Effective Dynamics for a Kinetic Monte–Carlo Model with Slow and Fast Time Scales

We consider several multiscale-in-time kinetic Monte Carlo models, in which some variables evolve on a fast time scale, while the others evolve on a slow time scale. In the first two models we consider, a particle evolves in a one-dimensional potential energy landscape which has some small and some large barriers, the latter dividing the state space into metastable regions. In the limit of infinitely large barriers, we identify the effective dynamics between these macro-states, and prove the convergence of the process towards a kinetic Monte Carlo model. We next consider a third model, which consists of a system of two particles. The state of each particle evolves on a fast time-scale while conserving their respective energy. In addition, the particles can exchange energy on a slow time scale. Considering the energy of the first particle, we identify its effective dynamics in the limit of asymptotically small ratio between the characteristic times of the fast and the slow dynamics. For all models, our results are illustrated by representative numerical simulations.     

A generalized master equation exciton model with consideration of emissions of fast and slow particles

Based on the Generalized Master Equation Model, the contribution of slow particle emission is considered in the present paper. In order to take account of the distinction between the emission of fast and of slow particles, two assumptions have been introduced:1) Only the direction of the emission of the fast particle is correlated with the incident direction, the direction of the emission of the slow particle is isotropic.2) The energy distribution of the slow particles in an exciton state corresponds to the Maxwell distribution. The calculated results fit the experimental data of (n, n′) and (α,P) reactions rather well even at backward angles.     

Adsorption of polymer chains at two impenetrable interfaces

We study the problem of adsorption of polymer chains in a system containing two impenetrable attracting interfaces within the mean-field approximation. We find the exact solution of this mean-field polymer adsorption problem that is controlled by a single scaling variable describing the coupling between the impenetrable interfaces due to the polymer chains. At the saturation point we obtain the total number of adsorbed monomers, the total energy of the system and the force acting between impenetrable interfaces that is turned to be strictly attractive and monotonously decaying towards zero for increasing distance between the interfaces.     

玻色-爱因斯坦凝聚体中的超流现象

在玻色－爱因斯坦凝聚（BEC）的超流现象的研究中，人们通常采用平均场近似下求解Gross-Pitaveskii方程的方法，我们采用更严格的准确对角化的方法对弱排斥相互作用下两维旋转N－Boson体系的凝聚状态进行了研究，研究表明，弱相互作用下的基态并不是人们通常认为的单一凝聚态，而是一个碎裂凝聚态，通过碎裂态能谱与平均场方法给出的能谱之间的比较以及条件几率分布函数的计算，我们指出这种碎裂凝聚态有着内在的不稳定性，很容易破缺到一个单一凝聚状态；计算给出的条件几率分布可以用来揭示破缺石的状态，其分布图案与平均场近似下得到的涡旋图形相类似，我们进一步注意到过去研究工作主要集中在弱相互作用极限下和强相互作用Thomas-Fermi近似极限下这两种极端情况，为考察两种极限间的中间过渡区域，我们研究了中等相互作用强度下体系的基态性质。     

用F-G-H方法研究玻色-爱因斯坦凝聚体基态性质

用F-G-H方法数值求解描述BEC凝聚体的非线性薛定谔方程-Gross-Pitaevskii方程.研究总粒子数、粒子间相互作用、谐振频率和一般幂指数外势对玻色凝聚体粒子数密度分布、基态能量的影响.结果表明,增大幂指数外势、谐振频率,降低粒子间的排斥作用会增加凝聚体中心的粒子数密度、缩小凝聚体半径;增大总粒子数、谐振频率、粒子间的排斥作用和幂指数外势的指数会增大体系的基态能量;随着总粒子数增大,数值结果与托马斯-费米近似结果渐趋一致,托马斯-费米近似在大粒子数条件下是一种较好的近似方法,在粒子数有限时,结果与真实情形偏差较大,应采用数值解法.     

Two Electron States in a Thin Spherical Nanolayer: Reduction to the Model of Two Electrons on a Sphere

Two electron states in a thin spherical nanolayer are discussed. Adiabatic approach is used to divide the system to fast (radial) and slow (angular) subsystems. This leads the Coulomb interaction to be dependent on angular variables, more precisely, on the relative angle between electrons. Approximated Coulomb interaction potential is discussed. Analytical solutions for angular part of Schrödinger equation as well as for energy spectrum for the case of harmonic approximation are obtained. Also the first order of correction energy is discussed by using perturbation theory. For the ground state an analytical expression for the first order correction energy dependent on effective radius of the nanolayer is obtained. Obtained results are compared with exact Coulomb interaction model presented by Loos and Gill.     

Heat fluctuations in a nonequilibrium bath

We measure the energy fluctuations of a Brownian particle confined by an optical trap in an aging gelatin after a very fast quench (less than 1 ms). The strong nonequilibrium fluctuations due to the assemblage of the gel are interpreted, within the framework of fluctuation theorem, as a heat flux from the particle towards the bath. We derive an analytical expression of the heat probability distribution, which fits the experimental data and satisfies a fluctuation relation similar to that of a system in contact with two baths at different temperatures.     

太阳耀斑与太阳高能粒子

考虑日冕区加速中相对论性粒子的扩散激波加速,结果表明:(1)粒子随时间的分布,其主要特点是随时问增加,一定能量的粒子分布迅速增加至最大后下降,并且能量越大,其最大就越向着大时间移动;(2)给出了相应的时间积分谱,它正比于具有指数截止的粒子动量的幂律.还讨论了粒子加速到高能区的条件及可能性.     

Electron energy spectra in an elliptic quantum wire and elliptic nanotube

In the effective mass approximation, the electron spectra in an elliptic quantum wire and elliptic semiconductor nanotube are investigated. An exact electron energy spectrum in the GaAs elliptic quantum wire and elliptic semiconductor nanotube with impenetrable walls is obtained and an approximate solution of the Schrödinger equation is derived for a finite potential barrier height in the GaAs/Al _x Ga _1?x As elliptic quantum wire. It is demonstrated that the ellipticity of the quantum wire and nanotube results in removal of degeneration of the quasiparticle energy spectrum. Dependences of energies of even and odd states on the ratio of the ellipse semiaxes are nonmonotonic in character. In the limiting case of degeneration of elliptic quantum wires and nanotubes into circular ones, the quasi-particle energy spectrum coincides with the corresponding spectrum in cylindrical nanosystems.     

A rearrangement of the Feenberg perturbation formula and elementary excitation interactions in bose fluids

The Feenberg perturbation energy for two quasiparticle excitations is rearranged to be valid in many-boson systems up to fifth order. Doubly excited states in many particle boson systems are studied using Feenberg perturbation theory. The effective interaction energy between quasiparticles, which is described by “ladder state diagrams” — in Bogoliubov approximation, is obtained. It is then shown that in this case the interaction energy depends on density (pressure) and changes its sign when density increases if the bare two-body potential qualitatively has short range repulsion and longer range attraction.     

Relativistic effects in one-dimensional hydrogen atom

The dependence of stationary levels of a Dirac particle in the regularized Coulomb potential V _??(z) = ?q/(|z| + ??) on the cutoff parameter ?? is studied. It is shown that, in 1 + 1 D, the energy spectrum of a Dirac particle in such a potential reveals some specific features which nonanalytically depend on the coupling constant q and are essentially relativistic in nature. These properties turn out to be most important for ?? ? 1, explicitly demonstrating the existence of a physically reasonable energy spectrum for an arbitrarily small ?? > 0 and, at the same time, the absence of regular limit ?? ?? 0 (hence, the absence of a well-defined spectral problem for the Dirac equation without regularization for arbitrary q in 1 + 1 D).     

Probability and shape of the spectral line of a single bulk characteristic energy loss of a fast electron in a medium with electron absorption and strong spatial dispersion

The probability of single characteristic energy loss of a fast electron in a reflection experiment has been calculated. Unlike many works concerning this subject, the bremsstrahlung of bulk plasmons in the non- Cherenkov ranges of frequencies and wavevectors of a plasmon has been taken into account. The contributions to the probability of single loss and to the shape of the spectral line from a quantum correction that is due to the interference of elastic and inelastic electron scattering events have been determined. The probability has been calculated in the kinetic approximation for the relative permittivity, where the short-wavelength range of the plasmon spectrum is correctly taken into account. In view of these circumstances, the expression for the mean free path of the electron with respect to the emission of a bulk plasmon that was obtained by Pines [D. Pines, Elementary Excitations in Solids (Benjamin, New York, 1963)] has been refined. The coherence length of the fast electron in the medium-energy range under consideration has been estimated. The shape of the spectral line of energy losses in the non-Cherenkov frequency range has been determined. It has been shown that the probability of the single emission of the bulk plasmon incompletely corresponds to the Poisson statistics.     

Single particle energies of nuclear matter and the reference spectrum method

The single particle energies and the ground state energy of a superfluid system of nuclear matter are investigated. There are two difficulties in calculating these quantitites in the t-matrix approximation: (1) On account of the structure of thet-matrix equation the single particle energy is a very complicated expression, which cannot be evaluated explicitly in general. (2) Due to the superfluidity of nuclear matter, there are singularities in thet-matrix. — To overcome these difficulties we apply the reference spectrum method, recently proposed byBethe, et al. The most important properties of a superfluid medium, the shift of the ground state energy and the gap in the single particle spectrum can then be very well described qualitatively. The quantitative results, however, are not satisfying. Furthermore, the estimation of the single particle potential is very much simplified. However, this is useful only for hole states. For particle statesk>k _F , the single particle energy cannot be calculated with sufficient accuracy on account of new complications coming from the rearrangement energy.     

Quantentheorie der Zeitmessung

As a consequence of its dynamical motion a quantum mechanical system may be considered as a quantum mechanical clock. If one demands that the time be an observable which corresponds to a hypermaximal time operator in Hilbert space, then, for systems having a continuous energy spectrum with a lower limit, in the framework of the nonrelativistic theory to be discussed here there must exist an upper limit of energy, too. Furthermore the time operator is not defined on the whole Hilbert space, but only on state functions satisfying a certain condition. Therefrom it results that a quantum mechanical clock of this kind can be read off only in a sequence of equidistant times separated by a “minimal time”. The beginning of the time measurement being arbitrary the scale of time may be shifted according to the homogenity in time. Especially for a free particle beside the minimal time also a minimal length is obtained. The equidistant scale in space is not absolute either, but permits an arbitrary choice of the point of reference according to homogenity in space. The modificated spreading of the probability distribution of particle position is discussed.     

Multiphoton atomic ionization in the field of a very short laser pulse

Closed analytic expressions are derived for the probability of multiphoton atomic and ionic ionization in a variable electric field ?(t), which are applicable for arbitrary Keldysh parameters γ. Dependencies of the ionization probability and photoelectron pulse spectrum on the shape of a very short laser pulse are analyzed. Examples of pulse fields of various forms, including a modulated light pulse with a Gaussian or Lorentz envelope, are considered in detail. The interference effect in the photoelectron energy spectrum during atomic ionization by a periodic field of a general form is examined. The range of applicability of the adiabatic approximation in the multiphoton ionization theory is discussed. The imaginary time method is used in the calculations, which allows the probability of particle tunneling through oscillating barriers to be effectively calculated.     

OCCUPATION RENORMALIZED HARTREE-FOCK APPROXIMATION IN LIPKIN MODEL

The occupation renormalized Hartree-Fock single particle potential is extended to include the 'particle' state occupation. The exac solution of the occupation renormalized Hartree-Fock approximation and that of the Hartree-Fock approximation are calculated in Lipkin Model. It turns out that the RHF solution is more close to the exact one than the HF solution. The effect of occupation probability depends on the strength of the interaction of the two body term.     

强激光场中氢负离子双光子电离能量谱的研究

利用强场近似(Strong field approximation,SFA)方法研究氢负离子(H-)在强激光场中双光子电离的能量谱,所得到的电离谱随角度的变化规律与实验结果符合得很好.进一步的研究表明,H-离子在强激光场中双光子电离的能量谱与有质动力能有关.激光场强度越大,光电子的有质动力能也越大,能量谱向左移动越明显...