可压流体Rayleigh-Taylor不稳定性的离散Boltzmann模拟

使用离散Boltzmann模型模拟了可压流体系统中多模初始情况下的Rayleigh-Taylor不稳定性.该离散Boltzmann模型等效于一个Navier-Stokes模型外加一个关于热动非平衡行为的粗粒化模型.通过模拟Riemann问题:Sod激波管、冲击波碰撞和热Couette流问题验证模型的有效性,所得数值结果与解析解一致.利用该模型对界面间断随机多模初始扰动的可压Rayleigh-Taylor不稳定性进行数值模拟研究,得到不稳定性界面演化过程的基本图像.由于黏性和热传导共同作用,一开始扰动界面被"抹平",演化较慢;随着模式互相耦合而减少,演化开始加速,并经历非线性小扰动阶段和不规则非线性阶段,而后发展成典型的"蘑菇状",后期进入湍流混合阶段.由于扰动模式的耦合与发展,轻重流体的重力势能、压缩能与动能相互转化,系统先是趋于热动平衡态,而后偏离热动平衡态以线性形式增长,接着再次趋于热动平衡态,最后慢慢远离热动平衡态.     

SENSITIVITY TO PERTURBATION IN QUANTUM CHAOTIC SYSTEM

Numerical results show that, for quantum autonomous chaotic system, the evolution of initially coherent states are sensitive to perturbation. The overlap of a perturbed state with the unperturbed one decays exponentially, which is followed by fluctuation around N^-1, N being the dimension of the Hilbert space. The matrix elements of the evolution operator in interaction picture tend to be a random distribution after sufficiently long time, where the interaction is the perturbation, even when the perturbation is very weak. The difference between a regular system and the chaotic one is shown clearly. In a regular system, the overlap shows strong revival. The distribution of the evolution matrix has only a few dominant terms.     

Dynamics of solitons in periodic systems with different nonlinear media

To analyze pulse dynamics in an optical system consisting of a periodic sequence of nonlinear media, a composite model is used. It includes a model of the resonance interaction of an ultrashort light pulse with the energy transition of the medium with allowance made for an upper level pump and an almost integrable model that describes the propagation of the light field in the other medium with a cubic nonlinearity and dispersion. Additional allowance is made for losses and other kinds of interaction by introducing perturbation terms. On the bases of the inverse scattering transform and perturbation theory, a simple method for analyzing specific features of soliton evolution in periodic systems of this kind is developed. It is used to describe various modes of soliton evolution in such a system, including chaotic dynamics.     

The factorization approximation for the Master Equation

We examine the validity of the application of the Factorization Approximation to derive the Master Equation for a microscopic system coupled to a reservoir. We developed a formal perturbation expansion for the time evolution of the system reduced density matrix. We employed a diagrammatic schemes to produce each term of the perturbation series. The diagrams in the time domain provide a distinct criteria to distinguish the diagrams which survive the Factorization Approximation. The Feynmann-like diagrams in the energy domain, originated from the Resolvent method, are used for execution of diagram summations to estimate their overall contributions. We demonstrated that for a two level atomic system, interacting with a thermal reservoir, the summation over the diagrams which survived the Factorization Approximation, yields the proper time evolution of the system, in agreement with the solution of the Master Equation. The summation of the diagrams which are excluded by applying the Factorization Approximation are characterized by a dimensionless parameter: Γ/ω₀, where ω₀ is the frequency of the transition line, and Γ is the line width. The Factorization Approximation is thus rigorously justified when this expansion parameter is very small.     

Return to equilibrium in theXY model

We prove that the locally perturbedXY model returns to equilibrium under the unperturbed evolution but the unperturbed model does not necessarily approach equilibrium under the perturbed evolution. In fact this latter property is false for perturbation by a local magnetization. The failure is directly attributable to the formation of bound states. If the perturbation is quadratic these problems are reduced to spectral analysis of the one-particle Hamiltonian. We demonstrate that the perturbed Hamiltonian has a finite set of eigenvalues of finite multiplicity together with some absolutely continuous spectrum. Eigenvalues can occur in the continuum if, and only if, the perturbation dislocates the system. Singular continuous spectrum cannot occur.     

A double quantum well in a driving laser field

The dynamic effect of electrons in a double quantum well under the influence of a monochromatic driving laser field is investigated. Closed-form solutions for the quasienergy and Floquet states are obtained with the help ofSU (2) symmetry. For the case of weak interlevel coupling, explicit expressions of the quasienergy are presented by the use of perturbation theory, from which it is found that as long as the photon energy is not close to the tunnel splitting, the electron will be confined in an initially occupied eigenstate of the undriven system during the whole evolution process. Otherwise, it will transit between the lowest two levels in an oscillatory behavior.     

Optical and magnetic studies on the phosphorescent state of phthalazine in polar and non-polar hosts

The ground state potential energy curve for the beryllium dimer is calculated using non-degenerate many-body perturbation theory and the multi-configuration self-consistent-field/configuration interaction method. Quasi-degeneracy in this system makes it useful in exploring the limitation of the applicability of the non-degenerate formulation of diagrammatic many-body perturbation theory. Both methods are applied within the algebraic approximation defined by a contracted gaussian basis set of triple zeta quality. It is shown that non-degenerate perturbation theory can lead to a potential energy curve which is in close agreement with the configuration interaction curve when taken to third order in the energy and [2/1] Padé approximants constructed.     

Rate processes in condensed media: Basic equations

A general theory of rate processes is developed. Starting from the first principles, the non-Markovian and Markovian type equations governing relaxation processes are derived. Under certain conditions (which are specified) these equations may be approximately reduced to master equations.The theory is applied to two specific models. In one of them the electron-nuclear system is represented by two intersecting electronic energy hyper-surfaces with a continuum of degrees of freedom plus a small perturbation causing transitions between these electronic states. The equations determining the time behaviour of the electronic subsystem in the general case do not coincide with master equations and the time evolution of the system has mixed oscillatory decaying behaviour.Another model takes into account a possible competition between electronic and vibrational relaxations. The corresponding kinetic equations are derived.     

Nonresonant interaction of femtosecond laser pulse with centrosymmetric molecules

We have derived a system of equations that describes the evolution of the density matrix of a centrosymmetric molecule interacting with a single nonresonant femtosecond laser pulse. The dynamics of the ground electronic state is expressed in terms of the effective Hamiltonian and the coherences between the ground an excited electronic states are functionals of the ground state density matrix. Using the time-dependent perturbation theory, we have calculated the energy deposited in the molecule as a result of rotational stimulated Raman scattering. The effective absorption coefficient is found to be proportional to the fourth power of the pulse amplitude and has a resonance-like dependence with respect to the pulse duration.     

Dissipative soliton-like plasmon-polariton pulses in extended medium

The propagation of the coupled state of the electron density perturbation in an extended metallic medium and the excitation of a two-level resonant medium are analyzed. The one- and two-photon transitions in the resonant medium are considered. The electron density perturbation is described using the hydrodynamic approximation. The formation of plasmon-polariton pulses is analyzed in the case when losses in the extended medium are compensated for by the pumping of the two-level dielectric medium. Numerical analysis carried out for the two models revealed that the losses in a soliton-like pulse in a thin metallic medium can be compensated for due to the energy transfer from the amplifying medium to electron density waves. It is shown that the dispersion of a medium containing a two-level component may considerably affect the characteristics of the pulses. The possibility of effectively controlling the evolution of soliton-like pulses by varying an external electromagnetic field and the characteristics of the matrix is demonstrated.     

Cooling kinetics of a granular gas of viscoelastic particles

The evolution of a granular gas of viscoelastic particles in the homogeneous cooling state is studied. The velocity distribution function of granular particles and the time dependence of the mean kinetic energy of particles (granular temperature) are found. The noticeable deviation of the distribution function from the Maxwell distribution and its non-monotonous evolution are established. The perturbation theory with respect to the small dispersion parameter is elaborated and the analytical expressions for the asymptotic time dependence of the velocity distribution function and the granular gas temperature are derived.     

Solution of the Fermi--Ulam Model in the Case of Periodic Perturbation

We discuss the evolution of the state and the average energy of the Fermi Ulam model in the case of periodic perturbation. By a perturbation technique, the time-dependent Sehr6dinger equation is solved and it is found that the particle will continuously absorb or radiate energy Jf the frequency of the oscillating wall meets the resonance condition. Usually, these two states cannot exist together at a certain frequency. However, there is an exception if the frequency is at some special values. We find these values and reveal that the energy for transmission has the minimum equivalent unit, which is in the form of a harmonic oscillator.     

Cosmic microwave background radiation anisotropies in brane worlds

We propose a new formulation to calculate the cosmic microwave background (CMB) spectrum in the Randall-Sundrum two-brane model based on recent progress in solving the bulk geometry using a low energy approximation. The evolution of the anisotropic stress imprinted on the brane by the 5D Weyl tensor is calculated. An impact of the dark radiation perturbation on the CMB spectrum is investigated in a simple model assuming an initially scale-invariant adiabatic perturbation. The dark radiation perturbation induces isocurvature perturbations, but the resultant spectrum can be quite different from the prediction of simple mixtures of adiabatic and isocurvature perturbations due to Weyl anisotropic stress.     

Effects of bias on dynamics of an AC-driven two-electron quantum-dot molecule

The effects of bias on the dynamical localization of two interacting electrons in a pair of coupled quantum dots driven by external AC fields have been numerically investigated. With an effective two-site model and Floquet formalism,the time-dependent Schroedinger equation is numerically solved and the Pmin, the minimum of the population evolution of the initial state within a certain time period, is used to quantify the degree of the dynamical localization. Results indicate that the bias can change the energy of the initial state and break the dynamical symmetry of the system with a pure AC field. And the amplitude of the AC field with dynamical localization phenomenon changes with bias. All the numerical results are explained by the perturbation theory and two-level approximation.     

Alternative analysis to perturbation theory in quantum mechanics

We develop an alternative approach to the time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function; additionally we can analyze the time evolution of the system for any initial condition, which may be bothersome in the standard method. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.     

A QUANTUM MECHANICAL DESCRIPTION FOR QUASI-LANDAU RESONANCES I:FORMULATION AND GENERAL PROPERTIES

The problem of a hydrogen atom in a strong magnetic field is solved quantum-mechanically in the (r,ρ,φ) coordinate system.The main part of the Hamillonian can be solved by separation variables and the remaining part is small and is treated as a perturbation,The zeroth order energy and wave function are obtained, the expression for the first perturbation energy is derived, the well-known quasi-Landau resonance interval 3/2h ω_C near thresold and the approximate scaling law ³γ≈1 are dediced amd the approximate dynamical symmetry possessed by this system is found.     

Hartree-Fock perturbation theory for systems with one-particle perturbation

The Hartree-Fock perturbation theory for theN-electron system with a one-particle perturbation is rederived using the resolvent operator formalism. It is shown that the second-order contribution to the total energy can be expressed in a compact form using a properly defined effective one-particle operator. Relations of the Hartree-Fock perturbation theory with both the many-body theory and the regular Hartree-Fock formalism are discussed.     

Stationary Classical Chaos of Trapped Two-Component Bose-Einstein Condensates in 1-D Optical Lattice Potentials

We study the nonlinear dynamics of two-component Bose-Einstein condensates in one-dimensional periodic optical lattice potentials. The stationary state perturbation solutions of the coupled two-component nonlinear Schrödinger/Gross-Pitaevskii equations are constructed by using the direct perturbation method. Theoretical analysis revels that the perturbation solution is the chaotic one, which indicates the existence of chaos and chaotic region in parameter space. The corresponding numerical calculation results agree well with the analytical results. By applying the chaotic perturbation solution, we demonstrate the atomic spatial population and the energy distribution of the system are chaotic generally.     

An Averaging Theorem for Hamiltonian Dynamical Systems in the Thermodynamic Limit

It is shown how to perform some steps of perturbation theory if one assumes a measure-theoretic point of view, i.e. if one renounces to control the evolution of the single trajectories, and the attention is restricted to controlling the evolution of the measure of some meaningful subsets of phase–space. For a system of coupled rotators, estimates uniform in N for finite specific energy can be obtained in quite a direct way. This is achieved by making reference not to the sup norm, but rather, following Koopman and von Neumann, to the much weaker L ² norm.     

Forced solitary Rossby waves under the influence of slowly varying topography with time

By using a weakly nonlinear and perturbation method, the generalized inhomogeneous Korteweg-de Vries (KdV)-Burgers equation is derived, which governs the evolution of the amplitude of Rossby waves under the influence of dissipation and slowly varying topography with time. The analysis indicates that dissipation and slowly varying topography with time are important factors in causing variation in the mass and energy of solitary waves.