Overview
Introductory lecture material
Programming
Basic numerical methods
Methods and Algorithms
Monte Carlo methods
Quantum Monte Carlo methods
Continuous Time Quantum Monte Carlo
HartreeFock method
Density functional theory
Molecular Dynamics


Left: Simulation of a bacteria growth by DLA method, Right: Molecular dynamics simulation of a small system of atoms
Simulation codes is available to download in lecture material.
This course introduces algorithmic concepts and familiarizes
students with the basic computational tools which are essential
for graduate students in computational physics, but are also very useful to most graduate students in STEM and related
areas, as well as to those students who plan to look for a job in the IT industry.
In this course, students work toward mastering computational
skills, and basic algorithms which appear in classical and quantum physics, but are not limited to those fields, for example
large scale minimization problems, high dimensional integration problems, and solving partial differential equations are constituting the bulk of the course,
but these same algorithms appear in all STEM fields and are also used by quants in major banks. While the examples are drawn mostly from quantum physics,
their applicability is far beyond this specific physics subfield.
As the programing language, we will use mostly Python and
its scientific library scipy & numpy.
To speed up parts of the code, we will also
use C++ (with pybind11) and fortran90 (f2py) for short examples, which will be used
through the Python interface.
This course has no prerequisites except for familiarity with
programming language. It is designed for the student who wishes to
broaden his/her knowledge of applications and develop
techniques.
To complete the homework and perform the handson
training, it is desired that students use their laptops and bring their own laptops to
the class (when in person).
Class Time: ARC 206 12:10pm1:30pm Monday and Thursday
Instructor: 
Kristjan Haule
Office: Serin E267
email: haule@physics.rutgers.edu
Phone: 4453881
Office hours: after lecture

Codes available at https://github.com/haulek/CompPhysics
Youtube videos from 2021:
Lecture 1,
Lecture 2,
Lecture 3,
Lecture 4,
Lecture 5,
Lecture 6,
Lecture 7,
Lecture 8,
Lecture 9,
Lecture 10,
Lecture 11,
Lecture 12,
Lecture 13,
Lecture 14,
Lecture 15,
Lecture 16,
Lecture 17,
Lecture 18,
Lecture 19,
Lecture 20,
Lecture 21,
Lecture 22,
Lecture 23,
Lecture 24,
Lecture 25,
Lecture 26
Preliminary Course Outline and Tentative List of Topics include
A) Introduction
 Installation, comparison of
programing languages by computing Mandelbrot set, speed up the code with numba, f2py, pybind11,
parallelization with openMP
 Numerical error accumulation, stable
recursion and Miller's algorithm
Source code: https://github.com/haulek/CompPhysics
Text for recursive Homework in pdf
local copy of codes:
Plots of Mandelbrot set using fortran, C++, Perl and Python
Glues fortran and C++ to Python using f2py and pybind11
Computes Bessel functions with upward and downward recursion, shows the error.
B) Learning high level programming with examples in Python(Numpy, SciPy, Pylab)
 00_Introduction (to Jupyter)
 01_Basic_Python
 02_Numpy
 03_Scipy
 04_Scipy_example_Hydrogen_atom
 05_Atom_in_LDA
Jupyter notebooks of these lectures can be downloaded at
https://github.com/haulek/CompPhysics/tree/main/Programing
This lectures are adopted from https://github.com/jrjohansson/scientificpythonlectures
Homeworks:
Homework 3,
Numerov algorithm
Homework 4,
Script for XC potential: excor.py
Total energies from NIST (Energies are given in Hartree's)
More literature on Learning Python:
Software carpentry
How to Think Like a Computer Scientist: Learning with Python
Python for beginners
Python documentation
Python regular expressions
C) Monte Carlo and Simulated Annealing
 Random numbers, multidimensional Vegas integration
(source code in html)
 Classical Monte Carlo, Simulated Annealing
(source code for Ising model,
Wang Landau,
Traveling Salesman)
 HighDimensional integration by Metropolis
Homework for highD integration by Metropolis
Source Codes:
 jupyter nb for Vegas algorithm
 jupyter nb for Ising model
 jupyter nb for Wang Landau
 jupyter nb for The Traveling Salesman problem
 jupyter nb for HighD integration by
Metropolis, mweight.py
C version of HighD integration
 Diffusion limited aggregation
 Other MC codes
Alternative implementation of Ising: online Ising model simulation
D) Basic numerical methods:
 Numeric integration (source code)
 Interpolation, Splines and Fourier transformation (source code)
 Differential equations (source code)
 Parallel programming with MPI ( source code)
Literature:
Numerical Recipes online
E) More advanced topics in Computational Condensed Matter physics:
 HartreeFock method
 Density functional theory
 Quantum Monte Carlo methods
 Continuous Time Quantum Monte Carlo method
 Molecular dynamics simulation
Literature:
 Computational Physics by J.M. Thijssen
 An introduction to Computer Simulation Methods by H. Gould, J Tobocnik and W. Christian
 Electronic Structure, Basic Theory and Practical Methods by Richard M. Martin(Very good book for the Density functional part of the course)
 An Introduction to Computational Physics by Tao Pang
 Computational Physics by Rubin H. Landau and Manuel J. Paez(More elementary but good book)
Students with Disabilities
