量子分析与非平衡响应
Quantum Analysis and Nonequilibrium Response
摘要：
导出了在量子统计物理中起基础作用的$e^{-A}, A^{-1}$和$\log A$的量子导数，并证明了它们在Hilbert空间中无界正算子$A$的收敛性.利用基于这些量子导数的量子分析，导出了非平衡系统中熵算符的基本方程，并将Zubarev理论推广到关于微扰的无限阶.利用熵算子的一般微扰展开式的一阶项，Kubo的线性响应被重新推导并表示为相关哈密顿量${\cal H}$的内导数$δ_{\cal H}$。对$σ(ω)$的电导率进行了讨论。
英文摘要：
The quantum derivatives of $e^{-A}, A^{-1}$ and $\log A$, which play a basic role in quantum statistical physics, are derived and their convergence is proven for an unbounded positive operator $A$ in a Hilbert space. Using the quantum analysis based on these quantum derivatives, a basic equation for the entropy operator in nonequilibrium systems is derived, and Zubarev's theory is extended to infinite order with respect to a perturbation. Using the first-order term of this general perturbational expansion of the entropy operator, Kubo's linear response is rederived and expressed in terms of the inner derivation $δ_{\cal H}$ for the relevant Hamiltonian ${\cal H}$. Some remarks on the conductivity $σ(ω)$ are given.
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