A Structure-Preserving Effective Linear Approximation of the Quantum Boltzmann Collision Operator
Abstract
We construct a structure-preserving effective linear approximation of the quantum Boltzmann collision operator for Bose and Fermi gases in the normal phase. For variable hard-sphere kernels, the resulting Fourier spectral evaluation costs O(Nv4log Nv), with Nv velocity nodes per direction and no angular quadrature factor. The continuous operator conserves mass, momentum and energy and satisfies a linearized H-theorem. We also use the operator at local quantum equilibrium as an approximate collision Jacobian in a modified Newton solver that retains the full nonlinear residual. Numerical tests show smaller errors than the quantum BGK model in homogeneous relaxation and fewer full collision evaluations for steady Couette and Fourier flows than the same Newton solver using a quantum BGK Jacobian.
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BibTeX
@misc{hu2026structurepreserving,
title = {{A Structure-Preserving Effective Linear Approximation of the Quantum Boltzmann Collision Operator}},
author = {Shuang Hu and Bo Lin and Zhenning Cai},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.17568},
eprint = {2610.17568},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.17568},
}
RIS
TY - UNPB
TI - A Structure-Preserving Effective Linear Approximation of the Quantum Boltzmann Collision Operator
AU - Shuang Hu
AU - Bo Lin
AU - Zhenning Cai
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.17568
UR - https://arxiv.org/abs/2610.17568
AB - We construct a structure-preserving effective linear approximation of the quantum Boltzmann collision operator for Bose and Fermi gases in the normal phase. For variable hard-sphere kernels, the resulting Fourier spectral evaluation costs O(N_v^4log N_v), with N_v velocity nodes per direction and no angular quadrature factor. The continuous operator conserves mass, momentum and energy and satisfies a linearized H-theorem. We also use the operator at local quantum equilibrium as an approximate collision Jacobian in a modified Newton solver that retains the full nonlinear residual. Numerical tests show smaller errors than the quantum BGK model in homogeneous relaxation and fewer full collision evaluations for steady Couette and Fourier flows than the same Newton solver using a quantum BGK Jacobian.
ER -