Scientific Computing Seminar

DATE2016-09-26 15:10-16:00


SPEAKER譚夢寧 博士(國家衛生研究院生醫工程與奈米醫學研究所

TITLEEfficient Modeling of Quantum Gases in the Inviscid Limit

ABSTRACT The study of quantum particle systems is of great interest for applications that involve dilute atomic vapors in ultra-low energy levels. Such low energy conditions are required to study the degenerate behavior of those quantum gas systems. At this level, the Boltzmann construction provides a tractable way as it provides the analytical tools to describe the transport phenomena of such complex particle systems. Following the philosophy of the Boltzmann Equation, extensions or generalization to deal with particles systems that follow the Bose-Einstein and Fermi-Dirac statistical distributions have been conceived. This generalization is called the quantum Boltzmann equation (QBE), and can be used to describe the dynamics of systems following any of the aforementioned quantum distributions. Although the path for solving is heavily nonlinear, it is well defined. However, the numerical solution of the QBE is numerically challenging task [1, 2]. A unified formulation based on the BGK model has been devised to achieve highly efficient numerical solutions in the inviscid fluid limit of quantum gasses. The present formulation [3] has the potential of rendering simpler schemes to model the dynamics of the quantum particle systems. In this work direct solutions based on finite difference WENO schemes [6] and the correction procedure via reconstruction (CPR) methods [4] are used to illustrate the potential of this new formulation in capturing the complex interaction of two-dimensional Riemann problems of quantum gasses.