發(fā)布時間：2017-12-27 21:46

  本文關(guān)鍵詞：量子開放系統(tǒng)中量子響應(yīng)及應(yīng)用的理論研究　出處：《大連理工大學(xué)》2016年博士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： 量子開放系統(tǒng) 主方程 量子響應(yīng) 霍爾電導(dǎo)

【摘要】：量子力學(xué)是20世紀(jì)初誕生的探索微觀粒子運動規(guī)律的科學(xué),它的誕生使得人們能更加深刻地認(rèn)識和了解物質(zhì)的微觀行為和規(guī)律,極大地促進(jìn)了量子光學(xué)、凝聚態(tài)理論、量子信息科學(xué)以及量子化學(xué)等各個學(xué)科的發(fā)展。隨著量子信息技術(shù)的高速發(fā)展,人們越來越重視以量子理論為基礎(chǔ)的理論發(fā)展以及量子物理相干器件的實驗實現(xiàn)。但是在研究具體問題中,外界環(huán)境不可避免地影響量子系統(tǒng)的演化,這將導(dǎo)致量子系統(tǒng)相干性的破壞。本文主要以量子開放系統(tǒng)為研究對象,研究量子開放系統(tǒng)中的量子響應(yīng)理論及其應(yīng)用,我們給出了量子開放系統(tǒng)的一般的非線性響應(yīng)的極化率公式,隨后把它推廣到非馬爾可夫量子開放系統(tǒng)中,發(fā)現(xiàn)了系統(tǒng)的極化率從非馬爾可夫到馬爾可夫區(qū)域轉(zhuǎn)變過程中的變化,這將對量子光學(xué)和凝聚態(tài)領(lǐng)域有很大的參考價值。全文共分為七章,每章的具體內(nèi)容安排如下：第一章具體介紹了與本文的研究內(nèi)容相關(guān)的量子力學(xué)的基本概念和研究現(xiàn)狀,隨后我們概述了量子開放系統(tǒng)的研究方法及其進(jìn)展,闡釋了開放系統(tǒng)量子響應(yīng)理論的重要性及其研究基礎(chǔ)。第二章,我們介紹了用于推導(dǎo)主方程的投影算符方法和二階微擾方法,分別在Heisenberg繪景和Schrodinger繪景中推導(dǎo)了量子Langevin方程及non-Markovian輸入輸出關(guān)系,然后我們介紹了開放系統(tǒng)中常用的近似方法-平均場近似和BBGKY級列近似,最后我們介紹了線性響應(yīng)理論的Kubo公式及其霍爾電導(dǎo)率的推導(dǎo)。第三章,我們發(fā)展了量子開放系統(tǒng)的非線性響應(yīng)理論,定義了非線性響應(yīng)極化率,并且把它展開到微擾參數(shù)的任意階。然后我們把它應(yīng)用到開放系統(tǒng)的霍爾電導(dǎo)率的推導(dǎo),計算結(jié)果指出拓?fù)湎嗟南嘧凕c對環(huán)境具有魯棒性。第四章,基于開放系統(tǒng)的微擾方法,我們發(fā)展了開放系統(tǒng)的線性響應(yīng)理論,推導(dǎo)了兩帶系統(tǒng)與環(huán)境耦合的霍爾電導(dǎo)。在退相干環(huán)境下,開放系統(tǒng)的霍爾電導(dǎo)可以寫為封閉系統(tǒng)的加上外界環(huán)境引起的霍爾電導(dǎo)。我們的結(jié)果指出,從霍爾電導(dǎo)率的觀點來看,開放系統(tǒng)沒有拓?fù)洳蛔冃�。第五�?我們研究了兩帶模型對量子化場的響應(yīng),定義了兩帶模型在量子場驅(qū)動下的霍爾電導(dǎo)率。使用自旋軌道耦合的兩帶模型演示了我們的理論,發(fā)現(xiàn)量子漲落抑制了經(jīng)典場的霍爾電導(dǎo),量子場在平均意義下對霍爾電導(dǎo)影響不大。第六章,考慮非馬爾可夫效應(yīng),我們推導(dǎo)了開放量子系統(tǒng)在含時外場下的線性響應(yīng)公式。指出通過調(diào)節(jié)環(huán)境的譜密度可以控制系統(tǒng)的極化率從非馬爾可夫到馬爾可夫區(qū)域的轉(zhuǎn)變。作為非馬爾可夫響應(yīng)理論的應(yīng)用,我們推導(dǎo)了兩帶模型與環(huán)境耦合的霍爾電導(dǎo)。最后,我們給出了本文的總結(jié)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.
【學(xué)位授予單位】：大連理工大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2016
【分類號】：O413

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