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Journal of Scientific Computing

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01-02-2015

Asymptotic-Preserving Exponential Methods for the Quantum Boltzmann Equation with High-Order Accuracy

Authors: Jingwei Hu, Qin Li, Lorenzo Pareschi

Published in: Journal of Scientific Computing | Issue 2/2015

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Abstract

In this paper we develop high order asymptotic preserving methods for the spatially inhomogeneous quantum Boltzmann equation. We follow the work in Li and Pareschi (J Comput Phys 259:402–420, 2014) where asymptotic preserving exponential Runge–Kutta methods for the classical inhomogeneous Boltzmann equation were constructed. A major difficulty here is related to the non Gaussian steady states characterizing the quantum kinetic behavior. We show that the proposed schemes achieve high-order accuracy uniformly in time for all Planck constants ranging from classical regime to quantum regime, and all Knudsen number ranging from kinetic regime to fluid regime. Computational results are presented for both Bose gas and Fermi gas.

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Strictly speaking, \(\theta _0=\left( \frac{2\pi \hbar }{mx_0v_0}\right) ^dN\), where \(m\) is the particle mass, \(x_0\) and \(v_0\) are the typical values of length and velocity, \(N\) is the total number of particles.

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Title: Asymptotic-Preserving Exponential Methods for the Quantum Boltzmann Equation with High-Order Accuracy
Authors: Jingwei Hu
Qin Li
Lorenzo Pareschi
Publication date: 01-02-2015
Publisher: Springer US
Published in: Journal of Scientific Computing / Issue 2/2015
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-014-9869-2

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