Convergence of a quantum lattice Boltzmann scheme to the nonlinear Dirac equation for Gross-Neveu model in 1+1 dimensions

N. Li, J. Zhang, Y. Zhang · 2023 · arXiv

| 编号 QC054 | 主题 量子格子玻尔兹曼 | 链接 arXiv:2302.00245 |

摘要

摘要保留原文（英文）

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This paper studies the quantum lattice Boltzmann scheme for the nonlinear Dirac equations for Gross-Neveu model in 1 + 1 dimensions. The initial data for the scheme are assumed to be convergent in $L^2$ . Then for any $T\ge 0$ the corresponding solutions for the quantum lattice Boltzmann scheme are shown to be convergent in $C([0,T];L^2(R^1))$ to the strong solution to the nonlinear Dirac equations as the mesh sizes converge to zero. In the proof, at first a Glimm type functional is introduce to establish the stablity estimates for the difference between two solutions for the corresponding quantum lattice Boltzmann scheme, which leads to the compactness of the set of the solutions for the quantum lattice Boltzmann scheme. Finally the limit of any convergent subsequence of the solutions for the quantum lattice Boltzmann scheme is shown to coincide with the strong solution to a Cauchy problem for the nonlinear Dirac equations.

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