Computational Physics 509

Instructor: Gabriel Kotliar, Serin Physics Lab Room 267.

Assistants: Viktor Udovenko Serin Physics Lab Room 256

Questions: If you have any inquiries about this course or the homework, please do not hesitate to contact me or Viktor via email at : kotliar@physics.rutgers.edu
udo@physics.rutgers.edu

Time and Place: We will meet in ARC 204, on Tuesdays and Fridays, 11:30 -12:50. Classes begin Tuesday January 18. The last lecture will take place on Monday May 3rd.

Office hour: Time to be arranged and also by appointment. Tel 445-4331

Grades: Grades will be determined on the basis of assignments and homework.

Current Exercises:(This page will be frequently updated to list the homework)

1. Assigment 1: pdf ps.gz
2. Related Material (program in fortran 90 which calculates the average of n random numbers) : pdf ps.gz
4. Random Numbers in fortran 90 .
5. Assigment 2: pdf ps.gz
6. Related Material (roundoff errors in numerical computations of derivatives ) pdf ps.gz
7. Solutions 2: mathematica notebook (postscript)
8. fortranprogram (postscript)
9. Assigment 3 ( Finding U's using LDA) homework3
10. Assigment 4 (Ising Model MC):pdf ps.gz
11. Assigment 5 (Fourrier Transformations in a Many Body Problem):pdf ps.gz
 

Scope of Course:

Computation is an integral part of modern science and the ability to exploit effectively the power offered by computers is now essential for a working physicist.

The goal of this course is to make students aware of what is involved in computational physics, and the large variety of tools which can help us do classical and quantum physics using the computer. Examples will be drawn from various areas of physics.

This course has no prerequsites except for familiarity with some programming language.

Problem sets will be handed out regularly and will be an integral part of the course. There will be no final examination. Instead the students will be encouraged to carry out a small computational project of their choice, with the aproval of the course instructor.

Preliminary Course Outline and Tentative List of Topics

• Introduction: physics, computers, numerical methods.
• Approximating functions: interpolation, curve fitting,least squares and splines. Numerical Integration and Differentiation
• Solving Equations on the Computer: Substitution Iteration, Newton and Broyden methods.
• Numerical Integration. Monte Carlo Method.
• Matrix operations on the computer: Gauss Elimination, the Singular Value Decomposition, Matrix inversion.
• Matrix Eigenvalue problems, Jacobi and Lanczos Methods.
• Fourier Analysis on the computer. The fast Fourier transform.
• Ordinary Differential Equations. Multistep and implicit methods.
• Boundary Value and Eigenvalue problems.
• Optimization: Conjugate Gradient Methods.
• Introduction to Symbolic Manipulation.
• Quantum Montecarlo Methods.
• Ill posed problems Regularization and Maximum Entropy Methods.
Throughout the course there will be applications of these technique to problems in classical mechanics, quantum mechanics, statistical physics, atomic physics and quantum many-body theory.

Examples include montecarlo calculations in classical statistical mechanics, chaos in classical mechanics, quantum many body physics and electronic structure calculations in solid state physics.

Bibiliography 

There are a large number of textbooks in this area. They reflect the growing importance of the field. I do not plan to follow a specific textbook, but here is a (very partial) list of books on the subject:

1. Numerical Recipes by W. Press S Teukolsky W. Vetterling and B. Flannery (excellent reference book on practical algorithms)
2. on line reference .
3. Computational Physics by S. Koonin, (elementary but to the point introduction to the subject)
4. Introduction to Numerical Analysis by J. Stoer and R. Bulirsch (classical textbook on numerical analysis)
5. An Introduction to Computational Physics by Tao Pang (more recent)
6. Computational Physics by J. M Thijssen (advanced but less detailed)
• Werner Krauth's
• Introduction to Montecarlo Algorithms a crystal clear introductions to the main ideas
• For some of the software available to our system see /import/positron/h6/devel/numrec
• Pang's Computational Physics .
• Thijssen's Computational Physics.
• Sun Documentation.
• pseudopotential code

 

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