Title

Mathematical analysis of Nonlinear Schrödinger Equations for modeling of Bose-Einstein condensate

Presenter Information

Nicholas Parris

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

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Apr 17th, 2:20 PM Apr 17th, 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.