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Text: Since the orbit bifurcations are of leading order inh, we now want to check if they have an increased influence on the amplitude of the conductance oscillations. In Fig. 3(a) we show the quantity Tr M of four typical periodic orbits (shown to the right) taking part in two successive bifurcations (where Tr M = 2) under variation of the magnetic field strength B. The left one is a tangent bifurcation, the right one a pitchfork bifurcation. In Fig. 3(b), the contribution of these orbits to the conductance is plotted. The dotted line gives the result of the trace formula Eq. (1). The amplitudes are diverging (arrows!) at the bifurcations. The uniform approximation (solid line) removes the divergences. Fig. 3(c) represents the corresponding **data** for a system scaled to have 10 times larger actions, thus being closer to the semiclassical limit. It is important now to note that the amplitudes in the uniform approximation are nearly constant over the bifurcations. We have thus shown that the bifurcations have no locally dominant influence on the conductance of the present system [23]. Having established this result, we can further simplify our semiclassical treatment. Whereas for individual orbits a uniform treatment of the bifurcations is vital, their influence becomes smaller if a larger number of orbits is included. This is demonstrated in Fig. 4, where the total δG xx has been calculated for s d = 1.86 including all relevant (∼ 60) periodic orbits. The solid line shows the result of the uniform approximation, whereas the dotted line corresponds to the standard Gutzwiller approach. To remove the spurious divergences in Eq. (1) (and those due to bifurcations of higher codimension in the uniform approach), we have additionally convoluted δG xx over the magnetic field B (cf. Ref. [24]). The results are very similar [25]. In particular, the maximum positions are practically identical. In the following, we therefore use simply Eq. (1) with an additional convolution over B.<|eot_id|><|start_header_id|>assistant<|end_header_id|>

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