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By A. B.; Krainov, V.; Leggett, Anthony J.(translator) Migdal

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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.

7). 529A. 15eV, with V1 being large enough to confine the electron cloud between B1 and B2. If the mean kinetic energy is chosen close to the resonance energy ER , the wave packet will diffuse Fig. 6. Time evolution of the charge Q(t). (a) =0, (b) =3, (Courtesy of G. ) 42 Chapter 3 by repeating a round trip through the double barriers. 6 shows the erratic behavior of Q(t) as a function of time for the case =3. 9) with C(t) in Fig. 7 shows a rapid decay of the correlation, followed by noisy ripples in the nonlinear ( 0) cases, whereas it retains a long-time correlation in the linear ( = 0) case.

This magneto-conductance of experiment has opened a way for us to study the quantum theory of chaos through advanced electron transport devices. 2. Magneto-Conductance in Stadium Billiard: Experimental Results At the interface of GaAs /AlxGa1 -xAs, Marcus et al. 14µm ; see Fig. 1. They also made circular quantum dots. 6 x 1011 cm-2) with average distance between electrons ~ 10-2µ m, one may suppress many-body effects. Further, owing to a relatively long mean free path -1 µ m, the electronic motion between successive bouncings is ballistic rather than diffusive.

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