By I. T. Todorov, D. Ter Haar

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Et al. (1989). Prog. Theor. Phys. Suppl. 99, 149. Allan, D. W. (1966). Proc. IEEE 54, 221. , and Thirring, W. (1987). Commun. Math. Phys. 112, 691. , and Horn, P. M. (1981). Rev. Mod. Phys. 53, 497. Esaki, L. (1985). In The Technology and Physics of Molecular Beam Epitaxy, E. H. C. Parker, ed. New York Plenum. , et al. (1987). Phys. Rev. Lett. 59, 2503. , et al. (1990). Phys. Rev. Lett. 64, 1581. Jauslin, H. R. (1991). Physica D51, 200. , et al. (1992). Phys. Rev. Lett. 68, 2269. Mandelbrot, B.

21a) up to terms of relatively short periodic orbits, one obtains well-converging results. In fact, using periodic orbits thus organized, Gutzwiller applied his trace 22 Chapter 2 formula to the calculation of irregular spectra of donors with anisotropic effective mass in silicon, obtaining eigenvalues in good agreement with exact quantum eigenvalues. But the eigenvalues derived from poles of (E) are always accompanied by small imaginary components. Another formidable problem around the trace formula is to find all periodic orbits without missing any one of them.

While studies on conductance fluctuations have rather focused on hyperbolic systems, where the escape from the billiard is exponentially fast, phase coherent phenomena in the generic case of systems with a mixed (chaotic and regular) classical phase space are much less trivial. Since in the generic systems there exist an infinite hierarchy of cantori (see Fig. 3), the escape from such a system is much slower than from hyperbolic systems and follows a power law. What will be a consequence of the conductance if the underlying classical dynamics Semiclassical Quantization of Chaos 27 bears such a mixed phase?