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物理代写|凝聚态物理代写Condensed Matter Physics代考|PHYS451 Graphical representation of elementary excitations and probe particles

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物理代写|凝聚态物理代写Condensed Matter Physics代考|Graphical representation of elementary excitations and probe particles

Elementary excitations, probe particles, and their interactions can be represented graphically (Feynman diagrams). When describing physical processes, it is often assumed that time develops from the left to the right, or from the bottom to the top of the diagram used to describe the process. Each elementary excitation or probe particle is depicted by a line (a different type of line for each type of excitation) and a label that characterizes its quantum numbers. Some graphic representations are shown in Fig. 1.5.

物理代写|凝聚态物理代写Condensed Matter Physics代考|Quasiparticle–boson interactions

Many physical processes in condensed matter systems involve the interactions of quasiparticles with bosons. The bosons may correspond to the collective excitations of the system or to the probe particles. Some examples are given in Fig. 1.6, where electrons and holes are used as the prototypes for the quasiparticles, and photons represent bosons. The following cases are given graphically in Fig. 1.6: (a) an electron having wavevector k emits a photon of wavevector $-\mathbf{q}$ and is scattered into a state described by wavevection $\mathbf{k}+\mathbf{q}$; (b) an electron with wavevector $\mathbf{k}$ absorbs a photon of wavevector $\mathbf{q}$ and is scattered into a state $\mathbf{k}+\mathbf{q}$; (c) a hole with wavevector $-\mathbf{k}-\mathbf{q}$ emits a photon at wavevector $-\mathbf{q}$ and is scattered into the state $-\mathbf{k}$; (d) a hole of wavevector $-\mathbf{k}-\mathbf{q}$ absorbs a photon of wavevector $\mathbf{q}$ and is scattered into the state $-\mathbf{k}$; (e) the creation of an electron of wavevector $\mathbf{k}+\mathbf{q}$ and a hole of wavevector $-\mathbf{k}$ by a photon of wavevector $\mathbf{q}$; and (f) the annihilation of an electron of wavevector $\mathbf{k}+\mathbf{q}$ and a hole of wavevector $-\mathbf{k}$ to produce a photon of wavevector $\mathbf{q}$.
The photon representing the boson in Fig. $1.6$ can be replaced by other bosons. Examples of common electron-boson interactions are shown in Fig. 1.7. These include the electron-photon interaction and others, such as the electron-phonon interaction and the electron-plasmon interaction. In each of these examples an electron with wavevector $\mathbf{k}$ emits a boson of wavevector $\mathbf{q}$ and is scattered into a state described by wavevector $\mathbf{k}-\mathbf{q}$

MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。