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math.AP2016
The quantum drift-diffusion model: existence and exponential convergence to the equilibrium
Olivier Pinaud
This work is devoted to the analysis of the quantum drift-diffusion model derived by Degond et al. The model is obtained as the diffusive limit of the quantum Liouville-BGK equatio…
math.AP2016
Local smoothing for the quantum Liouville equation
Olivier Pinaud
We analyze in this work the regularity properties of the density operator solu- tion to the quantum Liouville equation. As was recently done for the Strichartz inequalities, we ext…