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On the inhomogeneous magnetised electron gas
Kettenis, M.M.
Publication date
2001
Link to publication
Citation for published version (APA):
Kettenis, M. M. (2001). On the inhomogeneous magnetised electron gas. Ridderprint
offsetdrukkerij b.v.
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Epilogue e
Noww that we have completed the programme given in the introduction, it is perhaps timee for some concluding remarks.
Althoughh the model studied in this thesis appears to be rather simple (no particle inter-actions,, homogeneous magnetic field, flat hard wall), our investigation of the com-pletelyy degenerate electron gas has uncovered some interesting effects. The layered structuree of currents flowing in alternate directions close to the wall is certainly surpris-ing.. The complicated behaviour of the correlation functions is also rather unexpected.
Unlesss the magnetic field is weak, the layered structure mentioned above is confined too a thin layer near the wall. This can be concluded from the Gaussian decay of the asymptoticc expressions for the density profiles that we derived. For weak fields there is aa region where the decay is algebraic before the final Gaussian decay sets in, such that theree is an extended region where boundary effects are observable.
Forr the correlation functions, we have seen that there is a difference between correla-tionss close to the wall, and further away from it. For large distances from the wall, the correlationss in the direction perpendicular to the magnetic field and parallel to the wall havee a Gaussian decay, whereas closer to the wall we see an algebraic decay. A semi-classicall explanation of the increased range of these correlations may be sought in the so-calledd 'skipping orbits' of the electrons close to the wall.
Thee results mentioned above have been derived for the completely degenerate case at zeroo temperature. An extension to finite (but small) temperatures would be desirable. Anotherr question that remains unanswered is how the profiles and correlation functions behavee when the interactions between particles are included. We hope that the path-integrall techniques from chapter 3, in particular the path decomposition and multiple reflectionn expansions will be useful in a future investigation of this problem.
