开放量子系统时间演化方程的矩阵表示

开放量子系统是指主量子系统不可避免地与其周围的环境发生耦合所形成的新的量子系统。研究了描述开放量子系统时间演化过程的两个主方程所确定的量子过程的矩阵表示,分别给出了几种特殊演化过程下矩阵表示的刻画形式,并讨论了其相关性质。

质量含时谐振子运动的双波描述(英文)

应用双波理论描述质量含时谐振子的量子运动 。

二维谐振子的双波函数描述

用双波函数的量子理论研究二维谐振子力学量的时间演化方程及经典近似；证明了二维各向同性谐振子角动量守恒．

基于动态多步流动原理的快速测定SWCC方法及压力板仪改装研究

对以轴平移技术为原理的压力板测试系统进行改进,增加了数据自动采集系统,储水冲刷系统和气泡体积测量系统。解决了陶土板底部气泡体积测量问题。本次试验与常规平衡态测试非饱和土土-水特征曲线方法不同,在改进的压力板仪测试系统上对粉土试样开展动态多步流动实验。根据在Origin建立的非饱和土饱和度时间演化模型方程,对实测数据进行非线性拟合得出未知参数容水率C和特征时间τ,最终得到平衡状态下的土-水特征曲线的脱湿曲线。与常规平衡状态下测得的土-水特征曲线进行对比后能较好地重合。此方法在改进的压力板仪测试系统上测得一条脱湿曲线的时间为5 d左右,具有较高准确性,与常规平衡态测试方法相比可以大大节省时间,方便快捷。

Preserving Coherence of Coherent State Studied via Weyl-Wigner Correspondence

By means of the Weyl correspondence and the explicit normally ordered expression of the Wigner operatorwe convert the time evolution equation of coherent states,governed by some Hamiltonian operators,into seeking forconsistent solution of a set of evolution equtions of classical variables which can meet the requirment that an initialcoherent state remains coherent all the time.

Three-Step Difference Scheme for Solving Nonlinear Time-Evolution Partial Differential Equations

In this paper, a special three-step difference scheme is applied to the solution of nonlinear time-evolution equations, whose coefficients are determined according to accuracy constraints, necessary conditions of square conservation, and historical observation information under the linear supposition. As in the linear case, the schemes also have obvious superiority in overall performance in the nonlinear case compared with traditional finite difference schemes, e.g., the leapfrog(LF) scheme and the complete square conservation difference(CSCD) scheme that do not use historical observations in determining their coefficients, and the retrospective time integration(RTI) scheme that does not consider compatibility and square conservation. Ideal numerical experiments using the one-dimensional nonlinear advection equation with an exact solution show that this three-step scheme minimizes its root mean square error(RMSE) during the first 2500 integration steps when no shock waves occur in the exact solution, while the RTI scheme outperforms the LF scheme and CSCD scheme only in the first 1000 steps and then becomes the worst in terms of RMSE up to the 2500th step. It is concluded that reasonable consideration of accuracy, square conservation, and historical observations is also critical for good performance of a finite difference scheme for solving nonlinear equations.

Scaling in Rate-Changeable Birth and Death Processes with Random Removals

We propose a monomer birth-death model with random removals, in which an aggregate of size k can produce a new monomer at a time-dependent rate I（t）k or lose one monomer at a rate J（t）k, and with a probability P（t） an aggregate of any size is randomly removed. We then anedytically investigate the kinetic evolution of the model by means of the rate equation. The results show that the scaling behavior of the aggregate size distribution is dependent crucially on the net birth rate I（t） - J（t） as well as the birth rate I（t）. The aggregate size distribution can approach a standard or modified scaling form in some cases, but it may take a scale-free form in other cases. Moreover, the species can survive finally only if either I（t） - J（t） ≥ P（t） or [J（t） ＋ P（t） - I（t）]t ≈ 0 at t ≥ 1; otherwise, it will become extinct.

Evolution of Arbitrary States under Fock-Darwin Hamiltonian and a Time-Dependent Electric Field

The method of path integral is employed to calculate the time evolution of the eigenstates of a charged particle under the Fock-Darwin(FD) Hamiltonian subjected to a time-dependent electric field in the plane of the system.An exact analytical expression is established for the evolution of the eigenstates.This result then provides a general solution to the time-dependent Schro¨dinger equation.

裂变F-P方程的代数解法

本文介绍了时间演化方程的Lie代数解法。求出了谐振子势场中裂变F-P方程解析解的积分表式。该方法容易推广到变系数情形。

Adiabatic approximation in PT-symmetric quantum mechanics

In this paper, we present a quantitative sufficient condition for adiabatic approximation in PT-symmetric quantum mechanics,which yields that a state of the PT-symmetric quantum system at any time will remain approximately in the m-th eigenstate up to a multiplicative phase factor whenever it is initially in the m-th eigenstate of the Hamiltonian. In addition, we estimate the approximation errors by the distance and the fidelity between the exact solution and the adiabatic approximate solution to the time evolution equation, respectively.

Static flow on complete noncompact manifolds I:short-time existence and asymptotic expansions at conformal infinity

We study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant.For a static vacuum(Mn,g,V),we also compute the asymptotic expansions of g and V at conformal infinity.

A COMBINATORIAL ASPECT OF A DISCRETE-TIME SEMI-INFINITE LOTKA-VOLTERRA EQUATION

A graph is introduced,which allows of a combinatorial interpretation of a discrete-timesemi-infinite Lotka-Volterra (dLV) equation.In particular,Hankel determinants used in a determinantsolution to the dLV equation are evaluated,via the Gessel-Viennot method,in terms of non-intersectingsubgraphs.Further,the recurrence of the dLV equation describing its time-evolution is equivalentlyexpressed as a time-evolution of weight of specific subgraphs.

Optimization of the imaginary time step evolution for the Dirac equation

Taking the single neutron levels of 12C in the Fermi sea as examples,the optimization of the imaginary time step(ITS) evolution with the box size and mesh size for the Dirac equation is investigated.For the weakly bound states,in order to reproduce the exact single-particle energies and wave functions,a relatively large box size is required.As long as the exact results can be reproduced,the ITS evolution with a smaller box size converges faster,while for both the weakly and deeply bound states,the ITS evolutions are less sensitive to the mesh size.Moreover,one can find a parabola relationship between the mesh size and the corresponding critical time step,i.e.,the largest time step to guarantee the convergence,which suggests that the ITS evolution with a larger mesh size allows larger critical time step,and thus can converge faster to the exact result.These conclusions are very helpful for optimizing the evolution procedure in the future self-consistent calculations.

A New(γ_A,σ_B)-Matrix KP Hierarchy and Its Solutions

A new(γA,σB)-matrix KP hierarchy with two time series γA and σB,which consists of γA-flow,σB-flow and mixed γA and σB-evolution equations of eigenfunctions,is proposed.The reduction and constrained flows of(γA,σB)matrix KP hierarchy are studied.The dressing method is generalized to the(γA,σB)-matrix KP hierarchy and some solutions are presented.

Equal-Time and Equal-Space Poisson Brackets of the N-Component Coupled NLS Equation

Two Poisson brackets for the N-component coupled nonlinear Schrdinger(NLS) equation are derived by using the variantional principle. The first one is called the equal-time Poisson bracket which does not depend on time but only on the space variable. Actually it is just the usual one describing the time evolution of system in the traditional theory of integrable Hamiltonian systems. The second one is equal-space and new. It is shown that the spatial part of Lax pair with respect to the equal-time Poisson bracket and temporal part of Lax pair with respect to the equal-space Poisson bracket share the same r-matrix formulation. These properties are similar to that of the NLS equation.