Review of the linear response theory of quantum dissipation

Here I remind the reader of the quantum-mechanical linear response theory (LRT), as applied to a chaotic system. LRT in electron transport is considered to originate with Kubo [122] and Greenwood [84], and is often called the `Kubo formalism' [99]. It has more recently been applied to dissipation in closed chaotic systems [118,200,47,46]. As a primer, I will start with a conventional presentation of perturbation theory in a fixed basis. Then, once stochastic energy-spreading is established, I link up with the classical picture of Section 2.1. In particular, my aim is to show the connection between heating rate and a certain correlation spectrum $\tilde{C}^{{\mbox{\tiny qm}}}_{{\mbox{\tiny E}}}(\omega)$. Finally, because the energy-spreading picture differs markedly from the language of LRT in the condensed matter literature, I will make contact with the latter. I hope this will provide a useful bridge to the unified picture of Cohen[46].