Bernstein-Greene-Kruskal approach for the quantum Vlasov equation. (22nd December 2020)

• Record Type: Journal Article
• Authors: Haas, F.
• Is Part Of: Europhysics letters. Volume 132:Number 2(2020)
• Publication Date: 2020-12-22
• Subjects: 05.30.-d -- 02.30.Mv -- 52.35.Sb; Physics -- Periodicals; Electronic journals; 530.05
• DOI: 10.1209/0295-5075/132/20006
• Languages: English
• ISSNs: 0295-5075

Abstract

Abstract: The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables, similarly as in the solution of the Vlasov-Poisson system by means of the Bernstein-Greene-Kruskal method. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed and shown to be immediately integrable up to a recursive chain of quadratures in position space only. As it stands, the treatment of the self-consistent, Wigner-Poisson system is beyond the scope of the method, which assumes a given smooth time-independent external potential. Accuracy tests for the series expansion are also provided. Examples of anharmonic potentials are worked out up to a high order on the quantum diffraction parameter.