By Nakamura K.

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**Sample text**

1992) bears an effective nonlinearity arising from the mean-field approximation of many-body interactions involved in resonant tunneling through a double-barrier structure. Let us consider the external potential consisting of double wells b 1 and b2 surrounded by semi-infinite barriers B 1 and B2 (see Fig. 5): 40 Chapter 3 Fig. 5. Schematic diagram of a three-well two-barrier heterostructure. An electron cloud initially localized in the well 1 moves towards the well with a mean kinetic energy close to the resonance.

Consider the noninteracting electron Semiclassical Quantization of Chaos 23 gas confined in a conducting ring threaded by an Aharonov-Bohm magnetic flux . We choose the ring shape that guarantees complete chaos in the classical motion of a point particle. , a square conductor with a circular hollow in its inside (see Fig. 2). The contribution of a single-particle energy level En( ) to the persistent current is given by p dEn/d , where the mean density state ρ is the inverse of mean level separation.

The and present and next chapters will be devoted to the quantum semiclassical analyses of concave and convex billiards, respectively. Among concave billiards, Bunimovich's stadium billiard (Bunimovich, 1974; Benettin and Strelcyn, 1978) has received a wide attention as a paradigm of nonlinear dynamics. It belongs to the K system, showing the fully-chaotic orbits in marked contrast to regular orbits in a simple circle or rectangle. Its quantum-mechanical study showed the level statistics (McDonald and Kaufman, 1979) similar to those for the Gaussian orthogonal ensemble (GOE) and wavefunctions characterized by periodic-orbit scars (Heller, 1984), thereby heralding a new era of quantum chaos.