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Miloslav Znojil
Reviewer number:
Item's zbl-Number:
Espinoza Ortiz, J. S.; Ozorio de Almeida, A. M.:
Quantum section method for soft stadium.
Physica D 145, No. 3-4, 293-308 (2000).
Primary Classification:
81Q50Quantum chaos
Secondary Classification:
81Q20Semiclassical techniques including WKB and Maslov methods
82B10Quantum equilibrium statistical mechanics general
soft stadium, method of quantum section, Green's functions, overlaps, WKB-type approximants

One should probably start reading this paper from its very end.
Indeed, appendix B explains the essence of the section method on
an elementary solvable example (which is just generalized to a
``soft stadium" in the bulk text). Appendix A then offers more
details on the usual exact solution for comparison, and the reader
is prepared to study the preceding text devoted to the unsolvable
intermediate cases (hint and motivation: the standard billiard for
study of the quantum chaos is obtained in the large-exponent
limiting case). In the spirit of the method, a dissection of the
general system is to be performed in such a way that the
subsystems remain separable (and the method applicable) and, by
our recommendation, one first looks at section 8 where the results
of the comparison of the Appendices are presented in three
comprehensible figures. Then we are prepared to accept the main
message (section 9) and get easily convinced that the transition
to chaos is controlled by the level repulsion and that a good
agreement with the hard-billiard data is achieved comparatively
soon (for the variable ``measure of softness" equal to cca 13). At
this point, one already has enough time and returns to the
technicalities (especially, to the reliable evaluation of overlaps
using WKB approximants in the short secs. 4. bis 6) and, in the
last step, indulges in reading about the method itself (sec. 3)
and about its historical and classical background (secs. 1 and 2).
Remarks to the editors: