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Publication Date


First Advisor

Gary N. Felder

Document Type

Honors Project

Degree Name

Bachelor of Arts




Chaos theory, Quantum mechanics, Linear programming, Numerical calculation, Optimization


A numerical method was developed to calculate the distance between two quantal states in a chaotic system. The Wigner function was applied to formulate a quantal state at an arbitrary time, and given its quasi-distribution properties, the analogy of a ”sand pile” was used, where the optimal transportation cost between the two sand piles was mathematically equivalent to the distance between the two quantal states. 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% in comparison to the corresponding analytical solutions were able to be obtained. The efficiency of such calculation was greatly improved by the SciPy LP program with the computing time reduced from 3000 seconds to approximately 10 seconds.


©2021 Yuxin Lan. Access limited to the Smith College community and other researchers while on campus. Smith College community members also may access from off-campus using a Smith College log-in. Other off-campus researchers may request a copy through Interlibrary Loan for personal use.




66 pages : color illustrations Includes bibliographical references (page 66)