By Katsuhiro Nakamura (auth.)
Quantum and chaos, key innovations in modern technological know-how, are incompatible through nature. This quantity offers an research into quantum shipping in mesoscopic or nanoscale structures that are classically chaotic and indicates the luck and failure of quantal, semiclassical, and random matrix theories in facing questions rising from the mesoscopic cosmos. those conventional theories are significantly analysed, and this ends up in a brand new course. To reconcile quantum with chaos and to revive real temporal chaos in quantum platforms, a time-discrete variation of quantum dynamics is proposed.
Audience:This ebook may be of curiosity to graduate scholars and researchers in physics, chemistry and arithmetic, whose paintings includes primary questions of quantum mechanics in chaotic systems.
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Additional info for Quantum versus Chaos: Questions Emerging from Mesoscopic Cosmos
001 (filled square) and F=10 (open square). found the integer exponent v =2 and also showed the universality of this integer exponent by tuning both the width of barriers and strength of the applied field. We should emphasize many puzzling features of S matrices in tunneling-induced pseudo-chaos in quantum systems. 3. Resonant Tunneling in Double-Barrier Structure and Pseudo-Chaos Heterostructures provide another example of pseudo-chaos. , 1992) bears an effective nonlinearity arising from the mean-field approximation of many-body interactions involved in resonant tunneling through a double-barrier structure.
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.
The calculation of the trace formula itself, however, will encounter serious fundamental problems. In generic systems with elliptic islands coexisting with chaotic sea, symbolic coding of periodic orbits is much less obvious. 30 Chapter 2 Even if one could achieve this coding, one would meet another difficulty, namely that of nonconvergence in the Gutzwiller series due to the exponential proliferation of periodic orbits. This problem may be partly overcome either by smoothing the density of states or by inventing a way of conditional convergence by means of the Ruelle zeta function.