We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two a...We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.展开更多
Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The resul...Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.展开更多
Using temperature distribution as an external parameter to change symmetry and measuring frequency spectrum of acoustic resonances in aluminium blocks, we investigate the statistics and dynamics of energy levels in th...Using temperature distribution as an external parameter to change symmetry and measuring frequency spectrum of acoustic resonances in aluminium blocks, we investigate the statistics and dynamics of energy levels in the chaotic billiards. To extract the resonances accurately and eliminate the influence of noise, a filter-diagonalization method for harmonic inversion is used to overcome low resolution of conventional fast Fourier transform method for low quantity factor resonance systems. We present an improved and feasible simulation method to study chaotic characteristic of quantum systems experimentally.展开更多
文摘We use a recently defined quantum spectral function and apply the method of closed-orbit theory to the 2D circular billiard system. The quantum spectra contain rich information of all classical orbits connecting two arbitrary points in the well. We study the correspondence between quantum spectra and classical orbits in the circular, 1/2 circular and 1/4 circular wells using the analytic and numerical methods. We find that the peak positions in the Fourier- transformed quantum spectra match accurately with the lengths of the classical orbits. These examples show evidently that semi-classlcal method provides a bridge between quantum and classical mechanics.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 10374061 and 10774093)
文摘Based on the extended closed-orbit theory together with spectral analysis, this paper studies the correspondence between quantum mechanics and the classical counterpart in a two-dimensional annular billiard. The results demonstrate that the Fourier-transformed quantum spectra are in very good accordance with the lengths of the classical ballistic trajectories, whereas spectral strength is intimately associated with the shapes of possible open orbits connecting arbitrary two points in the annular cavity. This approach facilitates an intuitive understanding of basic quantum features such as quantum interference, locations of the wavefunctions, and allows quantitative calculations in the range of high energies, where full quantum calculations may become impractical in general. This treatment provides a thread to explore the properties of microjunction transport and even quantum chaos under the much more general system.
文摘Using temperature distribution as an external parameter to change symmetry and measuring frequency spectrum of acoustic resonances in aluminium blocks, we investigate the statistics and dynamics of energy levels in the chaotic billiards. To extract the resonances accurately and eliminate the influence of noise, a filter-diagonalization method for harmonic inversion is used to overcome low resolution of conventional fast Fourier transform method for low quantity factor resonance systems. We present an improved and feasible simulation method to study chaotic characteristic of quantum systems experimentally.
