Recently, using semiclassical Kubo formula, Budiyono and Nakamura showed  that the self-similar conductance is caused by the self-similar periodic orbits generated by pitchfork bifurcations of a straight-line liberating orbit oscillating toward saddle point in Henon-Heiles potential. This potential has three saddle points that give rise to the bifurcations, and is suitable to model a real triangle billiard with three leads . They argue that the existence of such harmonic saddles is essential and that the self-similar conductance phenomena should be observed in systems with non-Henon-Heiles potential. To support their idea, using their methods, we show theoretically the emergence of the self-similar magneto-conductance fluctuations in general-shaped soft-wall quantum billiards. First we calculate the monodromy matrices of the periodic orbits in the Barbanis potential with two harmonic saddles that give rise to the bifurcations. And using the above result, we show the self-similar conductance. Furthermore we will show the self-similar conductance in real systems with more general potentials. Finally we expect that our results confirm the experimental evidence observed by Micolich et al. , that the global shapes of billiards are not the relevant issue to discuss the dimension of the fractal fluctuation.
 A. Budiyono, K. Nakamura, submitted
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 Micolich et al., Phys Rev. Lett. 87, 036802 (2001)