量子开放系统中量子响应及应用的理论研究

发布时间：2017-12-27 21:46

本文关键词：量子开放系统中量子响应及应用的理论研究　出处：《大连理工大学》2016年博士论文　论文类型：学位论文

【摘要】：量子力学是20世纪初诞生的探索微观粒子运动规律的科学,它的诞生使得人们能更加深刻地认识和了解物质的微观行为和规律,极大地促进了量子光学、凝聚态理论、量子信息科学以及量子化学等各个学科的发展。随着量子信息技术的高速发展,人们越来越重视以量子理论为基础的理论发展以及量子物理相干器件的实验实现。但是在研究具体问题中,外界环境不可避免地影响量子系统的演化,这将导致量子系统相干性的破坏。本文主要以量子开放系统为研究对象,研究量子开放系统中的量子响应理论及其应用,我们给出了量子开放系统的一般的非线性响应的极化率公式,随后把它推广到非马尔可夫量子开放系统中,发现了系统的极化率从非马尔可夫到马尔可夫区域转变过程中的变化,这将对量子光学和凝聚态领域有很大的参考价值。全文共分为七章,每章的具体内容安排如下：第一章具体介绍了与本文的研究内容相关的量子力学的基本概念和研究现状,随后我们概述了量子开放系统的研究方法及其进展,阐释了开放系统量子响应理论的重要性及其研究基础。第二章,我们介绍了用于推导主方程的投影算符方法和二阶微扰方法,分别在Heisenberg绘景和Schrodinger绘景中推导了量子Langevin方程及non-Markovian输入输出关系,然后我们介绍了开放系统中常用的近似方法-平均场近似和BBGKY级列近似,最后我们介绍了线性响应理论的Kubo公式及其霍尔电导率的推导。第三章,我们发展了量子开放系统的非线性响应理论,定义了非线性响应极化率,并且把它展开到微扰参数的任意阶。然后我们把它应用到开放系统的霍尔电导率的推导,计算结果指出拓扑相的相变点对环境具有鲁棒性。第四章,基于开放系统的微扰方法,我们发展了开放系统的线性响应理论,推导了两带系统与环境耦合的霍尔电导。在退相干环境下,开放系统的霍尔电导可以写为封闭系统的加上外界环境引起的霍尔电导。我们的结果指出,从霍尔电导率的观点来看,开放系统没有拓扑不变性。第五章,我们研究了两带模型对量子化场的响应,定义了两带模型在量子场驱动下的霍尔电导率。使用自旋轨道耦合的两带模型演示了我们的理论,发现量子涨落抑制了经典场的霍尔电导,量子场在平均意义下对霍尔电导影响不大。第六章,考虑非马尔可夫效应,我们推导了开放量子系统在含时外场下的线性响应公式。指出通过调节环境的谱密度可以控制系统的极化率从非马尔可夫到马尔可夫区域的转变。作为非马尔可夫响应理论的应用,我们推导了两带模型与环境耦合的霍尔电导。最后,我们给出了本文的总结和展望。
[Abstract]:Quantum mechanics is the law of motion of micro particles on twentieth Century the beginning of the birth of science, its birth makes people more deeply understand the micro behavior and the rule of material, greatly promoted the development of various quantum optics, condensed state theory, quantum information science and quantum chemistry. With the rapid development of quantum information technology, people pay more and more attention to the development of theory based on quantum theory and the experimental realization of quantum physics coherent devices. But in the study of specific problems, the external environment inevitably affects the evolution of quantum systems, which will lead to the destruction of the coherence of the quantum system. This paper mainly to the open quantum system as the research object, the study of quantum open quantum systems in response theory and its application, we give a general nonlinear polarization response of open quantum system rate formula, then it is extended to non Markov quantum open system, found the polarizability in the system to change from the non Markov Markov regional change in the process, it will have great reference value for the field of quantum optics and condensed matter. This paper is divided into seven chapters, the specific content of each chapter is as follows: the first chapter introduces the basic concepts and research status of quantum mechanics and the research content of this article, we summarized the research methods and progress of open quantum systems, quantum open system response theory and its research foundation to explain the importance of. The second chapter, we introduced the projection operator method to deduce the master equation and two order perturbation method, Heisenberg and Schrodinger respectively in painting picture derived quantum Langevin equation and the input and output of non-Markovian, then we introduce the method of approximate common open system in the mean field approximation and BBGKY column approximation. Finally, we introduce the derivation of the linear response Kubo formula and Holzer conductivity theory. In the third chapter, we develop the nonlinear response theory of quantum open system, define the nonlinear response polarizability, and expand it to any order of perturbation parameter. Then we apply it to the derivation of the Holzer conductivity of the open system. The results show that the phase transition point of the topological phase is robust to the environment. The fourth chapter, the perturbation method based on open system, we developed a linear open system response theory, Holzer is derived from the system environment coupling two conductance. In the decoherence environment, the Holzer conductance of the open system can be written as the Holzer conductance caused by the enclosed environment and the external environment. Our results indicate that, from the point of view of Holzer's conductivity, the open system has no topological invariance. The fifth chapter, we study the response model of the two quantized field, define the Holzer model in two conductivity quantum field driven. The demonstration two spin orbit coupling model using our theory, found that quantum fluctuations control Holzer conductance of the classical field, the quantum field in the sense of the average conductance has little effect on Holzer. In the sixth chapter, considering the non Markovian effect, we derive the linear response formula of an open quantum system under the time-dependent external field. It is pointed out that by adjusting the spectral density of the environment, the polarizability of the system can be controlled from the non Markovian to Markov region. As a non Markovian response theory, we derive the Holzer conductance model and environment coupled with. Finally, we give the summary and Prospect of this article.
【学位授予单位】：大连理工大学
【学位级别】：博士
【学位授予年份】：2016
【分类号】：O413

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