Nonlinear Fokker-Planck-Kolmogorov Equation in the Semiclassical Coherent Trajectory Approximation

A semiclassical asymptotic of the Cauchy problem is constructed for the two-dimensional Fokker-Planck equation with nonlocal nonlinearity in the class of trajectory concentrated functions based on the complex WKB-Maslov method. The system of Einstein-Ehrenfest equations describing the dynamics of average values of the coordinate operator and centered moments is derived. The results obtained are illustrated by a number of examples. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 38–47, June, 2005.     

高动量分布对核反应中原子核的阻止本领的影响

利用同位旋相关的量子分子动力学模型研究了中能重离子碰撞过程中,具有不同中质比的中等质量核碰撞系统的高动量分布对原子核的阻止本领的影响,以及这种影响随入射能量的演化。研究结果表明:对于76Kr+76Kr,88Kr+88Kr碰撞系统,当入射能量较小时高动量分布对原子核的阻止本领影响很小;但当反应能量较大的时候,高动量分布对原子核的阻止本领影响较大,且这种影响随着入射能量和碰撞核质量的增大而增大。对于Ca同位素链的反应系统,高动量分布增大了反应系统的原子核的阻止本领。因此,高动量分布对中等质量核碰撞系统的原子核的阻止本领有重要影响,且与入射能量和碰撞核质量密切相关。Based on the isospin-dependent quantum molecular dynamics model, the effect of high momentum distribution on nuclear stopping in medium mass nuclear collision system is studied with different neutron-proton ratio in intermediate energy heavy ion collisions, and the evolution of this effect with the incident energy. The results show that when the incident energy is small, the high momentum distribution has little effect on the nuclear stopping. However, when the reaction energy is large, the high momentum distribution has a great influence on the nuclear stopping and the influence increases with the increase of incident energy and the mass of collision nucleus. For the Ca isotopes reaction system, high momentum distribution increases the nuclear stopping of the reaction system. Therefore, high momentum distribution has an important influence on nuclear stopping in medium mass nuclear collision system, and closely related to the incident energy and the mass of collision nucleus.     

A Uniform Semiclassical Calculation of the Rings in Photodetachment Microscope

We describe a uniform semiclassical theory for the spatial distribution of the photodetached electron of H^- in the presence of a static electric field. In this theory we propagate the photodetached electron wavefunction using a mixed position and momentum coordinate method to large distance where a uniform approximation to the electron flux distribution is calculated. Details are given for the propagation of the mixed coordinate wavefunction with cylindric symmetry and the transformation between configuration space wavefunction and the mixed position and momentum wavefunction.     

Fermion Tunneling from an Axis-Symmetric Black Hole beyond the Semiclassical Approximation

Based on the Hamilton-Jacobi method beyond the semiclassical approximation proposed by R. Baberjee and B.R. Majhi, Hawking radiation of Dirac particle as tunneling through the event horizon is calculated. It is shown that all quantum corrections in the fermion particle action are proportional to the usual semiclassical contribution. Under the conception of irreducible mass and the first law of thermodynamics, the modifications to Hawking temperature and Bekenstein-Hawking entropy are given for a Kerr-Newmann black hole.     

The Semiclassical Study of Nuclear High Spin States

Nuclear high spin states are studied in the extended Thomas-Fermi approximation.Explicit formula for rotational energy and various corrections are given.Concrete calculations are performed for three typical nuclei:¹¹⁶Sn,¹⁵⁸Yb and ²⁴⁰Pu.Qualitatively,the results are similar to that of liquid drop model.Quantum corrections to rotational energy (besides shell corrections) cannot be neglected in a quantitative study.     

A Semiclassical Theory of Multistep Nuclear Reaction Processes

The master equation theory of precompound and compound nuclear reactions has been generalized with inclusion of the conservation of angular momentum and parity. This improved semiclassical theory has been extended for application as an evaluation tool of the calculations of nucleon induced reaction cross sections and double differential cross sections. For structural materials at incident neutron energies below 20 MeV, it is demonstrated that the constructed model contains the Hauser-Feshbach, Weisskopf-Ewing as well as the exciton models as limiting cases. The unified treatment ofpre-equilibrium processes includes a number of interesting features, such as the exciton state densities with the exact Pauli exclusion correction which are renormalized to the back-shifted Fermi-gas formula, the introduction of formation factors of composite particle in calculations of pick-up type composite particle emission and the double differential cross sections (DDCS) for all kinds of particles in terms of the leading particle model.     

AGS能量下核系统的强阻止性

本文给出了一个简单的相对论性强子级联模型,并用它模拟了Si(14.6A GeV/c)+Au的反应.研究了共振态对质子π的快度分布以及质子横质量分布的影响.在此模型中,碰撞粒子的纵动量变化(非弹情形)由阻止律给出;而粒子的横动量分布通过指数分布或高斯分布抽样.我们的结果与E810(814)数据和E802的新结果较好地符合.这表明:共振态△的引入能更好地反映碰撞的物理过程;AGS能量下核系统的强阻止性已无可非议.     

密度分布对原子核阻止同位旋效应的影响

利用同位旋相关的量子分子动力学（IQMD）模型,分析了中能重离子碰撞过程中相对论平均场和SkyrmeHartrere－Fork等核结构模型给出的核密度分布对原子核阻止的影响。研究表明,从费米能到的较大能量范围内,无论小质量体系还是大质量体系,原子核阻止对同位旋相关的核子－核子碰撞截面都非常灵敏,而不同模型给出的核密度分布对原子核阻止影响不大,说明原子核阻止作为提取同位旋相关核子－核子碰撞截面的灵敏探针是与原子核结构模型无关的。 Influence of densitydistributionwhichisgivenbyRMFandSkyrme－Hartrere－Fork etalnuclearstructuremodelonnuclearstoppinginheavy－ioncollisionsatintermediateenergiesarestudiedbyusingisospin－dependentquantummoleculardynamics(IQMD)model.ResearchshowsthatrangeformtheFermienergytothelargerenergyof 100 Mev/u, for bothsmallandlargemasssystem,nuclearstoppingisfoundtobestronglydependentonthenucleon－nucleoncrosssections,andweaklyondifferentdensitydistribution.ThisshowsthatnuclearstoppingcanbeusedasaprobetoextracttheinformationontheisospindependenceN－Ncrosssectionsandhasnorelationshipwithnuclearstructuremodels.     

Hawking Radiation of Apparent Horizon in a FRW Universe as Tunneling Beyond Semiclassical Approximation

An analysis of Hawking radiation about apparent horizon in a FRW universe is performed by using the method developed in the paper (Banerjee, Majhi in JHEP 06:095 2008), in which the Hawking radiation of a black hole is treated as the quantum tunneling by Hamilton-Jacobi method beyond semiclassical approximation and then all the higher order quantum corrections can be given out. In our analysis, the Kodama vector instead of the Killing vector to define the energy of the particle plays a key role. We present our analysis under the Friedmann-Robertson-Walker like coordinate system and the much-like to Painlevé coordinate system respectively. The result show that the formulized procedure can be extended to fully analyse the Hawking radiation of a dynamical system.     

Weak-Coupling Theory for Semiclassical Periodically Driven Two-Level Systems: Beyond Rotating-Wave Approximation

We present a weak-coupling theory of semiclassical periodically driven two-level systems. The explicit analytical approximating solution is shown to reproduce highly accurately the exact results well beyond the regime of the rotating-wave approximation.     

Calculation of the Dynamic Stark Effect in the Many-Level Approximation

A new method for calculating the dynamic Stark effect in a circular polarized electric field of arbitrary strength and frequency is proposed. The basic equations of the method are given. By way of illustration the results of calculation of the shift and splitting of energy levels of a He atom in a circular polarized electric field are considered.     

Semiclassical Calculation of Recurrence Spectra of He Rydberg Atom in Strong External Fields

Using core-scattered closed-orbit theory and region-splitting iterative method, we calculated the scaled recurrence spectra of helium atom in parallel electric and magnetic fields. Closed orbits in the corresponding classical system have also been obtained. When we search the closed orbits, in order to remove the Coulomb singularity of the classical Hamiltonian motion equations, we implement the Kustaanheimo-Stiefel transformation, which transforms the system from a three-dimensional to a four-dimensional one. The Fourier transformed spectrum of helium atom has allowed direct comparison between peaks in such plot and the scaled action values of closed orbits. The results are compared with those of the hydrogen case, which shows that the core-scattered effects play an important role in the recurrence spectra of the multi-electron Rydberg atom.     

动量相关作用在原子核阻止作为探针中的重要性

最近的研究工作表明原子核阻止强烈地依赖于两核子碰撞截面而较弱的依赖同位旋相关的平均场 (对称势 ) .故原子核阻止可以作为提取介质中同位旋相关核子 -核子碰撞截面的探针 .详细的计算表明动量相关作用在提高原子核阻止对两体碰撞的敏感性和减弱对称对称势的敏感性中起了重要作用. The role of momentum dependence equation of state on the nuclear stoppings coming from the isospin dependence of nucleon-nucleon cross section (two-body dissipation ) and the isospin dependence of the mean field (one-body dissipation) are studied by using the isospin dependence quantum molecular dynamics. A detail studies indicate that the difference between the nuclear stoppings coming from the isospin dependence and the isospin independence of in-medium nucleon-nucleon...     

Calculation of Tensor Susceptibility Beyond Rainbow-Ladder Approximation

In this paper, we extend the calculation of tensor vacuum susceptibility in the rainbow-ladder approximation of the Dyson–Schwinger (DS) approach in Shi et al. (Phys Lett B 639:248, 2006) to that of employing the Ball–Chiu (BC) vertex. The dressing effect of the quark-gluon vertex on the tensor vacuum susceptibility is investigated. Our results show that compared with its rainbow-ladder approximation value, the tensor vacuum susceptibility obtained in the BC vertex approximation is reduced by about 10%. This shows that the dressing effect of the quark-gluon vertex is not large in the calculation of the tensor vacuum susceptibility in the DS approach.     

核温度的动力学计算

介绍了测量热力学微正则系综中哈密顿动力学系统温度的一种新的动力学途径,即在各态历经性的假设下,温度可作为函数（Ｈ／‖Ｈ‖２）在能量面上的时间平均算出．这一方法不仅给出了确定温度的一种有效的计算途径,而且也提供了动力学系统理论和哈密顿系统的统计力学之间的内在联系． A new dynamical approach for measuring the temperature of a Hamiltonian dynamical system in the microcanonical ensemble of thermodynamics is presented. It shows that under the hypothesis of ergodicity the temperature can be computed as a time average of the function, ·(H/‖H‖ 2) , on the energy surface. This method not only yields an efficient computational approach for determining the temperature, but also provides an intrinsic link between dynamical system theory and the statistical...