Hi, every one,(adsbygoogle = window.adsbygoogle || []).push({});

here i notice a loophole in the usual Kubo formalism for dealing with linear response. It assumes that the density operator evolve according to Heisenberg equation of motion. This implies that, the Boltzman factor is held time-independent, only the states evolving, which however cannot be exactly true. Because, the system under a perturbation will deviate from its present equilibrium state to reach, say, another equilibrium state after long time. In other words, in this case, the Boltzman factor must change.

BTW, as noted many years ago, the Kubo formulation has premised that, the system is initially in equilibrium, which may also be not true. This loophole seems filled with the Keldysh framework.

My question is, does Keldysh formaulation have anything to do with the first loophole ?

Thank you.

hiyok

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# A loophole in Kubo formula

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