Classical and quantum dynamics of electrons in open equilateral triangular billiards

Coupling-driven transition from multiple to single-dot interference in open quantum-dot arrays

“…Although not shown here, these slower oscillations persist with only a weakly reduced amplitude to temperatures higher than 7 K, suggesting that they result from a classical magnetofocusing effect. 16,25 To subtract these oscillations from the raw data, we simply mimic the low-frequency magnetoconductance variation with an appropriate polynomial fit. ͑While the specific choice of this background may affect the low-frequency components of the fluctuations, it will have little influence on the high-frequency components, whose characteristics we will be concerned with for an analysis in this report.͒ Returning to the data presented in Fig.…”

Exploring the effect of fractional degeneracy and the emergence of ray-wave duality in solid-state lasers with off-axis pumping

“…For a given set of (P, Ö), it follows that the frequency levels are degenerate because there may be many combinations of (n, m, I) satisfying the equation A' = [IQ + im-\-n-\-\)P], resulting in frequency gaps in the spectrum fn,m.i/ML as A' changes by unity. The accidental degeneracy in the quantum spectra has been discussed to play a crucial role in the relationship between quantum shell structures and classical periodic orbits, especially in the mesoscopic systems [27][28][29][30][31][32]. In the optical cavity, the occurrence of the mode degeneracy can also be linked to the appearance of the periodic ray paths.…”

“…Numerous modem laser systems have been developed as analogous systems to visualize various quantum phenomena [22][23][24][25]. In mesoscopic quantum systems [26][27][28][29][30][31][32], the emergence of classical periodic orbits has been found to be tightly associated with the level degeneracy as well as the conductance fluctuation. Therefore, it is believed that exploring the emergence of ray-wave duality and the effect of fractional degeneracy in optical resonators can provide 'Corresponding author: Department of Electrophysics, National Chiao Tung University, 1001 TA Hsueh Road, Hsinchu 30010, Taiwan; yfchen@cc.nctu.edu.tw valuable insights, not only into laser physics but also into mesoscopic quantum phenomena.…”

Magnetoconductance fluctuations and weak localization in quantum dots: Reliability of the semiclassical approach

“…8,9 We find however that the SC approach gives qualitatively different conductance/reflectance for different current directions as well as inconsistent WL corrections for the conductance and reflectance; it does not satisfy the current conservation requirements and does not reproduce the corresponding quantum-mechanical results. Moreover, in a billiard with only one single lead where the reflection coefficient must be identically equal to the number of incoming channels, the SC approach yields nonzero WL corrections.…”

“…Under these conditions the conductance of the dot ͑often referred to as an electron billiard͒ is dominated by reproducible fluctuations which are due to quantum-mechanical interference of the electron waves. [1][2][3][4][5][6][7][8][9][10] In order to provide a quantitative description of the fluctuations various approaches have been adopted including the random matrix theory, 11 numerical solution of the Schrödinger equation, 3,12,4,7 and the semiclassical ͑SC͒ methods. In the latter approach the conductance of the dot is given as a sum of all classical trajectories connecting the leads, each of them carrying the quantum-mechanical phase.…”