Xu Xue-You

Semiclassical Ballistic Transport through a Circular Microstructure in Weak Magnetic Fields

We study magneto-transport through a weakly open circular microstructure in the perpendicular weak magnetic fields by a semiclassical approximation within the framework of the Fraunhofer diffraction effect at the lead openings. It is found that the peak positions of the transmission power spectrum can be related to simple trajectories according to classical dynamics. Moreover, we formulate the fluctuations in the transmission amplitude as functions of both the wave number k and the magnetic field B in terms of different classical trajectories, and the Aharonov—Bohm phase of the directed areas enclosed by these trajectories that reflect the quantum interference effect.

Semiclassical approximation for transmission through open Sinai billiards

We use a semiclassical approximation to study the transport through the weakly open chaotic Sinai quantum billiards which can be considered as the schematic of a Sinai mesoscopic device, with the diffractive scatterings at the lead openings taken into account. The conductance of the ballistic microstructure which displays universal fluctuations due to quantum interference of electrons can be calculated by Landauer formula as a function of the electron Fermi wave number, and the transmission amplitude can be expressed as the sum over all classical paths connecting the entrance and the exit leads. For the Sinai billiards, the path sum leads to an excellent numerical agreement between the peak positions of power spectrum of the transmission amplitude and the corresponding lengths of the classical trajectories, which demonstrates a good agreement between the quantum theory and the semiclassical theory.

The quantum spectral analysis of the two-dimensional annular billiard system

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.

Harmonic Inversion of Recurrence Spectra of Nonhydrogen Atom in an Electric Field

An extended harmonic inversion method is analytically continued to approach bifurcation region of the closed orbits thus to obtain highly resolved spectra of lithium atom in external field. The suitable band-limited signal is generated by a semiclassical uniform approximation. By decimating the selected signal window and solving the algebraic set of nonlinear equations the quantum eigenvalues are properly fitted, which reveal the fine resonance structure hidden in low resolution spectrum. The study is made at the scaled energy e = −2.7, relevant bifurcation effects and core-scattered impacts have to be taken into account. It is demonstrated that the present method is a useful technique for the semiclassical quantization of system with mixed regular-chaotic classical dynamics.

Semiclassical Calculations of Autoionization Rate for Lithium Atoms in Paralle Electric and Magnetic Fields

By using a semiclassical method, we present theoretical computations of the ionization rate of Rydberg lithium atoms in parallel electric and magnetic fields with different scaled energies above the classical saddle point. The yielded irregular pulse trains of the escape electrons are recorded as a function of emission time, which allows for relating themselves to the terms of the recurrence periods of the photoabsorption. This fact turns to illustrate the dynamic mechanism how the electron pulses are stochastically generated. Comparing our computations with previous investigation results, we can deduce that the complicated chaos under consideration here consists of two kinds of self-similar fractal structures which correspond to the contributions of the applied magnetic field and the core scattering events. Furthermore, the effect of the magnetic field plays a major role in the profile of the autoionization rate curves, while the contribution of the core scattering is critical for specifying the positions of the pulse peaks.

Fractal Analysis of Transport Properties in a Sinai Billiard

Research contacting chaos with fractals is carried out. First, we employ the theoretical quarter Sinai billiard model to study its chaos by using the stationary expansion method. When the billiard is chaotic, the singular point shows self-similarity. We further utilize the method of simplified box counting to calculate the fractal dimension. The result evidently proves the self-similarity of the singular point before escaping from a potential well.

Semiclassical Calculation of Conductance Transmission through an Open Equilateral Triangular Billiards

We study the transport property passing through a weakly open equilateral triangular billiards by using the semiclassical method. We extend the Green function and the transport matrix theory to include the multiple scattering effect at the boundary and the diffractions of the pair of the lead apertures. For analysing the structure of semiclassical pseudo path kinks, the geometric and the special dynamical symmetries of the system are simultaneously taken into account. The conductance is calculated by Landauer formula as a function of the electrons Fermi wave number. Its Fourier transformation, the quantum path-length spectrum, is qualitatively in accordance with the results of the classical trajectories, which indicates that such approach provides an obvious improvement of the semiclassical description.

Semiclassical Analysis of Quarter Stadium Billiards

An expansion method for stationary states is applied to obtain the eigenfunctions and the eigenenergies of the quarter stadium billiard, and its nearest energy-level spacing distribution is obtained. The histogram is consistent with the standard Wigner distribution, which indicates that the stadium billiard system is chaotic. Particular attention is paid to pursuing the quantum manifestations of such classical chaos. The correspondences between the Fourier transformation of quantum spectra and classical orbits are investigated by using the closed-orbit theory. The analytical and numerical results are in agreement with the required resolution, which corroborates that the semiclassical method provides a physically meaningful image to understand such chaotic systems.

The quantum spectra analysis of the circular billiards in wells

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-classical method provides a bridge between quantum and classical mechanics.