Quantum Hydrodynamic models derived from the entropy principle
Quantum Hydrodynamic models derived from the entropy principle
复制标题
从熵原理导出的量子流体动力学模型
DOI：
10.1090/conm/371/06850
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
C. Ringhofer
中科院分区：
文献类型：
--
作者：
P. Degond;F. Méhats;C. Ringhofer
在这项工作中，我们给出了最近得到的量子流体力学和扩散模型的概述。量子局域平衡被定义为受局域矩约束(如给定局域质量、动量和能量密度)的量子熵的最小化。这些平衡以非局域的方式将热力学参数(如温度或化学势)与密度联系起来。通过对由量子平衡封闭的量子动力学方程进行矩展开，得到量子流体动力学模型。我们还推导了量子动力学模型的碰撞算符，这些碰撞算符降低了量子熵并松弛到量子平衡。然后，通过量子动力学方程的扩散极限，建立了各类模型，它们是经典的能量输运模型和漂移扩散模型的量子推广。
In this work, we give an overview of recently derived quantum hydrodynamic and diffusion models. A quantum local equilibrium is defined as a minimizer of the quantum entropy subject to local moment constraints (such as given local mass, momentum and energy densities). These equilibria relate the thermodynamic parameters (such as the temperature or chemical potential) to the densities in a non-local way. Quantum hydrodynamic models are obtained through moment expansions of the quantum kinetic equations closed by quantum equilibria. We also derive collision operators for quantum kinetic models which decrease the quantum entropy and relax towards quantum equilibria. Then, through diffusion limits of the quantum kinetic equation, we establish various classes of models which are quantum extensions of the classical energy-transport and drift-diffusion models.