤对角化方法。
中学生心理健康2.通过一些特定的实验手段及信号处理方法，研究了本课题中构造的量子台球体系能谱的统计特征。这些特征包括最近邻能级间距分布和谱刚度，这两种特
征展现了量子体系中的混沌特性，为无规矩阵等量子混沌学科中的理论研究提供了实验依据。
3.研究了量子体系中的能级动力学，并在实验模拟中观察并分析得到了能级动力学中的一种特殊现象—能级回避交叉。该现象展现了能级动力学在线性可积系统与混沌非线性系统中的不同表现，它同样为理论研究提供了实验依据。
关键词：量子混沌，过滤对角化，最近邻能级间距分布，谱刚度，能级回避交叉
廉政工作总结
Study of the Experimental Simulation of the Quantum Chaos
ABSTRACT
八年级家长会
Since the cond half of the twenty century, the development of the study of the chaos is so fast that it has become a very important advanced interdiscipline. It has been ud in many traditional domain of science such as physics, biology and so on. Quantum chaos is the application of chaos in the quantum field, which purpo is to find out the expression of the chaos in the quantum field. The achievements of scientistshave expand our knowledge greatly in this field.
In the process of study the chaos phenomenon in the quantum field, the scientists have founded a theory named mi classical theory which is ud to explain the characteristic which relate to classical chaos. Nowadays, it has become the main tool which is ud for studying the chaos phenomenon in the quantum field. In recent years, another method named experimental simulation appeared. The contribution is that it can synthesize experiment, theory and simulation, and it has the virtue of being easy to implement comparing with other methods. So it is ud by more and more scientists and have obtained a ries of rearch results at prent.
In our rearch subject, we ud one of the experimental simulation methods—experimental simulation of acoustic elastic wave. This article introduced the knowledge about chaos, quantum chaos, mi classical theory and so on. After that the knowledge about the principle of experimental simulation of acoustic elastic wave, experimental equipment and so on was introduced. In the end, w
e have obrved, counted and analyzed a ries of characteristic of chaos in quantum billiards which was constructed in our experiment. The sum total of the study in the subject includes the following part:
高山仰止的意思>农村社会工作1. Two methods ud in signal processing were studied, one is fast Fourier transform, another is filter-diagonalization method. The relative merits was studied according to the principles of the two methods. According to the analysis of a signal in our experiment by the two ways, we picked up the filter-diagnalization method to analyze the signal of our experiment.
2. Using some special experimental methods and the analysis of signal of experiment, some statistical characters of level spectral were studied in our quantum billiard. The characters contains the nearest neighbor spacing distribution and the spectral rigidity. The characteristic exhibit the chaos property of quantum system, and they also provided experimental evidence for the theoretic study in the quantum chaos subjects, for example random matrix.
3. Level dynamics in quantum system was studied, a special phenomenon
-avoided crossing in level dynamics was found also by obrving and anlyzing the experimental simulation. This phenomenon reprent difference exhibitation of level dynamic between linear integr
able system and nonlinear chaos system. It also provided experimental evidence f for the theoretic study.
KEYWORD: quantum chaos, filter-diagonalization, the nearest neighbor spacing distribution, spectral rigidity, avoided crossing.
目录
第一章 综述...........................................．．．．．．．．．．．．．1§1.1 经典混沌学的产生与发展．．．．．．．．．．．．．．．．.．．．．．．．．．．．．．．．．．．．．．．．1 §1.2 量子混沌的研究．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．.．．2 §1.2.1 半经典近似理论．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．.．．．．4 §1.2.2 量子混沌的实验模拟及其研究进展．．．．．．．．．．．．．．．．．．．．．．．.．．．．5 §1.3 本课题的主要研究内容....................................．．．．．．7 §1.4 本章小结.....................................．．．．．．．．．．．．．．.．8
第二章 量子混沌声弹性波的模拟实验..........．．．．．．．．．．．．．．．．．．．．．．．9§2.1 量子台球体系..................．．．．．．．．．．．．．．．．．．．．．．．．．．．．．.．．9 §2.2 声弹性波的实验模拟理论．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．10 §2.3 实验装置及实验过程........．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．12 §2.2 本章小结......................．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．15
第三章 傅立叶变换和过滤对角化方法........................．．．．．．．．．16 §3.1离散信号的傅立叶变换及快速傅立叶变换...........．．．．．．．．．．．．．．16 §3.1.1 傅立叶变换..........．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．16 §3.1.2 离散傅立叶变换......．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．17 §3.1.2 快速傅立叶变换......．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．18 §3.2过滤对角化方法................．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．19 §3.
3 FFT和FDM方法的对比分析..........．．．．．．．．．．．．．．．．．．．．．．．．．．．．．21 §3.4 本章小结............................．．．．．．．．．．．．．．．．．．．．．．．．．23
第四章 量子混沌的能谱统计特征及其能级动力学研究...．．．．．．．．．．．．．．．．24§4.1无规矩阵理论和高斯正交系综．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．24 §4.1.1 无规矩阵理论................．．．．．．．．．．．．．．．．．．．．．．．．．．．．．24 §4.1.2 高斯正交系综..................．．．．．．．．．．．．．．．．．．．．．．．．．．．25 §4.2 最近邻间距分布和谱刚度分析．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．27§4.2.1量子系统的规则谱与不规则谱.........．．．．．．．．．．．．．．．．．．．．．．．27 §4.2.2 最近邻能级间距分布......．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．．28 §4.2.3 本量子台球体系中的最近邻能级间距分布......．．．．．．．．．．．．．．．31 §4.2.4 谱刚度分析................................．．．．．．．．．．．．．．．34 §4.3 能级动力学研究及能级交叉回避.........．．．．．．．．．．．．．．．．．．．．．．．35 §4.3.1 能机动力学研究....................．．．．．．．．．．．．．．．．．．．．．．．35
