課程資訊
課程名稱
 計算物理
Computational Physics 
開課學期
 109-1 
授課對象
 理學院  物理學研究所  
授課教師
 趙挺偉 
課號
 Phys7030 
課程識別碼
 222EM2710 
班次
  
學分
 3.0 
全/半年
 半年 
必/選修
 選修 
上課時間
 星期二3,4,5(10:20~13:10) 
上課地點
 新物304 
備註
 本課程以英語授課。
總人數上限：50人
外系人數限制：5人 
Ceiba 課程網頁
 http://ceiba.ntu.edu.tw/1091Phys7030_CP 
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課程概述

This course introduces numerical methods for solving problems in sciences and engineering whose complexity or difficulty is beyond analytic solution or human endurance. Since computer simulation has become an integral part of basic and applied sciences and has been serving as a bridge between theoretical and experimental sciences, this course focuses on Monte Carlo simulation of physical systems, and the related algorithms. It is assumed that students have learned the basic programming techniques in C and/or Fortran, and C is the primary programming language in this course. 

課程目標
 Basic Mathematical Operations
Differentiation and Integration
Monte Carlo Integration
Monte Carlo Simulation of Spin Systems
Probability and Statistics, Random Number Generators
System of Linear Equations
Differential Equations
Partial Differential Equations
Introduction to Quantum Field Theory
Path Integral Formulation of QFT
Monte Carlo Simulation of QFT 
課程要求
 Each student is required to attend the lectures, to work out the problem sets, and the term project. The proposal for the term project should be submitted before November 24, 2020. Two students can collaborate on one term project, and prepare their reports individually. 
預期每週課後學習時數
  
Office Hours
 每週三 10:00~11:00 備註： or by appointment 
指定閱讀
 B. Kernigan and D. Ritchie, ``C Programming Language”, 2nd Edition, 1988, Prentice Hall.
R. Landau, M. Paez and C. Bordeianu, ``Computational Physics" 2nd Edition, Wiley (2007).
Press, W.H., et. al., ``Numerical Recipes, The Art of Scientific Computing", Cambridge (1992).
Philipp O.J. Scherer, “Simulation of Classical and Quantum Systems”, Third Edition (2017)
https://link.springer.com/book/10.1007/978-3-319-61088-7  
參考書目
 C. Gattringer and C. Lang, "Quantum Chromodynamics on the Lattice", Springer(2010)
https://link.springer.com/book/10.1007/978-3-642-01850-3 
評量方式
(僅供參考)
  
No.
項目
百分比
說明
1. 
 Term Project  
20% 
  
2. 
 Homework Assignment 
80% 
  
 
課程進度
週次
日期
單元主題
Week 1
 2020/09/15  Introduction.
Basic Mathematical Operations. Differentiation. 
Week 2
 2020/09/22  Numerical Integration,
Introduction to Monte Carlo Simulation,
Metropolis algorithm,
von Neumann's rejection algorithm. 
Week 3
 2020/09/29  Metropolis algorithm,
Heat bath algorithm,
Error estimation in the Monte Carlo simulation,
Integrated auto-correlation time,
The binning method
The jackknife method 
Week 4
 2020/10/6  Monte Carlo simulation of the Ising Model,
Metropolis algorithm
Heat bath algorithm,
Single cluster algorithm,
Exact solution of 1-Dim Ising model 
Week 5
 2020/10/13  Spontaneous Symmetry Breaking in the 2D Ising Model,
Pseudo-Random Number Generators 
Week 6
 2020/10/20  RNG with a Specified Distribution,
System of Linear Equations,
LU decomposition 
Week 7
 2020/10/27  Conjugate gradient algorithm,
Conjugate gradient with mixed-precision
Solve Poisson Equation with CG 
Week 8
 2020/11/3  Solve Poisson Equation with mixed-precision CG  
Week 9
 2020/11/10  Ordinary Differential Equation
Runge-Kutta Method
Real-time Graphic Animation with OpenGL 
Week 10
 2020/11/10  Partial Differential Equation
Vibrating String
Heat Diffusion  
Week 11
 2020/11/17  Introduction to quantum field theory,
Path integral formulation of QFT,
Real scalar field theory on the lattice
 
Week 12
 2020/11/24  Real scalar field theory in 1D
Lattice field theory
Monte Carlo Simulation of QFT
Hybrid Monte Carlo simulation
 
Week 13
 2020/12/01  Fermion Field Theory, Lattice Fermion 
Week 14
 2020/12/08  Lattice Dirac Operators, Chiral Symmetry 
Week 15
 2020/12/22  Gauge Symmetry, Gauge Field on the Lattice 
Week 16
 2020/01/05  Monte Carlo Simulation of Fermion Field Theory  
Week 17
 2021/01/21  Introduction to lattice QCD