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Publication Date
2023-5
First Advisor
Gary Felder
Document Type
Honors Project
Degree Name
Bachelor of Arts
Department
Physics
Keywords
quantum mechanics, chaos, quantum chaos, adaptive grid, Earth mover's distance, computational physics, Wigner foundation, nonlinear dynamics
Abstract
The correspondence between classical chaos and quantum mechanics is not well understood. One understudied definition of quantum chaos directly borrows from that of its classical counterpart– a quantum system that is characterized by a positive quantum Lyapunov exponent characterizing an exponential rate of separation of trajectories with infinitesimally close initial conditions in phase space. Describing an exponential rate of separation of trajectories is a challenging problem in quantum mechanics. In phase space, quantum systems are described by their Wigner function rather than a single point, making defining and computing a distance between quantum states a challenge. One metric that can be used to define distances between probability density distributions is the Earth Mover’s Distance (EMD), a distance that can be reformulated as a transportation problem. Current methods for EMD are too computationally intensive to compute quantum Lyapunov exponents. This thesis presents QuadTreeN, a program which produces an N-dimensional adaptive grid to compute the EMD, which was demonstrated to simultaneously improve both the accuracy and speed of EMD calculations in cases where the analytical answer is known. Additionally, we present a Mathematica program to calculate the EMD over time between quantum states and present states of the harmonic oscillator as an example in this work.
Rights
©2023 Jessica Kaijia Jiang. 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.
Language
English
Recommended Citation
Jiang, Jessica Kaijia, "An Adaptive Grid to Compute Earth Mover’s Distances in Search of Quantum Chaos" (2023). Honors Project, Smith College, Northampton, MA.
https://scholarworks.smith.edu/theses/2559
Comments
96 pages : color illustrations, charts. Includes bibliographical references (pages 93-96).