矩形弹子球中的量子波包分析(英文)

利用波包分析量子力学体系的动力学行为在研究经典和量子的对应关系方面越来越成为一个非常重要的方法.利用高斯波包分析方法,我们计算了矩形弹子球体系的自关联函数,自关联函数的峰和经典周期轨道的周期符合的很好,这表明经典周期轨道的周期可以通过含时的量子波包方法产生.我们还讨论了矩形弹子球的波包回归和波包的部分回归,计算结果表明在每一个回归时间,波包出现精确的回归.对于动量为零的波包,初始位置在弹子球内部的特殊对称点处,出现一些时间比较短的附加的回归.     

Three-dimensional molecular wave packets: Calculation of revival times from periodic orbits

We present a theoretical analysis of revivals and fractional revivals of three-dimensional wave packets, which describe the coupled vibrational motion of phosphaethyne (HCP) in its ground electronic state. The wave packets studied are chosen to evolve along the periodic orbits, which quantize the states in the three fundamental progressions. The revival times T_rev are found to depend strongly on the particular mode excited and on the mean excitation energy. Based on a semiclassical analysis, T_rev is shown to be determined by the dependence of the period of the orbits on the classical action along them.     

一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=γrk (-20)作用下波包的回归和部分回归.对于排斥势(γ>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似.这一结果表明能级结构相同的体系具有相同的波包回归结构.对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同.对于库仑吸引势,波包回归和部分回归出现;但是对于其它的k值, 经过一段时间后,波包出现坍塌.本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法.     

一般幂指数中心势作用下的波包回归和部分回归

利用WKB近似和自关联函数方法,我们研究了一般幂指数中心势V(r)=rk (-20)作用下波包的回归和部分回归。对于排斥势(>0, k>0), 势是一长程势,量子化能级结构中只有一个量子数,波包的回归结构和一维幂指数势的情况类似。这一结果表明能级结构相同的体系具有相同的波包回归结构。 对于吸引势,能级结构中有两个量子数, 当 k取不同的值时,波包的回归结构不同。对于库仑吸引势,波包回归和部分回归出现; 但是对于其它的k值, 经过一段时间后,波包出现坍塌。本文的研究对于探讨里德堡原子和分子中电子运动的经典极限提供了一个新的方法。     

Fisher information,nonclassicality and quantum revivals

Wave packet revivals and fractional revivals are studied by means of a measure of nonclassicality based on the Fisher information. In particular, we show that the spreading and the regeneration of initially Gaussian wave packets in a quantum bouncer and in the infinite square-well correspond, respectively, to high and low nonclassicality values. This result is in accordance with the physical expectations that at a quantum revival wave packets almost recover their initial shape and the classical motion revives temporarily afterward.     

Phase control of rotational wave packets and quantum information

Lasers can create rotational wave packets in gas-phase molecules which periodically revive as field-free, aligned distributions. We control the wave packet evolution with relatively weak laser pulses at fractional revivals which modify the phase between wave packet components. We demonstrate two phase control effects in oxygen: coherently switching revivals off and on, and doubling the revival frequency. When viewed as a quantum logic system, these effects correspond to a Hadamard and a T operation.     

Wave packet approach to lattice electrons in external galvanomagnetic fields

A closed expression for free wave packets in an homogeneous magnetic field is derived. A Gaussian function in the coordinates with time dependent coefficients is obtained, such that the mean values of position and momentum can be calculated exactly. The wave packets are found to move on a circle, their width is determined by the magnetic fieldB and independent of time. The weight function in an expansion of the wave packets in stationary solutions of the Schrödinger equation is approximately a Poisson distribution with the relative energy widthΔE/E=(B/E)^1/2.     

Control of Wave Packet Revivals Using Geometric Phases

Wave packets in a system governed by a Hamiltonian with a generic nonlinear spectrum typically exhibit both full and fractional revivals. It is shown that, by varying the parameters in the Hamiltonian cyclically with a period T and thus inducing suitable geometric phases in the states, fractional revivals can be eliminated at the relevant times T, 2T,... . Further, with the introduction of this time step T, the occurrence of near full revivals can be mapped onto that of Poincaré recurrences in an irrational rotation map of the circle. The distinctive recurrence statistics of the latter can thus serve as a clear signature of the dynamics of wave packet revivals.     

Exact solution of the Schrödinger equation for a particle in a regular N-simplex

We present the exact solution for the Schrödinger equation for a particle inside an N-dimensional regular simplex shaped enclosure. This result extends and unifies the earlier results for equilateral triangle and K-tetrahedron billiards.     

A study of the n-n interaction from a complete experiment of the n + d break-up at 14.5 MeV

Results of the analysis of two complete experiments on ²H(n, nnp) at 14.5±0.1 MeV are given. In the first n-n final-state-interaction (f.s.i.) experiment (neutron lab angles θ₁ = θ₂ = +30°, n-n relative energy E_nn measured between 0 and ≈ 800 keV) about 4400 events were recorded. In the second n-p f.s.i. experiment (neutron lab angles θ₁ = +30°, θ₂ = −80°, and E_np ? 500 keV) about 2860 events were recorded. The analysis has been done by exact solutions of the Faddeev equations with separable potentials: the Amado model was extended using the Yamaguchi potential with charge-independent (a_nm = a_np) and with charge-dependent (a_nn = −16 fm, a_np = −23.7 fm) parameters. The results are: (a) the charge-independent (a_nn = −23.7 fm) model seems to give a better fit for the shape of the n-n f.s.i. peak, but (b) the two-nucleon separable potential calculations disagree by a factor ≈ 2 with the absolute cross sections measured for the f.s.i. peaks.     

High energy proton-carbon scattering in the alpha-particle model

We investigate elastic and inelastic 0⁺–2⁺ high energy proton-¹²C scattering in the alpha-particle model. We use a rigid equilateral triangle nuclear wave function with a Gaussian dispersion function allowing theα-particles of the¹²C-nucleus to deviate from their most probable positions at the triangle vertices. Expressions for the differential scattering cross sections are deduced using Glauber multiple diffraction theory. Thus we need thep?α-particle scattering amplitude, which is calculated from a Gaussian nucleon-nucleon profile function. Numerical calculations show that the model reproduces the experimental results onp?α andp-¹²C scattering.     

Any J-State Solution of the Duffin–Kemmer–Petiau Equation for a Vector Deformed Woods–Saxon Potential

By using the Pekeris approximation, the Duffin–Kemmer–Petiau (DKP) equation is investigated for a vector deformed Woods–Saxon (dWS) potential. The parametric Nikiforov–Uvarov (NU) method is used in calculations. The approximate energy eigenvalue equation and the corresponding wave function spinor components are calculated for any total angular momentum J in closed form. The exact energy equation and wave function spinor components are also given for the J?=?0 case. We use a set of parameter values to obtain the numerical values for the energy states with various values of quantum levels (n, J) and potential’s deformation constant q and width R.     

Entanglement dynamics and quasiprobability distribution for the degenerate Raman process

In this paper, we consider the model which consists of a degenerate Raman process involving two degenerate Rydberg energy levels of an atom interacting with a single-mode cavity field. The influence of the atomic coherence on the von Neumann entropy of the atom and the atomic inversion is investigated. It is shown that the atomic coherence decreases the amount of atom-field entanglement. It is also found that the collapse and revival times are independent of the atomic coherence, while the amplitude of the revivals is sensitive to this coherence. Moreover, the Q function and the entropy squeezing of the field are examined. Some new conclusions can be obtained.     

Theoretical study of trigonal Fe center in SrCl2:Fesystem

The presence of Fe³⁺ centers with trigonal symmetry in chlorinated SrCl₂ crystal is an interesting phenomenon. By diagonalizing the complete energy matrices for a d⁵ configuration ion in a trigonal ligand-field and simulating the EPR low-symmetry parameters D and (a−F) simultaneously, the local lattice structure around trigonal Fe³⁺ center in SrCl₂:Fe³⁺ system has been studied. It is shown that Nistor et al.'s viewpoint about replacement is right, but the Cl⁻ ion along 〈111〉 axis around the Fe³⁺ center is replaced not by an O²⁻ ion but by some negative ion with effective charge to be less than that of Cl⁻ ion. Our results indicate that when the ratio of the effective charge of the negative ion to that of Cl⁻ ion is 0.8 as well as the distortion angle of the upper triangle is Δθ=−4.682°, the EPR parameters D and (a−F) can be explained satisfactorily.     

Systematic Measurement of pd Breakup Cross Section Around Space Star

Space Star (SS) anomaly in nd breakup cross section was first reported in 1989 at E _n = 13 MeV (Strate et al. in Nucl Phys A 501:51, 1989), but its origin has not been found yet. In order to obtain suggestions for its origin, we made systematic measurements of pd breakup cross section around SS. In SS configuration, three outgoing nucleons form an equilateral triangle and the triangle is perpendicular to the beam axis. Necessity of the equilateral and perpendicular conditions of SS anomaly was investigated by systematic experiments. Also energy dependence of SS anomaly is being studied at energies from E _p = 7.5 to 13 MeV.     

Wave packet revivals and the energy eigenvalue spectrum of the quantum pendulum

The rigid pendulum, both as a classical and as a quantum problem, is an interesting system as it has the exactly soluble harmonic oscillator and the rigid rotor systems as limiting cases in the low- and high-energy limits, respectively. The energy variation of the classical periodicity (τ) is also dramatic, having the special limiting case of τ→∞ at the ‘top’ of the classical motion (i.e., the separatrix.) We study the time-dependence of the quantum pendulum problem, focusing on the behavior of both the (approximate) classical periodicity and especially the quantum revival and superrevival times, as encoded in the energy eigenvalue spectrum of the system. We provide approximate expressions for the energy eigenvalues in both the small and large quantum number limits, up to fourth order in perturbation theory, comparing these to existing handbook expansions for the characteristic values of the related Mathieu equation, obtained by other methods. We then use these approximations to probe the classical periodicity, as well as to extract information on the quantum revival and superrevival times. We find that while both the classical and quantum periodicities increase monotonically as one approaches the ‘top’ in energy, from either above or below, the revival times decrease from their low- and high-energy values until very near the separatrix where they increase to a large, but finite value.     

Quantum wave packet revival in two-dimensional circular quantum wells with position-dependent mass

We study quantum wave packet revivals on two-dimensional infinite circular quantum wells (CQWs) and circular quantum dots with position-dependent mass (PDM) envisaging a possible experimental realization. We consider CQWs with radially varying mass, addressing particularly the cases where M(r)∝rw with w=1,2, or −2. The two PDM Hamiltonians currently allowed by theory were analyzed and we were able to construct a strong theoretical argument favoring one of them.     

氢负离子在梯度电场中光剥离的波包动力学研究

利用含时微扰论和闭合轨道理论相结合的方法, 给出了氢负离子在梯度电场中自关联函数的计算公式, 并且对体系的自关联函数进行了计算和分析. 重点探讨了激光脉冲的宽度、梯度电场中背景电场强度及电场梯度对氢负离子体系的自关联函数的影响. 研究结果表明, 当激光脉冲的脉冲宽度较短, 远小于剥离电子的闭合轨道的周期时, 量子波包的回归现象显著, 自关联函数中会出现一系列比较明显的回归峰, 这是由于沿闭合轨道返回的电子波包和出射的电子波包之间产生干涉形成的. 但是随着激光脉冲宽度的增加, 量子波包的回归现象减弱. 当脉冲宽度和闭合轨道的周期相差不是很大时, 自关联函数中的回归峰逐渐变宽, 振荡渐趋平缓, 相邻的峰之间发生相互干涉, 从而导致对应关系消失. 除此之外, 我们还发现梯度电场中背景电场强度和电场梯度对体系的自关联函数也会发生显著的影响. 随着背景电场强度和电场梯度的增加, 剥离电子的闭合轨道的周期变短, 自关联函数中回归峰的个数逐渐增加, 量子回归现象增强. 因此, 我们可以通过改变脉冲的宽度、外加电场强度的大小对氢负离子发生光剥离的自关联函数进行调控. 我们的结果对于实验研究原子或离子体系在外场中的波包动力学性质可以提供一定的参考价值.     

Analysis of the coincidence method for comparing atomic and nuclear lifetimes

A fully quantum-mechanical analysis is presented of the process in which an incident proton excites both a nuclear resonance and, by electron emission, also a hole in theK-shell which then decays by X-ray emission. The ratio of the intensities of the X-rays emitted before and after compound-nucleus decay is calculated (a) for the case of an isolated nuclear resonance, and (b) for strongly overlapping resonances. We show that in both cases the measured quantity is a branching ratio. The influence of the energy-resolution of the detectors, of the energy spread of the incident beam, and of the structure of the wave packets describing the individual particles in the incident beam is discussed.