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We present a dynamical study of the disordered quantum p = 2 spherical model at long times. Its phase behavior as a function of spin-bath coupling, strength of quantum fluctuations and temperature is characterized, and we identify different paramagnetic and coarsened regions. A quantum critical point at zero temperature in the limit of vanishing dissipation is also found. Furthermore we show analytically that the fluctuation-dissipation theorem is obeyed in the stationary regime.

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A recipe for the generalization of the Boltzmann equation to a quantum kinetic equation is given for cases in which only level shift and broadening are considered, while coherence phenomena can be neglected. We also consider a specific problem: Hot luminescence from a quantum wire near the threshold for optical phonon emission. The problem is first discussed within the framework of the Boltzmann equation. After pointing out the failure of this description, the Boltzmann equations are generalized to a set of quantum kinetic equations, which in turn are solved in order to describe the luminescence spectra.

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