基于有限元法的光子并矢格林函数重整化及其在自发辐射率和能级移动研究中的应用

任意微纳结构中量子点的自发辐射率和能级移动均可用并矢格林函数表达.当源点和场点在同一位置时,格林函数的实部是发散的.为解决这一发散问题,可采用重整化格林函数方法.本文提出一种计算重整化格林函数和散射格林函数的方法.该方法利用有限元,计算点电偶极子的辐射场,将其在量子点体积内做平均得到重整化的并矢格林函数,减去均匀空间中解析的重整化格林函数,得到重整化的散射格林函数.在均匀空间情况下,本方法所得数值结果与解析解一致.将该方法应用到银纳米球系统,以解析的散射格林函数作为参考,结果表明该方法能准确处理散射格林函数的重整化问题.将该方法应用到表面等离激元纳米腔中,发现有极大的自发辐射增强和能级移动,且该结果不依赖于量子点的体积.这些研究在光与物质相互作用领域具有积极的意义.     

低维纳米材料量子热输运与自旋热电性质 ——非平衡格林函数方法的应用

低维材料不断涌现的新奇性质吸引着科学研究者的目光. 除了电子的量子输运行为之外, 人们也陆续发现和确认了热输运中显著的量子行为, 如 热导低温量子化、声子子带、尺寸效应、瓶颈效应等. 这些小尺度体系的热输运性质可以很好地用非平衡格林函数来描述. 本文首先介绍了量子热输运的特性、声子非平衡格林函数方法及其在低维纳米材料中的研究进展; 其次回顾了近年来在 一系列低维材料中发现的热-自旋输运现象. 这些自旋热学现象展现了全新的热电转换机制, 有助于设计新型的热电转换器件, 同时也给出了用热产生自旋流的新途径; 最后介绍了线性响应理论以及在此理论框架下结合声子、电子非平衡格林函数方法进行的一些有益的探索. 量子热输运的研究对热效应基础研究以及声子学器件、能量转换器件的发展有着不可替代的重要作用.     

光子增减叠加相干态在热环境中的退相干

研究了由光子增减叠加操作作用于相干态而得量子态的非经典性及其在热环境中的退相干问题.通过解析导出了Mandel's Q参数、光子数分布、Wigner函数等,讨论其非经典性.研究表明一阶光子增减相干叠加相干态在相空间总是取负值,只要满足条件∣2z* +α-α*∣2＜1.基于Wigner函数的演化积分公式,解析地推导出了在热环境中Wigner函数的简洁表达式.研究首次表明:如果κt＜1/2ln[(2(η)+2)/(2(η)+1)]得以满足,一阶光子增减相干叠加相干态在相空间最小值点处Wigner函数分布总存在负部.此外,根据Wigner函数负部体积讨论了其非经典特性.     

三终端原子环的弹道热整流

提出并通过非平衡格林函数法验证了一个弹道热整流理论模型——以原子环为中心散射区,非对称连接三条半无限长原子链作为左热极、控制热极和右热极.对三终端六元环结构的计算发现控制热极与左右热极之间的声子透射率有显著差异.左右热极之间的热整流比随着温差的增加而显著上升,正向热流可以达到反向热流的几倍以上.另外对该模型中弹道热整流的形成机理也做了详细说明.     

激光热弹超声的等效电路

本文以热弹理论为基础，提出了一种描述激光热弹超声的等效电路模型，该模型将激光直接照射区同周围的声传播媒质分开考虑，采用三端口网络描述了热一弹能量的直接转换，传播声场的影响则以辐射阻抗的形式出现。由于电路是由单频情况导出，故任意时间响应可通过ＩＦＦＴ算法得到。本文针对三种典型照射区，既圆板、柱和球、建立了绝抽条件下的热弹等效电路，计算了各自的时间响应，结果与格林函数解相符。     

微量子腔结边电荷极化结构中的线性和二阶非线性动态电导性质的研究

采用有效哈密顿量和有相互作用的分立势模型，利用格林函数和耦合参量得出了量子点(腔)在有结边电荷积累极化时的线性和二阶非线性交流电导虚部(emittance)的明确表达式.发现在经典情况下，电导虚部和电化学电容都等于经典的几何电容.在非经典情况下，如果发生全反射，电导虚部和电化学电容相等，但两者皆不等于经典的几何电容.在有隧穿的情况下，电导虚部和电化学电容以及经典电容三者都不相等.该结果对于量子器件中的电容测量具有指导作用. 关键词： 格林函数 交流电导 电化学电容     

多端耦合量子点分子桥的量子输运特性研究

利用非平衡格林函数方法,对五个量子点连结而成的有四个终端的耦合量子点分子桥进行了理论研究和数值模拟,得出了入射电子通过耦合量子点分子桥传输到各个终端的电子隧穿概率的规律. 关键词： 耦合量子点分子桥 非平衡格林函数 量子输运     

界面尺寸对铜/石墨烯界面热导的影响

采用原子格林函数(AGF)方法研究了界面尺寸对铜/单层石墨烯(SLG)界面热导的影响.建立了有限和无限界面尺寸的AGF计算模型,计算得到的界面热导均在铜的迪拜温度(343 K)附近收敛,但两者计算得到的透射系数和界面热导存在明显差别:有限界面尺寸时计算得到的透射系数在1.5 THz附近达到峰值0.84,而无限界面尺寸时...     

石墨烯p-n结在磁场中的电输运热耗散

石墨烯是一种特殊的二维材料,其独特的能带结构允许人们通过电场来调控其载流子的类型和浓度,因此,在构建双极型纳米电子器件方面具有潜在应用前景.本文基于紧束缚格点模型,利用非平衡格林函数方法及Landauer-Büttiker公式,研究了石墨烯p-n结在磁场中的电输运热耗散问题.在强磁场作用下,结的两边均处于量子霍尔相,存在拓扑保护的手性边缘态.直觉上,这种拓扑保护的手性边缘态应当是无热耗散的.但本文研究发现,当有耗散源时,尽管手性边缘态受到拓扑保护,热耗散却依然可以发生.对于完美的石墨烯,单极结输运时热耗散发生在体系边缘;偶极结输运时在体系边缘和结的界面处均可以发生热耗散.当无序存在时,无论单极结还是偶极结,无序均能增强热耗散.此外,本文还研究了不同位置处的电子能量分布,发现热耗散是否发生只取决于电子是否处于非平衡分布.这些结果表明拓扑只能保护电子的传播方向,却不能禁止热耗散的发生.     

三套闭路格林函数的变换关系

给出三套闭路格林函数之间的变换关系和若干运算规则,同时得到多点推迟和超前格林函数的一般定义。证明多点格林函数之间的一些代数关系,是闭路上相连格林函数生成泛函W[J₊,J_-]_(J+=J-=J)=0这一性质的后果。 关键词：     

Functional methods in thermofield dynamics: A real-time perturbation theory for quantum statistical mechanics

A generating functional is constructed for real-time Green functions in quantum statistical mechanics in the context of thermofield dynamics. The KMS condition is taken as an axiom which together with field equations fixes the generating functional for causal Green functions in an interacting quantum field theory. This leads to Feynman rules for diagrammatic real-time perturbation theory.     

Multi-loop Feynman integrals and conformal quantum mechanics

New algebraic approach to analytical calculations of D-dimensional integrals for multi-loop Feynman diagrams is proposed. We show that the known analytical methods of evaluation of multi-loop Feynman integrals, such as integration by parts and star-triangle relation methods, can be drastically simplified by using this algebraic approach. To demonstrate the advantages of the algebraic method of analytical evaluation of multi-loop Feynman diagrams, we calculate ladder diagrams for the massless φ³ theory. Using our algebraic approach we show that the problem of evaluation of special classes of Feynman diagrams reduces to the calculation of the Green functions for specific quantum mechanical problems. In particular, the integrals for ladder massless diagrams in the φ³ scalar field theory are given by the Green function for the conformal quantum mechanics.     

Introduction of Anomalous Green Functions into Quantum Chromodynamics

The nonperturbative vacuum structure of Quantum Chromodynamic is studied with the help of a generalization of the formalism of Green functions which corresponds to the method of Gorkov and Nambu in the theory of superconductivity. Taking into account the existence of gluon condensation the selfenergy of the gluon-quasi-particles is calculated with the help of modified rules for Feynman diagrams. The resulting integral equations for the effective field parameters contain particular solutions with an energy gap in the spectrum of the quasi-particles and a phase transition at a critical momentum.     

Renormalization of QED in an external field

The Schwinger equations of QED are rewritten in three different ways as integral equations involving functional derivatives, which are called weak field, strong field, and SCF quantum electrodynamics. The perturbative solutions of these equations are given in terms of appropriate Feynman diagrams. The Green function that is used as an electron propagator in each case is discussed in detail. The general renormalization rules for each of the three equations are provided both in a non perturbative way (Dyson relations) and for Feynman diagrams.     

Renormalization theory in superspace

The auxiliary mass BPHZ renormalization procedure is extended to include theories defined in superspace. Ultraviolet and infrared power counting formulas for Feynman integrands in superspace are derived. A general momentum-superspace subtraction scheme is given which allows time-ordered Green functions of superfields to be defined as tempered distributions. Superfield normal product Green functions are introduced and the Zimmermann identity relating differently subtracted such products is established. Finally normal product field equations and the renormalized quantum action principle in superspace are derived.     

Asymptotic expansions in limits of large momenta and masses

Asymptotic expansions of renormalized Feynman amplitudes in limits of large momenta and/or masses are proved. The corresponding asymptotic operator expansions for theS-matrix, composite operators and their time-ordered products are presented. Coefficient functions of these expansions are homogeneous within a regularization of dimensional or analytic type. Furthermore, they are explicitly expressed in terms of renormalized Feynman amplitudes (at the diagrammatic level) and certain Green functions (at the operator level).     

Algebras with operator and Campbell-Hausdorff formula

We introduce some new classes of algebras and establish within these algebras Campbell-Hausdorff-like formulae. We describe the application of these constructions to the problem of the connectivity of the Feynman graphs corresponding to Green functions in quantum fields theory.     

Convergence theorems for renormalized Feynman integrals with zero-mass propagators

A general momentum-space subtraction procedure is proposed for the removal of both ultraviolet and infrared divergences of Feynman integrals. Convergence theorems are proved which allow one to define time-ordered Green functions, as tempered distributions, for a wide class of theories with zero-mass propagators.Research supported in part by National Science Foundation Grant MPS-74-21778.     

Isolating vacuum amplitudes in quantum field calculations at finite temperature

In calculating Feynman diagrams at finite temperature, it is sometimes convenient to isolate subdiagrams which do not depend explicitly on the temperature. We show that, in the imaginary time formalism, such a separation can be achieved easily by exploiting a simple method, due to Gaudin, to perform the sum over the Matsubara frequencies. In order to manipulate freely contributions which may be individually singular, a regularization has to be introduced. We show that, in some cases, it is possible to choose this regularization in such a way that the isolated subdiagrams can be identified with analytical continuations of vacuum n-point functions. However, at least with the regularization used in this paper, this simple analytical structure does not hold for arbitrary diagrams, as revealed by counter-examples. As an aside illustration of Gaudin's method, we use it to prove the main part of a recent conjecture for a relation, in the imaginary time formalism, between the expressions of a Feynman diagram at zero and finite temperature.