Mathematical and Computational Studies on Bose-Einstein Superfluid

点击翻译按钮获取中文摘要

Bose-Einstein condensate (BEC), predicted by S. Bose and A. Einstein in the early 1920s, is a state of matter near absolute zero temperature for which all atoms lose their individual properties and condense into a macroscopic coherent 'super-wave'. Since its first experimental realization in 1995 (2001 Nobel Prize in Physics awarded to E. A. Cornell, W. Ketterle, and C. E. Wieman), BEC has been the focus of active research both experimentally and theoretically. It not only provides a new platform to investigate quantum properties of matter but also opens new perspectives for understanding the phenomena of superconductivity and superfluidity. The recent launch of the Cold Atom Laboratory to the space station on May 21, 2018 has once again drawn the spotlight to BEC superfluidity. This project focuses on the fundamental mathematical and computational issues arising in the study of Bose-Einstein superfluids to understand its behavior under the influence of artificial gauge fields and long-range dispersive interactions. It could potentially benefit the development of advanced technologies, for instance, superconducting quantum interference devices and atom interferometer-based sensors. The main objectives of this research are to build mathematical and computational treatments for the magnetic Schrodinger equations, to promote the understanding of Bose-Einstein superfluidity, so as to advance the experiments and applications of BEC. This project proposes systematic research on the mathematical modeling and numerical simulations of BEC superfluids in the presence of long-range dispersion interactions. On one hand, new mathematical and numerical issues introduced by the long-range dispersion will be investigated in detail. First, effective absorbing boundary conditions will be developed to avoid the artificial reflections of waves at the computational boundary, one persistent problem in wave simulations. Then accurate and efficient numerical methods will be designed to discretize the magnetic Schrodinger models. On the other hand, the solution properties of BEC will be studied analytically and numerically to understand the influence of long-range dispersion interaction and its interplay with nonlinear interactions. Both stability analysis and numerical simulations will be carried out to study the modulation instability and wave collapse due to the competition of dispersion and nonlinear interactions. Moreover, the properties of quantized vortices in the presence of artificial gauge field and nonlocal dispersive and/or nonlinear interactions will be investigated, so as to advance the understanding of BEC superfluidity.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.