Simulation of classical and quantum random walkers through mazes

Motion of a classical random walker within a variety of boundary conditions and potentials is a well studied problem. Recently, quantum random walkers under various effects have also attracted interest. (See for example, this reference.) The problem has relevance to transport through disordered media.

The project will involve:

• Construction of a random maze through which the particle will move.
• Simulation of the random classical walker through the maze and obtaining the final probability distribution of its position.
• Simulation of the random quantum walker through the maze and obtaining the final probability distribution of its position.

The student is expected to

• have a reasonable amount of computational skill, (Improvement of computational skills should also be seen as a part of the aims of this project.)
• have passes the Quantum Mechanics courses,
• discuss the project with me before applying for assignment.