A numerical method was developed to calculate the distance between two quantal states in a chaos system. The Wigner function was applied to formulate a quantal state at an arbitrary time, and given its quasi-distribution properties, the analogy of “sand pile” were used, the optimal transportation cost between the two sand piles was mathematically equivalent to the distance between the two quantal states by the definition of Monge distance. The concept of linear programming (LP) was applied to find the optimal cost with the SciPy Optimization package, and for special cases that can be calculated analytically, numerical solutions within 1% of percent error were able to be obtained.
A poster deriving from SURF and Honors Thesis with Gary Felder, Professor of Physics.