Bernstein-Greene-Kruskal approach for the quantum Vlasov equation
- URL: http://arxiv.org/abs/2102.09610v1
- Date: Thu, 18 Feb 2021 20:55:04 GMT
- Title: Bernstein-Greene-Kruskal approach for the quantum Vlasov equation
- Authors: Fernando Haas
- Abstract summary: The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables.
In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
- Score: 91.3755431537592
- License: http://creativecommons.org/licenses/by/4.0/
- 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.
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