Computational Physics: Simulation of Classical and Quantum Systems
計算物理：經(jīng)典和量子系統(tǒng)的模擬

Author: Philipp O.J. Scherer

下載地址：https://www.zhisci.com/pdfshow/17740

This textbook presents basic and advanced computational physics in a very didactic style. It contains very-well-presented and simple mathematical descriptions of many of the most important algorithms used in computational physics. Many clear mathematical descriptions of important techniques in computational physics are given. The first part of the book discusses the basic numerical methods. A large number of exercises and computer experiments allows to study the properties of these methods. The second part concentrates on simulation of classical and quantum systems. It uses a rather general concept for the equation of motion which can be applied to ordinary and partial differential equations. Several classes of integration methods are discussed including not only the standard Euler and Runge Kutta method but also multistep methods and the class of Verlet methods which is introduced by studying the motion in Liouville space. Besides the classical methods, inverse interpolation is discussed, together with the popular combined methods by Dekker and Brent and a not so well known improvement by Chandrupatla. A general chapter on the numerical treatment of differential equations provides methods of finite differences, finite volumes, finite elements and boundary elements together with spectral methods and weighted residual based methods. A comparison of several methods for quantum systems is performed, containing pseudo-spectral methods, finite differences methods, rational approximation to the time evolution operator, second order differencing and split operator methods.
這本教科書介紹了基礎和先進的計算物理在一個非常說教的風格。它包含了計算物理中使用的許多最重要算法的非常好的呈現(xiàn)和簡單的數(shù)學描述。對計算物理中的重要技術給出了許多清晰的數(shù)學描述。書的第一部分討論了基本的數(shù)值方法。大量的練習和計算機實驗允許研究這些方法的性質(zhì)。第二部分集中于經(jīng)典系統(tǒng)和量子系統(tǒng)的模擬。它對運動方程使用了一個相當普遍的概念，可以應用于常微分方程和偏微分方程。討論了幾種積分方法，不僅包括標準Euler和Runge-Kutta方法，還包括多步方法和通過研究Liouville空間中的運動引入的Verlet方法。除了經(jīng)典方法外，還討論了逆插值，以及Dekker和Brent的常用組合方法以及Chandrupatla的一個不為人所知的改進。關于微分方程數(shù)值處理的一般章節(jié)提供了有限差分法、有限體積法、有限元法和邊界元法以及基于譜法和加權(quán)殘差法的方法。比較了量子系統(tǒng)的幾種方法，包括偽譜方法、有限差分方法、時間演化算子的有理逼近、二階微分和分裂算子方法。

The book gives simple but non trivial examples from a broad range of physical topics trying to give the reader insight into the numerical treatment but also the simulated problems. Rotational motion is treated in much detail to describe the motion of rigid rotors which can be just a simple spinning top or a collection of molecules or planets. The behaviour of simple quantum systems is studied thoroughly. One focus is on a two level system in an external field. Solution of the Bloch equations allows the simulation of a quantum bit and to understand elementary principles from quantum optics. As an example of a thermodynamic system, the Lennard Jones liquid is simulated. The principles of molecular dynamics are shown with practical simulations. A second thermodynamic topic is the Ising model in one and two dimensions. The solution of the Poisson Boltzman equation is discussed in detail which is very important in Biophysics as well as in semiconductor physics. Besides the standard finite element methods, also modern boundary element methods are discussed. Waves and diffusion processes are simulated. Different methods are compared with regard to their stability and efficiency. Random walk models are studied with application to basic polymer physics. Nonlinear systems are discussed in detail with application to population dynamics and reaction diffusion systems. The exercises to the book are realized as computer experiments. A large number of Java applets is provided. It can be tried out by the reader even without programming skills. The interested reader can modify the programs with the help of the freely available and platform independent programming environment "netbeans".
這本書給出了簡單但不平凡的例子，從一個廣泛的物理主題試圖給讀者洞察數(shù)字處理，也模擬問題。旋轉(zhuǎn)運動被詳細地處理來描述剛性轉(zhuǎn)子的運動，這些轉(zhuǎn)子可以是簡單的旋轉(zhuǎn)陀螺，也可以是分子或行星的集合。對簡單量子系統(tǒng)的行為進行了深入的研究。其中一個重點是外部領域的兩級系統(tǒng)。布洛赫方程組的求解可以模擬量子比特，并從量子光學中理解基本原理。作為一個熱力學系統(tǒng)的例子，對Lennard-Jones液體進行了模擬。通過實際模擬，說明了分子動力學原理。第二個熱力學主題是一維和二維的伊辛模型。詳細討論了泊松-玻爾茲曼方程的求解方法，該方程在生物物理和半導體物理中都是非常重要的。除了標準的有限元方法外，還討論了現(xiàn)代邊界元方法。模擬了波浪和擴散過程。比較了不同方法的穩(wěn)定性和效率。研究了隨機游走模型及其在聚合物基礎物理中的應用。詳細討論了非線性系統(tǒng)在人口動力學和反應擴散系統(tǒng)中的應用。這本書的練習是作為計算機實驗來實現(xiàn)的。提供了大量的Java小程序。即使沒有編程技巧，讀者也可以試用它。感興趣的讀者可以在免費的、獨立于平臺的編程環(huán)境netbeans的幫助下修改程序。

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