关于线性微分方程的刘维尔公式组

对线性微分方程中的刘维尔公式做了适当的补充和讨论.     

Energy identities and blow-up analysis for solutions of the super Liouville equation

In this paper, we study the super Liouville equations, a natural generalization of the Liouville equation. We establish energy identities and a precise blow-up analysis for solutions of the super Liouville equations.     

Coupling Integrable Couplings of an Equation Hierarchy

Based on a kind of Lie algebra G proposed by Zhang, one isospectral problem is designed. Under the framework of zero curvature equation, a new kind of integrable coupling of an equation hierarchy is generated using the methods proposed by Ma and Gao. With the help of variational identity, we get the Hamiltonian structure of the hierarchy.     

Production and detection of ultracold Cs2 molecules via four-photon adiabatic passage

We study theoretically how to produce and detect the ultracold ground-state Cs2molecule from Feshbach state. Numerical calculations are performed by solving the quantum Liouville equation based on multilevel Bloch model. The producing efficiency reaches 55% and the detecting efficiency is 31%. The producing and detecting efficiencies are closely related to the Rabi frequencies of laser pulses. The decay of relevant electronic and vibrational states obviously reduces the producing and detecting efficiencies.     

New Matrix Loop Algebra and Its Application

A new matrix Lie algebra and its corresponding Loop algebra are constructed firstly, as its application, the multi-component TC equation hierarchy is obtained, then by use of trace identity the Hamiltonian structure of the above system is presented. Finally, the integrable couplings of the obtained system is worked out by the expanding matrix Loop algebra.     

A collocation/quadrature-based Sturm–Liouville problem solver

We present a computational method for solving a class of boundary-value problems in Sturm–Liouville form. The algorithms are based on global polynomial collocation methods and produce discrete representations of the eigenfunctions. Error control is performed by evaluating the eigenvalue problem residuals generated when the eigenfunctions are interpolated to a finer discretization grid; eigenfunctions that produce residuals exceeding an infinity-norm bound are discarded. Because the computational approach involves the generation of quadrature weights and arrays for discrete differentiation operations, our computational methods provide a convenient framework for solving boundary-value problems by eigenfunction expansion and other projection methods.     

CLASSICAL R-MATRIX APPROACH TO THE SYSTEM ASSOCIATED WITH THE THREE-WAVE INTERACTION EQUATIONS

1IntroductionTher-matrixmethodisanimportanttoolforstudyingthefinite--dimensionalintegrablesystems.Fromther-matrixformulathecommutativityofmotionintegralsgeneratedfromtheLaxoperatorcanbeeasilyobtained[1].AnrmatrixalsoallowsonetocanonicallyconstructthematrixMoftheLaxpair[:l.In[3],Y.T.WuandX.G.Gengintroduceda3x3matrixspectralproblemwithsixpotentialsasfollowswherethepotentialvectoru=(u12,u21,u135u31)u23,u,,)',Aisaconstantspectralparameter,allaZanda3arethreedistinctconstants,andproposedacorres…     

Correlations between quantum and stochastic systems with a dephasing coupling

Correlations between single qubit and classical environment are studied by means of the stochastic Liouville equation, where a dephasing coupling between them is assumed. When the dephasing of the qubit is characterized by the two-state-jump Markov process, the properties of the total, classical and quantum correlations are examined.