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Quantum Analysis and Nonequilibrium Response

Masuo Suzuki
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Abstract

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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Masuo Suzuki. 1998-08-05. Quantum Analysis and Nonequilibrium Response. https://doi.org/10.1143/ptp.100.475

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