We address the trans-Planckian problem of Hawking radiation by studying how the state of the low-energy quanta is procured within an effective theory which breaks Lorentz invariance at some high energy scale. We use a model where Lorentz violation can be associated to both nonlinear dispersion and dissipation occuring at the high energy scale. The usual vacuum prescription for the quantum field is hence replaced by a more complicated picture which may allow for a phenomenological treatment of some possible effects of quantum gravity.
We show that the Hawking effect is robust with respect to such high-energy modifications of the theory in that the corrections to Hawking radiation are suppressed by powers of the high energy scale. We also study the quantum correlations between the final low-energy quanta and find that dissipation and thermal excitation from the bath can destroy the coherence of the state. However, if the bath is at zero temperature, coherence remains strong enough to retain the non-classical (i.e., quantum) character of the correlations.