Photodetachment of H- near Elastic Surface in Parallel Electric and Magnetic Fields

The photodetachment cross section of H^- in parallel electric and magnetic fields near an elastic surface is derived and calculated by using the closed orbit theory. It is found that the elastic surface can produce some interesting effects. Besides the closed orbits previously found by Peters et al. for the H^- in parallel electric and magnetic fields, some additional closed orbits are produced due to the effect of the elastic surface. The results show that the cross section oscillation is much more complicated in comparison with the cross section of H^- in parallel external fields without surface. Each peak in the Fourier transformed cross section corresponds to the period of one detached electron closed orbit. This study provides a new understanding of the photodetachment of negative ions in the presence of external fields and surface.     

Calculations of Photo-Ionization Cross Sections for Lithium Atoms

Photo-ionization cross sections for the ground and the ≤5 excited states of lithium atoms are calculated in the photoelectron energy ranging from threshold to 0.5 Rydberg. The wavefunctions for both the bound and continuum states are obtained by solving the SchrSdinger equation numerically in a symplectic scheme. Our results are in excellent agreement with the recent experimental measurements and in harmony with other theoretical calculations.     

Semiclassical limits for the QCD Dirac operator

We identify three semiclassical parameters in the QCD Dirac operator. Mutual coupling of the different types of degrees of freedom (translational, colour and spin) depends on how the semiclassical limit is taken. We discuss various semiclassical limits and their potential to describe spectrum and spectral statistics of the QCD Dirac operator close to zero virtuality.     

Semiclassical theory of transport in antidot lattices

Motivated by a recent experiment by Weiss et al. [Phys. Rev. Lett. 70, 4118 (1993)], we present a detailed study of quantum transport in large antidot arrays whose classical dynamics is chaotic. We calculate the longitudinal and Hall conductivities semiclassically starting from the Kubo formula. The leading contribution reproduces the classical conductivity. In addition, we find oscillatory quantum corrections to the classical conductivity which are given in terms of the periodic orbits of the system. These periodic-orbit contributions provide a consistent explanation of the quantum oscillations in the magnetoconductivity observed by Weiss et al. We find that the phase of the oscillations with Fermi energy and magnetic field is given by the classical action of the periodic orbit. The amplitude is determined by the stability and the velocity correlations of the orbit. The amplitude also decreases exponentially with temperature on the scale of the inverse orbit traversal time/T . The Zeeman splitting leads to beating of the amplitude with magnetic field. We also present an analogous semiclassical derivation of Shubnikov-de Haas oscillations where the corresponding classical motion is integrable. We show that the quantum oscillations in antidot lattices and the Shubnikov-de Haas oscillations are closely related. Observation of both effects requires that the elastic and inelastic scattering lengths be larger than the lengths of the relevant periodic orbits. The amplitude of the quantum oscillations in antidot lattices is of a higher power in Planck's constant and hence smaller than that of Shubnikov-de Haas oscillations. In this sense, the quantum oscillations in the conductivity are a sensitive probe of chaos.This paper is dedicated to Prof. H. Wagner on the occasion of his 60th birthday     

? expansions in semiclassical theories for systems with smooth potentials and discrete symmetries

We extend a theory of first order ? corrections to Gutzwiller’s trace formula for systems with a smooth potential to systems with discrete symmetries and, as an example, apply the method to the two-dimensional hydrogen atom in a uniform magnetic field. We exploit the C_4v-symmetry of the system in the calculation of the correction terms. The numerical results for the semiclassical values will be compared with values extracted from exact quantum mechanical calculations. The comparison shows an excellent agreement and demonstrates the power of the ? expansion method.     

Tunneling in quantum superlattices with variable lacunarity

Fractal superlattices are composite, aperiodic structures comprised of alternating layers of two semiconductors following the rules of a fractal set. The scattering properties of polyadic Cantor fractal superlattices with variable lacunarity are determined. The reflection coefficient as a function of the particle energy and the lacunarity parameter present tunneling curves, which may be classified as vertical, arc, and striation nulls. Approximate analytical formulae for such curves are derived using the transfer matrix method. Comparison with numerical results shows good accuracy. The new results may be useful in the development of band-pass energy filters for electrons, semiconductor solar cells, and solid-state radiation sources up to THz frequencies.     

Semiclassical and quantum motions on the non-commutative plane

We study the canonical and the coherent state quantizations of a particle moving in a magnetic field on the non-commutative plane. Using a θ-modified action, we perform the canonical quantization and analyze the gauge dependence of the theory. We compare coherent states quantizations obtained through Malkin-Man'ko states and circular squeezed states. The relation between these states and the “classical” trajectories is investigated, and we present numerical explorations of some semiclassical quantities.     

An alternative quantum fidelity for mixed states of qudits

We give an alternative definition of quantum fidelity for two density operators on qudits in terms of their Hilbert-Schmidt inner product and their purity. It can be regarded as the well-defined operator fidelity for the two operators and satisfies all Jozsa's four axioms up to a normalization factor. This fidelity is not computationally demanding.     

Quantum effects of periodic orbits for the kicked top

We analyze traces of powers of the time evolution operator of a periodically kicked top. Semiclassically, such traces are related to periodic orbits of the classical map. We derive the semiclassical traces in a coherent state basis and show how the periodic orbits can be recovered via a Fourier transform. A breakdown of the stationary phase approximation is detected. The quasi energy spectrum remains elusive due to lack of knowledge of sufficiently many periodic orbits. Divergencies of periodic orbit formulas are avoided by appealing to the finiteness of the quantum mechanical Hilbert space. The traces also enter the coefficients of the characteristic polynominal of the Floquet operator. Statistical properties of these coefficients give rise to a new criterion for the distinction of chaos and regular motion.     

Electron Dynamics of Atoms in Parallel Electric and Magnetic Fields

Through an analysis of the nearest neighbor level fields, we investigate the evolution of the electron spacing statistics for atoms in parallel electric and magnetic dynamics as electric field strength increases. In the ＇inter-l mixing＇ predominant region, the electron shows complex dynamics while in the ＇inter-n mixing＇ predominant region, its dynamics behaves in a relatively stable way and the characteristic quantity ξ shows a slight oscillation. Comparing the dynamics for hydrogen and barium, we find that the core effect makes the main contribution to the chaotic behavior in non-hydrogen atoms.     

能量ε<0时Li原子在平行电磁场中的光吸收谱研究

利用包括实散射的闭合轨道理论和分区自洽的迭代算法,计算了标度能量为ε =- 0 .0 3,标度电场F =0 .0 1时的平行电磁场中n≈ 4 0 ,m =0的Li原子闭合轨道以及光吸收谱.介绍了谱的标度特性 ,它对理解量子与经典之间的对应关系具有非常重要的意义.并与同样情况下的氢原子谱作了比较 .验证了离子实对光吸收过程的重要作用. By employing the semiclassical closed-orbit theory including core-scattering and region-splitting consistent iterative method, we calculate the closed-orbits and the recurrence spectra of n≈40, m=0 Li Rydbergatom in parallel electric and magnetic fields at scaled energy ε=-0.03. The constant scaled electric field is =0.01 . The novel spectral structures are compared with those of hydrogen obtaines by standard closed orbit theory. The effect of the core-scattering has been discussed.     

Eigenstates and scattering solutions for billiard problems: A boundary wall approach

It was proposed about a decade ago [M.G.E. da Luz, A.S. Lupu-Sax, E.J. Heller, Phys. Rev. E 56 (1997) 2496] a simple approach for obtaining scattering states for arbitrary disconnected open or closed boundaries C, with different boundary conditions. Since then, the so called boundary wall method has been successfully used to solve different open boundary problems. However, its applicability to closed shapes has not been fully explored. In this contribution we present a complete account of how to use the boundary wall to the case of billiard systems. We review the general ideas and particularize them to single connected closed shapes, assuming Dirichlet boundary conditions for the C’s. We discuss the mathematical aspects that lead to both the inside and outside solutions. We also present a different way to calculate the exterior scattering S matrix. From it, we revisit the important inside-outside duality for billiards. Finally, we give some numerical examples, illustrating the efficiency and flexibility of the method to treat this type of problem.     

Bandt-Pompe-Tsallis quantifier and quantum-classical transition

We concern ourselves with statistical quantifiers of semiclassical time-evolutions and their classical limit. The system of interest represents the interaction between matter and a given field. Our tool here is the so-called Permutation Entropy, evaluated by recourse to the so-called Bandt-Pompe technique, within a Tsallis scenario. We encounter that the most salient details of the quantum-classical transition are well-described, indeed, in a better fashion than that of previous approaches.     

Incipience of quantum chaos in the spin-boson model

The peculiar spectral properties of the spinboson model make it suitable for an investigation of quantum nonintegrability effects and level statistics from a new perspective. For fixed spin quantum numbers, its energy spectrum consists of 2s+1 sequences of levels with no upper bound. These sequences are identified and labelled consecutively by means of a quantum invariant calculated from the time average of a non-stationary operator. For integrable cases, level repulsion (on the energy axis) is limited to states within each sequence. From the observed spectral properties, we infer a series ofs-dependent level-spacing distributions. They converge towards a Poisson distribution fors. For nonintegrable cases, level repulsion becomes a universal phenomenon, but the amount of repulsion between two states decreases with increasing separation (in label) of the two sequences to which they belong. For smalls, the quantum nonintegrability effects are compelling but not at all chaotic. Nevertheless, they contain all the ingredients necessary to produce the symptoms commonly described as indicators of quantum chaos. In this model, we can observe quantum chaos in the making under very controllable conditions.     

强电,磁场中的原子

简要地叙述了强电场和强磁场中的原子物理问题的研究进展，着重介绍了原子电场电离的实验结果和理论分析，对称性对磁场中原子行为的影响，以及与经典混沌和量子谱相关的共振现象。     

Boundary-Dependent Chaotic Regions for a Bose-Einstein Condensate Interacting with Laser Field

Spatial chaos of a Bose Einstein condensate perturbed by a weak laser standing wave and a weak laser δ pulse is studied. By using the perturbed chaotic solution we investigate the new type of Melnikov chaotic regions, which depend on an integration constant co determined by the boundary conditions. It is shown that when the │co│ values are small, the chaotic region corresponds to small values of laser wave vector k, and the chaotic region for the larger h values is related to the large │co│ values. The result is confirmed numerically by finding the chaotic and regular orbits on the Poincarg section for the two different parameter regions. Thus, for a fixed co the adjustment of k from a small value to large value can transform the chaotic region into the regular one or on the contrary, which suggests a feasible method for eliminating or generating Melnikov chaos.     

Photodetachment of a Negative Hydrogen Molecular Ion near an Interface

Photodetachment of a negative hydrogen molecular ion near an interface is studied by using the two-centre model and the closed orbit theory. The calculation results show that the photodetachment cross section is related to the distance between the two centres in the H₂^- and different molecular ion-interface distances. The comparison between the cross section of H₂^- near an interface with the section of Hˉ shows that at the equilibrium distance of two centres and at low photon energy, the photodetachment cross section of H₂^- is about twice the cross section of Hˉ, which shows that the interference of the two nuclei is very strong; when the distance between the two centres is large, the section of H₂^- is almost the same as the cross section of Hˉ near one interface, which indicates that the interference effect of the two centres anishes.