Computing

MATLAB

Hands-on training

• MATLAB: Getting Started
• MATLAB: Sparse Matrices
• MATLAB: FFT
• MATLAB Student Center
• Some Common MATLAB Programming Pitfalls and How to Avoid Them

Reference

• MATLAB Brief List of Commands
• MATLAB Documentation
• Rapid code iteration using cells in the Editor

Books and notes

• C. Moler: Numerical Computing with MATLAB (SIAM, Philadelphia, 2004). [PDF]
• UD Crash Course on Matlab

Implementation Tools

• Running MATLAB m-files in the background under Linux
• Multithreaded MATLAB performance on multicores

M-files

• electron_density.m (code for Problem 1 in Homework Set 1)
• disordered_nanowire.m (code for Problems 2 & 3 in Homework Set 2)
• dos_negf.m (code to compute the density of states of a nanowire using Green functions)
• graphene_dos.m (code to compute the density of states of graphene sheet using Green functions)
• qt_1d.m (code to compute the conductance and total and local density of states of a 1D nanowire, with possible potential barriers or impurities, attached to two semi-infinite electrodes)
• 8zgnr.m (code to compute the subband structure of an infinite zigzag graphene nanoribbon discussed in the Lecture notes)
• gnr_cond_recursive.m,bstruct.m, blocktosparse.m, sparsetoblock.m, h_zigzag.m, invnn.m, Self.m, (code to compute the conductance of a finite graphene nanoribbon attached to two semi-infinite graphene electrodes)

M-functions

• matrix_exp.m (Exponential, or any other function with small changed in the code, of a Hermitian matrix)
• visual_graphene_H.m (For a given tight-binding Hamiltonian on the honeycomb lattice, function plots position of carbon atoms and draws blue lines to represent hoppings between them; red circles to represent on-site potential between them; and cyan lines to represent the periodic boundary conditions; it can be used to test if the tight-binding Hamiltonian of graphene is set correctly); This function calls another three function which should be placed in the same directory (or in the path): atomCoord.m, atomPosition.m, and constrainView.m
• self_energy.m (Self-energy of the semi-infinite ideal metallic lead modeled on the square tight-binding lattice - the code shows how to convert analytical formulas of the lead surface Green function into a working program)

Mathematica

Hands-on training

• Mathematica: Getting Started
• Mathematica: Differential Equations
• Mathematica: Linear Algebra
• Wolfram hands-on start to Mathematica

Tutorials

• J. J. Kely, Essential Mathematica for students of science
• L. Pryadko, Exploring many-body quantum physics with Mathematica

Books

• H. Ruskeepaa, Mathematica Navigator [publisher Website]