PATH INTEGRAL CALCULATION OF QUANTUM TUNNELING FOR CUBIC POTENTIAL AT FINITE TEMPERATURE

The periodic instanton method is used to study the decay rates of metastable ground state and excited states of the cubic potential. The imaginary part of the energy is calculated through the standard procedure in the path-integral scheme. A formula of the decay rate valid for the entire region of energy is obtained. This formula provides a linkage between classical thermal activation at high temperatures and purely quantum tunneling at zero temperature. It is shown that in the low energy limit this more general result reduces exactly to the vacuum result. The temperature dependence of the decay rate agrees with earlier works in the literature.     

Complex free energies and metastable lifetimes

For two simple models we consider the analytic continuation of the free energy across a first-order phase transition. For each system we also study an associated stochastic dynamics and decay rates for passage to the stable equilibrium. We then investigate the relation between the imaginary part of the free energy and the decay rate per unit volume.Supported in part by U.S.-Israel Binational Science Foundation and by National Science Foundation Grant MCS 77-20683.Alfred P. Sloan Research Fellow. On leave from Indiana University, Bloomington, Indiana.     

Numerical evaluation of the Feynman integral-over-paths in real and imaginary-time

New techniques are described for Monte Carlo evaluation of the propagation of quantum mechanical systems in both real and imaginary-time using the Feynman integral-over-paths formulation of quantum mechanics. For imaginary-time calculations path translation is used to augment the technique of Lawande et. al. This simple-yet-powerful technique allows the equilibrium probability density to be accurately evaluated in the presence of multiple potential wells. It is shown that path translation permits the calculation of the unknown ground-state energy of one confining potential by comparison with the known ground-state energy of another. A double finite-square-well potential and a finite-square-well/parabolic-well pair are presented as examples. For real-time calculations, a weighted analytical averaging of the exponential in the classical action is performed over a region of paths. This “windowed action” has both real and imaginary components. The imaginary component yields an exponentially decaying probability for selecting paths, thereby providing a basis for the Monte Carlo evaluation of the real-time integral-over-paths. Examples of a wave-packet in a parabolic well and a wave-packet impinging upon a potential barrier are considered.     

Structural and electrical characteristics of rare earth simple perovskite oxide La0.57Nd0.1Pb0.33Mn0.8Ti0.2O3

Polycrystalline La_0.57Nd_0.1Pb_0.33Mn_0.8Ti_0.2O₃ (LNPMT) is prepared by the solid-state reaction technique. The formation of single phase material was confirmed by X-ray diffraction studies, and it was found to be a rhombohedral phase at room temperature. The impedance plane plot shows semicircle arcs at different temperatures and an electrical equivalent circuit has been proposed to explain the impedance results. The frequency dependent conductivity spectra follow the universal power law. The activation energy deduced from analysis of the imaginary part of electric modulus and imaginary impedance is found to be ∼75 meV. Such a value of activation energy indicates that the conduction mechanism for the sample is due to electron hopping. The imaginary part of the electric modulus suggests that the relaxation describes the same mechanism at various temperatures.     

Impedance as a characteristic of relaxation polarization

The electrical characteristics of a dielectric material that can be used to determine the parameters of relaxation polarization arising in a dielectric and the influence on these characteristics of the steady leakage electrical conductivity are discussed. For weak relaxation processes at high electrical conductivities, the imaginary part of impedance can be used as such a characteristic. Extrema in the impedance frequency dependence are observed at any conductivity. However, the frequency dependence of the imaginary part of impedance contains two maxima whose frequency positions depend not only on the relaxation time but on other characteristics of the dielectric as well. In addition, the temperature shifts of the extrema of these curves depend not only on the activation energy of the relaxation process but on the activation energy of the electrical conductivity as well.     

Competition among molecular fragmentation channels described with Siegert channel pseudostates

To describe multiple interacting fragmentation continua, we develop a method in which the vibrational channel functions obey outgoing wave Siegert boundary conditions. This paper demonstrates the utility of the Siegert approach, which uses channel energy eigenvalues that possess a negative imaginary part. The electron scattering energy in each such channel is rotated upward, giving it an equal and opposite imaginary part. This permits a natural inclusion of vibrational continua without requiring them to appear as explicit channels in the scattering matrix. Calculations illustrate the application of this theory to photoionization, photodissociation, and dissociative recombination.     

基于自洽输运理论的介观体系动态电导的研究

基于介观体系电子动态输运的自洽理论,讨论了介观结构的动态电导.作为该理论的应用,采用一介观相干平行板电容器模型来进行研究. 结果表明:体系的动态电导与外场频率和体系费米能有关,为一复数且有有限虚部. 当外场频率较小时,动态电导随费米能的变化所呈现的特性和直流情形非常相似,但是随着外场频率的增加,两者差异就变得非常明显,体系动态电导随外场频率的变化呈现一些峰值结构. 在给定体系费米能时,动态电导随着外场频率的变化而产生振荡,并且出现了负的电导虚部,电导虚部的正负表明了体系的电容特性和电感特性. 关键词： 自洽输运理论 相干平行板电容器 电导 介观体系     

Complex microscopic optical potential between two nuclei based on Dirac-Brueckner theory for nuclear matter

The real and imaginary parts of the optical-model potential between two nuclei are calculated in the energy density formalism. The energy density is derived from the Dirac-Brueckner approach to nuclear matter. In this approach, both free NN scattering and the saturation properties of nuclear matter can be explained starting from a realistic NN interaction. The relativistic features incorporated in the Dirac-Brueckner approach make the real part of the optical potential less attractive than that obtained in a non-relativistic calculation while the imaginary part is enhanced. The comparison of the calculated differential cross section for elastic ¹²C-¹²C scattering with the experimental data suggests that the enhancement of the imaginary part due to the relativistic treatment is favourable while its repulsive contribution to the real part is unfavourable.     

Imaginary-time method in quantum mechanics and field theory

An imaginary-time method was developed for calculating the probability of particle transmission through smooth barriers variable with time. Within the imaginary-time method, the tunneling process is described by using classical equations of motion written in terms of an imaginary time (t → it), while the probability of tunneling is determined by the imaginary part of the action functional, this imaginary part being calculated along the subbarrier particle trajectory. The fundamentals of the imaginary-time method are surveyed, and its applications in the theory of atomic-state ionization under the effect of constant electric and magnetic fields that have various configurations, in the field of intense monochromatic laser radiation and of an ultrashort electromagnetic pulse, in the process of Lorentz ionization of atoms and ions during their motion in a strong magnetic field, etc., are outlined. The applications of the imaginary-time method in relativistic cases—for example, in the theory of ionization of levels of multiply charged ions whose binding energy is commensurate with the electron rest energy—and in quantum field theory (Schwinger effect, which consists in the production of electron-positron pairs from a vacuum by a superstrong external field) are briefly described. Particular attention is given to methodological issues and details of the imaginary-time method that are of importance in solving specific physics problems, but which are usually skipped in original publications.     

单层石墨烯水分子吸附对其光学性质的影响

用MS软件对水分子吸附在单层石墨烯表面进行计算,采用第一性原理中的密度泛函理论。使用广义梯度近似和周期性平面模型,得到不同数量的水分子吸附在石墨烯表面上的吸附能,并且计算了相对应的光学性质。得到的结果是吸附能很小,主要是范德瓦尔斯相互作用。石墨烯具有高疏水性,水分子在石墨烯表面对石墨烯的电子结构几乎没有作用,吸附不同个数的水分子后对石墨烯的光学性质有一定影响,其中吸附单个水分子后变化并不明显,吸附2或3个水分子后吸收率和光电导率略有下降;折射率和消光率下降不明显,说明吸附水对石墨烯的透明度影响不大;介电函数的实数部分变化趋于平缓,虚数部分有明显下降;能量损失增加。     

单层石墨烯水分子吸附对其光学性质的影响

用基于第一性原理中的密度泛函理论MS软件对水分子吸附在单层石墨烯表面进行计算,使用广义梯度近似和周期性平面模型,得到不同数量的水分子吸附在石墨烯表面上的吸附能,并且计算了相对应的光学性质.得到的结果是吸附能很小,主要是范德瓦尔斯相互作用.石墨烯具有高疏水性,水分子在石墨烯表面对石墨烯的电子结构几乎没有作用,吸附不同个数的水分子后对石墨烯的光学性质有一定影响,其中吸附单个水分子后变化并不明显,吸附2或3个水分子后吸收率和光电导率略有下降;折射率和消光率下降不明显,说明吸附水对石墨烯的透明度影响不大;介电函数的实数部分变化趋于平缓,虚数部分有明显下降;能量损失增加.     

A stochastic process with metastability and complex free energy

Analytic continuation has been proposed as a way to understand metastable states in statistical physics. In that view, the imaginary part of the continued free energy is associated with the decay rate of the metastable system. In this article we show how the relation has been confirmed on a simple stochastic system, spin flip dynamics for the Curie-Weiss ferromagnet.     

A level-density-dependent imaginary potential for heavy ions

Under the assumption that compound-nucleus formation is the only channel competing with elastic scattering, an L-dependent imaginary potential is defined with the help of the compound-nucleus level density. For the latter an expression is used which seems to be accurate enough for excitation energies of several tens of MeV and with a substantial part of rotational energy. Associated with a double-folded real part, this imaginary potential is shown to reproduce well the elastic scattering data of eight systems of medium size (total mass between 36 and 72) at various energies not very high above the Coulomb barrier. The results are equivalent to those obtained with a folding real potential and a Woods-Saxon imaginary potential with parameters adjusted for each set of data with the advantage that our approach only needs two parameters to fit the data for a wide range of energies for each scattering system.     

Bi掺杂ZnO光电性能的第一性原理研究

采用基于密度泛函理论的第一性原理平面波超软赝势方法,利用Material studio程序包中的Castep模块计算研究不同浓度Bi原子掺杂对ZnO电子结构和光学性能的影响.研究表明：不同Bi原子数的掺杂,对ZnO禁带宽度影响的变化趋势不一致.Bi掺杂ZnO的介电函数虚部峰值变大,并向低能量方向红移;高能量区域的吸收峰、反射峰和能量损耗峰随着掺杂原子的增多逐渐减小,透光性增强.掺杂样品在可见光和紫外光的吸收系数和反射系数均显著提高,可促进ZnO材料对可见光的有效利用.     

Kinetics versus thermodynamics in materials modeling: The case of the di-vacancy in iron

Monte Carlo models are widely used for the study of microstructural and microchemical evolution of materials under irradiation. However, they often link explicitly the relevant activation energies to the energy difference between local equilibrium states. We provide a simple example (di-vacancy migration in iron) in which a rigorous activation energy calculation, by means of both empirical interatomic potentials and density functional theory methods, clearly shows that such a link is not granted, revealing a migration mechanism that a thermodynamics-linked activation energy model cannot predict. Such a mechanism is, however, fully consistent with thermodynamics. This example emphasizes the importance of basing Monte Carlo methods on models where the activation energies are rigorously calculated, rather than deduced from widespread heuristic equations.     

Re-study of Nucleon Pole Contribution in J/ψ → NN^-π Decay

We re-study nucleon pole contribution in J/ψ → NN^-π decays by including the imaginary part for the propagator of the off-shell nucleon with energy above π N threshold. It is found that when including the imaginary part in the propagator, the branching ratio of the decay width will descend about 11% compared with the result without including the imaginary part, no matter whether including the off-shell form factors or not. It also leads to a phase of up to 25° for the off-shell nucleon propagator at invariant mass around 1400 MeV. This effect needs to be considered for detailed partial wave analysis of N^＊ resonances around this mass region.     

Semi-fermionic representation of SU(N) Hamiltonians

We represent the generators of the SU(N) algebra as bilinear combinations of Fermi operators with imaginary chemical potential. The distribution function, consisting of a minimal set of discrete imaginary chemical potentials, is introduced to satisfy the local constraints. This representation leads to the conventional temperature diagram technique with standard Feynman codex, except that the Matsubara frequencies are determined by neither integer nor half-integer numbers. The real-time Schwinger-Keldysh formalism is formulated in the framework of complex equilibrium distribution functions for auxiliary semi-fermionic fields. We discuss the continuous large N and SU(2) large spin limits. We illustrate the application of this technique for magnetic and spin-liquid states of the Heisenberg model. Received 26 February 2001 and Received in final form 25 April 2001     

原子吸收限附近完整晶体内的能流方向

研究了原子吸收限附近对称劳厄和布拉格情况下完整晶体内的能流方向．发现在对称劳厄情况下，只有当原子散射因子的虚部对衍射的贡献可以与实部的贡献相比较时，晶体内与色散面上某一结点相对应的能流会偏离色散面的实部的法向；而在对称布拉格情况下，即使在原子散射因子的虚部对衍射的贡献可以忽略时，在所谓的“全反射”区内也会偏离．当衍射仅由原子的虚部引起时，这种偏离在对称劳厄情况下最大，而在对称布拉格情况下最小． 关键词：     

Correlation of Two Coupled Particles in Viscoelastic Medium

Considering the viscoelastic memory effect, we study the correlated motion of two hydrodynamically coupled colloidal particles, each of which confined in a harmonic potential well, in a Kelvin-type and Maxwell-type viscoelastic medium. We find that viscoelastic relaxation plays a significant role in modifying the correlation, particularly the cross correlation. We also find that both the real and imaginary parts of the response function are significantly different from the viscous medium case. In particular there is a phase shift between the vanishing imaginary part and the maximal real part of the response function in a viscoelastic medium. In addition imaginary part of the cross correlation response function exhibits a net energy loss （gain） behavior when the elasticity parameter of the medium is larger （smaller） than the critical value for Kelvin （Maxwell） viscoelastic fluid. Some implication of our results and their connection with previous works are discussed.     

Nonequilibrium Linear Response for Markov Dynamics, I: Jump Processes and Overdamped Diffusions

Systems out of equilibrium, in stationary as well as in nonstationary regimes, display a linear response to energy impulses simply expressed as the sum of two specific temporal correlation functions. There is a natural interpretation of these quantities. The first term corresponds to the correlation between observable and excess entropy flux yielding a relation with energy dissipation like in equilibrium. The second term comes with a new meaning: it is the correlation between the observable and the excess in dynamical activity or reactivity, playing an important role in dynamical fluctuation theory out-of-equilibrium. It appears as a generalized escape rate in the occupation statistics. The resulting response formula holds for all observables and allows direct numerical or experimental evaluation, for example in the discussion of effective temperatures, as it only involves the statistical averaging of explicit quantities, e.g. without needing an expression for the nonequilibrium distribution. The physical interpretation and the mathematical derivation are independent of many details of the dynamics, but in this first part they are restricted to Markov jump processes and overdamped diffusions.