From quantum spectra to classical orbits： Varying rectangular billiards

王德华, 于永江, 林圣路

Achim Köhler, R. Blümel

Ulrich Kuhl, Emil Persson, Michael Barth +1 more

Jun Lu

The quantum-spectrum function is introduced by means of the eigenvalues and the eigenfunctions in the system of varying rectangular billiards. It is found that the Fourier transform of the quantum-spectrum function corresponds with the classical orbits in the system. These results give new evidence about the classical-quantum correspondence.

Wang De-Hua

Using the periodic orbit theory,the quantum spectra in the two dimensional rectangular billiard are calculated and analyzed.The results show that each peak in the Fourier transformed spectrum of this system corresponds to the contribution of one classical periodic orbit;and with the increase of the length of the orbit,the number of the classical periodic orbit increases,and the peaks in the corresponding quantum spectra have also increased.This study suggests the good correspondence between the quantum spectra and the classical orbits in the rectangular billiards.Therefore,the correctness of the periodic orbit theory has been verified,which further deepen people's awareness of the relations between the classical and quantum mechanics.

T.A. Brun, N. Gisin, Patrick F. O’Mahony +1 more