Computational Physics

This course aims to give the students competence in the methods and techniques of calculations using computers. At the end of the course the student is expected to have a hands on experience in modeling, algorithm development, implementation and calculation of physical quantities of relevance in interacting many body problems in physics. Both quantum and classical computational tools will be introduced.INTENDED AUDIENCE: Masters students in physics, engineering physics students and scientists interested in quantum and/OR molecular modelling.PREREQUISITES: Basic Statistical Physics and quantum mechanics.INDUSTRY SUPPORT: Shell, Unilever,TCS

Week 1: Rapid overview of Fortran programming LanguageWeek 2: Random Number generation and testing, Generation of random numbers with given distributionWeek 3: Numerical Integration: (a) Deterministic: Trapezoidal method & (b) Multi-dimensional Integration
using stochastic methods.Week 4: Lattice Monte Carlo simulations using Ising model to understand phase transitions: Metropolis
algorithm, understanding kinetic barriers, finite size effects, role of thermal fluctuationsWeek 5: Metropolis algorithm, understanding kinetic barriers, finite size effects, role of thermal fluctuations;
Principle of detailed balance, calculating thermodynamic averagesWeek 6: Determining transition temperature using Binders cumulant
Week 7: Solving differential equationsWeek 8: Linear, non-linear and coupled differential equations
Week 9: Solving differential equations Schrodinger eqn. in Quantum Mechanics with Numerov’s algorithm
and variational principle.
Week 10:Classical Molecular Dynamics simulations using Lennard-Jones’ potential
Week 11:Classical Molecular Dynamics simulations using Lennard-Jones’ potential
Week 12:Classical Molecular Dynamics simulations using Lennard-Jones’ potential