| Issue |
EPL
Volume 132, Number 2, October 2020
|
|
|---|---|---|
| Article Number | 20006 | |
| Number of page(s) | 7 | |
| Section | General | |
| DOI | https://doi.org/10.1209/0295-5075/132/20006 | |
| Published online | 22 December 2020 | |
Bernstein-Greene-Kruskal approach for the quantum Vlasov equation
Instituto de Física, Universidade Federal do Rio Grande do Sul - Av. Bento Gonçalves 9500, 91501-970 Porto Alegre, RS, Brasil
Received: 10 June 2020
Accepted: 11 September 2020
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.
PACS: 05.30.-d – Quantum statistical mechanics / 02.30.Mv – Approximations and expansions / 52.35.Sb – Solitons; BGK modes
© 2020 EPLA
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.