Mathematical analysis of Nonlinear Schrödinger Equations for modeling of Bose-Einstein condensate
Department
Mathematics and Statistics
Major
Math and Physics
Research Advisor
Murphy, Jason
Advisor's Department
Mathematics and Statistics
Abstract
This project aims to bridge the gaps between the pure mathematical analysis, the applied mathematical modeling, and the physical experimentation associated with the NLS by: deriving an effective model for the dynamics of phenomena related to BECs using the NLS, rigorously analyze the model both theoretically and numerically, and explaining observed phenomena by comparing the mathematical results with real physical experiments. The analytic approach will allow the computational model to be robust and flexibility in the parameters of the NLS, providing a time evolution of the NLS.
Biography
Nicholas has worked at the MST physics Laboratory for Atomic Molecular and Optical Research (LAMOR) under the guidance of Dr. Daniel Fischer for over two years. This work has exposed Nicholas to the theory of Bose-Einstein condensates and cold atom systems and is where he completed an OURE for absorption imaging system of ultracold quantum gases. Further, Nicholas is a coauthor on a to-be-published LAMOR paper currently in review for the journal Physical Review A (arxiv number: 1712.01200.)
Some background in harmonic analysis and partial differential equations is required for the analysis of nonlinear partial differential. For physical application, knowledge of quantum mechanics and nonlinear dynamics is required. Nicholas will have completed the following key courses by the end of the 2018 fall semester: Partial Differential Equations, Intermediate Differential Equations, Quantum Mechanics 2, ‘Chaos, Fractals and Nonlinear Dynamics’ and Harmonic Analysis. This coursework should synergize with his study of Nonlinear Schrodinger Equations in the fall.
Presentation Type
OURE Fellows Proposal Oral Applicant
Document Type
Presentation
Location
Turner Room
Presentation Date
17 Apr 2018, 2:20 pm - 2:40 pm
Mathematical analysis of Nonlinear Schrödinger Equations for modeling of Bose-Einstein condensate
Turner Room
This project aims to bridge the gaps between the pure mathematical analysis, the applied mathematical modeling, and the physical experimentation associated with the NLS by: deriving an effective model for the dynamics of phenomena related to BECs using the NLS, rigorously analyze the model both theoretically and numerically, and explaining observed phenomena by comparing the mathematical results with real physical experiments. The analytic approach will allow the computational model to be robust and flexibility in the parameters of the NLS, providing a time evolution of the NLS.
