By Boris V. Chirikov (auth.), W. Dieter Heiss (eds.)
Beforehand the $64000 proposal of quantum chaos has remained a bit sick outlined. This quantity tackles the ever-present borderline among classical and quantum mechanics, learning specifically the semiclassical restrict of chaotic platforms. the results of disease from dynamics and their relation to stochastic structures, quantum coherence results in mesoscopic structures, and the appropriate theoretical ways are fruitfully mixed during this quantity. the most important paradigms of what's referred to as quantum chaos, random matrix thought and functions to condensed topic and nuclear physics are awarded. exact discussions of experimental paintings with specific emphasis on atomic physics are integrated. The publication can be necessary for graduate-student seminars.
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Additional resources for Chaos and Quantum Chaos: Proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics Held at Blydepoort, Eastern Transvaal South Africa, 13–24 January 1992
Here ce is the etching depth (~ 2 to 5 nm in the experiment). To define the mapping it is convenient to introduce two complex planes, one where the complex variable is ze = xe + iye, which is 34 J. Martorell, D. W. L. Sprung, M. Girlanda, and M. Macucci mapped onto a second plane, the z plane, where we write z = x + iy. The profile of the etched surface is defined by the following points (which are the vertices of an open Schwarz Christoffel (SC) polygon that will be used for the conformal mapping): tu0 = —oo+iO, w\ = —W/2+iO, 102 = —W/2+ice, W3 = +W/2 + ice , w4 = +W/2 + iO and w$ — +00 + iO.
The reason for this apparent contrast lies in the fact that we should instead compare the variation in the confinement energy and the energy separation between the two polarization configurations, which is very small. In Fig. 94/ S3 CD > •c p -" - 1 "i 1 1 , ~ i 0 Driver cell polarization 1 Fig. 1. Polarization of the driven cell P i versus the polarization of the driver cell P2 as a function of the driver cell asymmetry. 0 5d/d (10 _ 3 ) 4 Fig. 2. Shift of the zero of polarization P i (threshold for switching) as a function of the driver cell asymmetry.
4. Gate layout for the definition of a four-dot cell in the 2-dimensional gas obtained by modulation doping in a heterostructure. 42 J. Martorell, D. W. L. Sprung, M. Girlanda, and M. Macucci We compute the cell-to-cell response function for a few values of the 2DEG depth and report the results in Fig. 5 V. The driver cell is assumed to be fully polarized, located at a distance of 400 nm (distance between cell centers) from the cell being considered. It is apparent that the cell-to-cell response gets smoother as the depth of the 2DEG is increased: this does not come as a surprise, since, as the 2DEG gets further from the gate, the depth of the potential dips representing the dots decreases, thus the barriers seen by the electrons between the dots are lowered, and therefore a smoother transition of charge is expected to take place, as discussed in the previous chapter.
Chaos and Quantum Chaos: Proceedings of the Eighth Chris Engelbrecht Summer School on Theoretical Physics Held at Blydepoort, Eastern Transvaal South Africa, 13–24 January 1992 by Boris V. Chirikov (auth.), W. Dieter Heiss (eds.)