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1991; 1993a,b) have performed theoretical studies of BCF (ballistic conductance fluctuation) and BWL (ballistic weaklocalization). s. of areas A. (Note: =hc/e . , 1994, 1995). However, their semi-classical theory has been limited to a weak B-field 50 Chapter 4 region, where the cyclotron radius of an electron is much larger than device dimensions, and to high energy regions where the number of injected modes is large. Therefore, the quantum-classical correspondence in wider field regions is far from obvious.

1990). 35) where 0 =hc /e is the magnetic flux quantum and 1 , with xA=B, is the accumulated area enclosed by the scattering orbit s. 36) In the semiclassical limit, Ss and Su>> is guaranteed. 36) can be regarded as a complex random number su with mean < su>=0 and variance < su su>= ss uu' . 38b) one finds Semiclassical Quantization of Chaos 29 Thus, for 2, conductance vs. magnetic field shows a feature of the same stochastic process as a fractional Brownian motion (Mandelbrot, 1982) with mean zero and and variance (see Fig.

And Gossard, A. C. (1992). Phys. Rev. Lett. 69, 506. Miller, W. H. (1975). Adv. Chem. Phys. 30, 77. Sinai, Y. G. (1976). Introduction to Ergodic Theory. Princeton: Princeton University Press. , and Altshuler, B. L. (1993). Phys. Rev. Lett. 70, 587. Chapter 3 Pseudo-Chaos Without Classical Counterpart in One-Dimensional Quantum Transport While there exists no genuine chaos in quantum systems due to the linearity of Schrödinger equation, we show in this chapter two interesting examples of pseudo-chaos in 1-dimensional (1-d) quantum transport.

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