Zhang Yan-Hui

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 Calculations of Recurrence Spectra for Lithium Atoms in Parallel Electric and Magnetic Fields

By using the region-splitting consistent and iterative method, we calculate the recurrence spectra of lithium atoms in parallel strong external electric and magnetic fields, and obtain the novel resonance structure in the photoabsorption spectrum above the ionization threshold with a constant scaled electric field at = 0.036, and a scaled energy at ? = 0.58 and ? = 0.006, respectively. The results are compared with those of hydrogen obtained by using standard closed orbit theory. It is demonstrated that the core-scattered effects exhibited in combination recurrence play a great role.

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.

The chaotic property in the autoionization of Rydberg lithium atom

This paper presents theoretical computations of the ionization rate of Rydberg lithium atom above the classical ionization threshold using semiclassical approximation. The yielded random pulse trains of the escape electrons are recorded as a function of emission time such that they can be related to the terms of the recurrence periods of the photoabsorption. This fact illustrates that it is ionic core scattering processes which give rise to chaos in autoionization dynamics and this is verified by comparison of our results with the hydrogen atom situation. In order to reveal the chaotic properties in detail, the sensitive dependence of the ionization rate upon the scaled energy is discussed for different scaled energies. This approach provides a simple explanation for the chaotic character in autoionization decay of Rydberg alkali–metal atoms.

Correspondence between classical dynamics and recurrence spectra of Rydberg hydrogen atom near a metal surface

The chaotic behaviours of the Rydberg hydrogen atom near a metal surface are presented. A numerical comparison of Poincare surfaces of section with recurrence spectra for a few selected scaled energies indicates the correspondence between classical motion and quantum properties of an excited electron. Both results demonstrate that the scaled energy dominates sensitively the dynamical properties of system. There exists a critical scaled energy ec, for e ec, with the increase of e, the system tends to be non-integrable, the ergodic motion in phase space presages that chaotic motion appears, and more and more electrons are adsorbed on the metal surface, thus the spectrum becomes gradually simple.

The dynamical properties of Rydberg hydrogen atom near a metal surface

The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincaré surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number asn=20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distanced. Whend is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. Whend becomes smaller, there exists a critical valuedc. Ford>dc, the system is near-integrable and the motion is regular. While chaotic motion appears ford<dc, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.The dynamical properties of Rydberg hydrogen atom near a metal surface are presented by using the methods of phase space analysis and closed orbit theory. Transforming the coordinates of the Hamiltonian, we find that the phase space of the system is divided into vibrational and rotational region. Both the Poincare surface of section and the closed orbit theory verify the same conclusion clearly. In this paper we choose the atomic principal quantum number asn=20. The dynamical character of the exited hydrogen atom depends sensitively on the atom-surface distanced. Whend is sufficiently large, the atom-surface potential can be expressed by the traditional van der Waals force and the system is integrable. Whend becomes smaller, there exists a critical valued c. Ford>d c, the system is near-integrable and the motion is regular. While chaotic motion appears ford<d c, and the system tends to be non-integrable. The trajectories become unstable and the electron might be captured onto the metal surface.

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.