相对论性隧穿时间的研究

【作者】 赵静；

【导师】 龙超云；

【作者基本信息】 贵州大学 ， 理论物理， 2007， 硕士

【摘要】 量子隧穿时间是一个古老而基础的问题，自从1931年被提出以来学术界就没有停止过对这一问题的争论。这一问题之所以引起关注，不仅是因为其理论价值，比如超光速隧穿现象的解释，更因为其与高新科技的紧密联系，特别是近几十年，随着基于隧穿过程的高速电子设备广泛使用，以及隧穿效应在核子聚变裂变中重要性认识，这一问题引起了越来越多关注。本文首先在前言中简要的介绍了隧穿时间的研究历史，以及隧穿时间中争论最多的问题(如各种隧穿时间定义的应用范围，各种时间定义间联系，以及超光速隧穿的物理意义等问题)。在本文的第二章，我们具体翔实的介绍了当前存在的几种常用的关于隧穿时间的定义，即：相时(the phase-time)；the Buttiker and Landauer times；拉莫时间(the Larmor times)；复时间(the complex[path-integral and Bohm]times)；驻留时间(the dwell time)，给出了它们适用范围，和各个方法之间联系区别，简要的介绍了各种方法给出的Hartman effect。在本文的第三部分，我们首先介绍了一些前人的工作，指出了当前隧穿时间研究中相对论背景文献不多，同时这些文献中多半采用传统的静态计算方式，应用这一方式在有的情况下并不能得到完全精确的计算结果(如相对论the Larmor times计算)。为了避免这一缺陷，并且在同一相对论背景下讨论各个时间关系，通过一定的计算(静态的，含时的)，我们给出了相对论背景下the Larmor times和the dwell time的一般表达式，对比了它们之间的联系，同时在非相对论极限下退化到了之前文献。最后我们简要的计算了最简单也最具代表性的方势垒隧穿时间，讨论了它们的超光速隧穿现象(Hartman effect)。在本文的结束部分我们展望了未来的工作。更多还原

【Abstract】 Quantum tunneling times is an old and fundamental problem; it has been debated for decades since it was first pointed out in 1931.the interest on this subject has grown up, not only for it’s theoretical valuable, for example the physical meaning of superluminal tunneling; but also for it’s connect with hi-tech, especially during the last twenty years, for the increaseing use of high-speed electronic devices (based on tunneling processes) as well as for the acknowledged importance of the tunnel effect in nuclear fission and fusion, more and more interest be taken on this problem. In this paper we firstly introduce the history of tunneling times in introduction, and the major debated questions in tunneling times (the validity of the various tunneling times, the relation between those tunneling times, and the physical meaning of superluminal transmission times). In the second part we examine in detail some existing definitions for the tunneling times, namely: the phase-time; the B’uttiker and Landauer times; the Larmor times; the complex (path-integral and Bohm) times; the dwell time; and give the using condition of the various tunneling times, the relation between those tunneling times, the Hartman effect of those times. In the third part we firstly introduce some previous works, we find only a few papers have discussed relativistic tunneling time, and the tunneling time has been also traditionally examined for stationary state which is inaccurate in certain condition(for example, the relativistic Larmor time). In order to avoid the weakness and discuss the relation between those tunneling times, we give the general forms of the dwell time and the Larmor time, and compare the relationship between two times; in nonrelativistic limit we reduced our calculation to the previous nonrelativistic papers. Finally, we calculate tunneling times of the square barrier which is most simple and representative, and analyze the superluminal tunneling (Hartman effect). In the last part we introduce our next works.The debates focused on the validity of the various tunneling times, the relation between those tunneling times, and the physical meaning of superluminal transmission times indicated by a number of experiments. One commonly cited reason for these debates is time enters in quantum theory as a parameter rather than an observable, in other words, a quantum-mechanical time operator is nonexistent, and there is no direct way to calculate tunneling times. Thus a series of approaches have been proposed to address this issue, but there have been no clear-cut solutions to this old and fundamental problem.更多还原