Mathematical and Computational Studies on Bose-Einstein Superfluid

玻色-爱因斯坦超流体的数学和计算研究

• 批准号: 1913293
• 负责人: Yanzhi Zhang
• 金额: $ 17.5万
• 依托单位: Missouri University of Science and Technology
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-07-01 至 2023-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1913293&HistoricalAwards=false
• 关键词: Mathematical; Computational; Studies; Bose; Einstein

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.

Bose-Einstein冷凝物（BEC）在1920年代初由S. bose和A. Einstein预测，是一种接近绝对零温度的物质状态，所有原子都会失去其单个特性并将其浓缩到宏观的相干“超波”中。自1995年首次实现实验性实现（2001年诺贝尔物理学奖授予E. A. Cornell，W。Ketterle和C. E. Wieman）以来，BEC一直是实验和理论上积极研究的重点。它不仅提供了一个新的平台来研究物质的量子特性，而且还为理解超导性和超流量的现象提供了新的观点。 2018年5月21日，Cold Atom实验室最近推出了空间站，再次引起了人们的关注。该项目着重于在人造量规场和远程分散互动的影响下，在研究Bose-Einstein超流体研究中引起的基本数学和计算问题。它可能有益于高级技术的开发，例如，超导量子干扰设备和基于原子干涉仪的传感器。这项研究的主要目标是为磁性施罗宾格方程建立数学和计算处理，以促进对Bose-Einstein超流量的理解，以推动BEC的实验和应用。该项目提出了有关在存在远程分散相互作用的情况下BEC超流体的数学建模和数值模拟的系统研究。一方面，将详细研究由远程色散引入的新数学和数值问题。首先，将开发有效的吸收边界条件，以避免在计算边界处波浪的人为反射，这是波浪模拟中的一个持续问题。然后，将设计准确有效的数值方法来离散磁性弓形模型。另一方面，将在分析和数值上研究BEC的解决方案属性，以了解远程分散相互作用的影响及其与非线性相互作用的相互作用。稳定性分析和数值模拟都将进行研究，以研究由于分散和非线性相互作用竞争而导致的调节不稳定性和波浪塌陷。此外，将研究量化涡流的量化量的特性和非局部分散和/或非线性相互作用，以提高人们对BEC超虚拟率的理解。该奖项反映了NSF的法定任务，并通过评估该基金会的知识绩效和广泛的影响来评估NSF的法定任务，并被视为值得的支持。

项目成果

Highly accurate operator factorization methods for the integral fractional Laplacian and its generalization

积分分数拉普拉斯算子的高精度算子分解方法及其推广

• DOI: 10.3934/dcdss.2022016
• 发表时间: 2022
• 期刊: Discrete & Continuous Dynamical Systems - S
• 作者: Wu, Yixuan;Zhang, Yanzhi
• 通讯作者: Zhang, Yanzhi

A unified meshfree pseudospectral method for solving both classical and fractional PDEs

• DOI: 10.1137/20m1335959
• 发表时间: 2020-09
• 期刊: SIAM J. Sci. Comput.
• 作者: J. Burkardt;Yixuan Wu;Yanzhi Zhang