On the inhomogeneous magnetised electron gas

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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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Contents s

11 Introduction 1 1.11 Diamagnetism 1 1.22 Basic techniques 5 1.33 Outline 13 22 Density profiles 15

2.11 Green Junctions; charge and current density 16

2.22 Explicit form of Green function; parabolic cylinder functions 18 2.33 Asymptotic expansions 22

2.44 Discussion 28

2.. A Appendix: Asymptotics of en ( K ) 30

2.BB Appendix: Asymptotics of the normalisation factor 30

33 More density profiles 35

3.11 Path-decomposition expansion 36 3.22 Magnetic field 42

3.33 Asymptotics (non-degenerate case) 44 3.44 Asymptotics (degenerate case) 50

3.AA Appendix: Higher-order terms in the PDXseries 53

44 Weak magnetic fields 57

4.11 Magnetic field perpendicular to the wall 57 4.22 Magnetic field parallel to the wall 66 4.AA Appendix: Properties of J(w, u) 71 55 Correlations 75

5.11 Correlation Junctions 77 5.22 Correlations in the bulk 78 5.33 Path-decomposition expansion 82 5.44 Parabolic cylinder Junctions 86

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Vlll l _{Contents Contents}

5.55 Correlations for large separations |r — r ' | 92 5.66 Correlations near the wall 98

5.77 Discussion and conclusion 101

5.AA Appendix: Zeroes of the parabolic cylinder junctions 103

Epiloguee 105 Bibliographyy 107 Samenvattingg 111 Dankwoordd 115