http://arxiv.org/abs/1701.02235
We consider a model for the interaction between the cosmological perturbations and another environmental field during inflation, in order to study decoherence, the quantum to classical transition and the impact on quantum correlations. Given an explicit interaction between the system and environment, we derive a quantum master equation for the reduced density matrix of perturbations, drawing parallels with quantum Brownian motion, where we see the emergence of fluctuation and dissipation terms. Although the master equation is not in Lindblad form, we see how typical solutions exhibit positivity on super-horizon scales, leading to a physically meaningful density matrix. This allows us to write down a Langevin equation with stochastic noise for the classical trajectories which emerge from the quantum system on super-horizon scales. Our master equation reveals many important features characteristic of the quantum to classical transition which are not captured by an isolated pure state. In particular, we find that decoherence grows in strength as modes exit the horizon, and memory effects are negligible, implying that the Langevin description involves white noise. In contrast to pure states, entropy and the spread of the Wigner function increase in time due to environmental interactions, with their evolution determined by the relative strength of squeezing and decoherence. Finally, we use our master equation to quantify the strength of quantum correlations as captured by discord. We show that environmental interactions have a tendency to decrease the size of the discord, but that these corrections are perturbatively small in the coupling. We interpret this in terms of the competing effects of particle creation versus environmental fluctuations, which tend to increase and decrease the discord respectively.
T. Hollowood and J. McDonald
Tue, 10 Jan 17
30/75
Comments: 22 pages, 12 figures