Note on Dispersive Effects in Quantum Kinetic Equations

Anton Arnold, Elidon Dhamo, Chiara Manzini


We present a global-in-time well-posedness result for the
Wigner-Poisson-Fokker-Planck system, a kinetic evolution equation
for an open quantum system with a non-linear Hartree potential. Our
purely kinetic -analysis allows a unified treatment of
the elliptic and hypo-elliptic cases. The crucial tool is to exploit in the quantum
framework the dispersive effects of the free transport equation.
This yields a local-in-time a-priori estimate for the electric field which allows a
new nonlocal-in-time definition of the self-consistent potential. The -regularity
of the Wigner function is established for positive times.

[DOI: 10.1685 / CSC06011] About DOI

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