简并费米气体的量子流体力学和非线性微分方程
Quantum hydrodynamics and nonlinear differential equations for degenerate Fermi gas
摘要：
本文提出了一维费米气体时空关联函数的新的非线性微分方程。我们考虑的关联函数描述了非平稳的平衡过程。我们得到的方程是可积方程。它们推广了已知的平衡态下关联函数的非线性微分方程，为研究电子系统的非平衡态动力学提供了重要的工具。我们发展的方法仅基于Wick定理和费米气体的流体动力学描述。微分方程直接以双线性形式出现。
英文摘要：
We present new nonlinear differential equations for spacetime correlation functions of Fermi gas in one spatial dimension. The correlation functions we consider describe non-stationary processes out of equilibrium. The equations we obtain are integrable equations. They generalize known nonlinear differential equations for correlation functions at equilibrium and provide vital tools to study non-equilibrium dynamics of electronic systems. The method we developed is based only on Wick's theorem and the hydrodynamic description of the Fermi gas. Differential equations appear directly in bilinear form.
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