Xixia Ma
Published 2020-08-05Version 1
By using the Wigner transform, it is shown that the nonlinear Schr$\ddot{\textmd{o}}$dinger equation can be described, in phase space, by a kinetic theory similar to the Vlasov equation which is used for describing a classical collisionless plasma. In this paper we mainly show Landau damping in the quantum sense, namely,quantum Landau damping exists for the Wigner-Poisson system. At the same time, we also prove the existence and the stability of the nonlinear Schr$\ddot{\textmd{o}}$dinger equation under the quantum stability assumption.
Comments: 21pages. arXiv admin note: text overlap with arXiv:1810.10955, arXiv:1807.05254; text overlap with arXiv:quant-ph/0505004 by other authors
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