Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in Rn akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978) [2], Dodson, Dickinson (2000) [18] and Beresnevich, Bernik, Kleinbock, Margulis (2002) [8]. In the case of planar curves, the complete Hausdorff dimension theory is developed.     

A pairing theorem between multi-parameter bialgebra and its dual bialgebra

This paper constructs a dual bialgebra for a multi-parameter FRT-bialgebra related to a Hayashi’sR-matrix by using the skew-derivation method and proves that the pairing between them is non-degenerate.     

Hierarchic Natures and Dynamics of Photoinduced Structural Phase Transition in Non-Degenerate Charge Density Wave States Via Successive Photoexcitations

We investigate the adiabatic and dynamical natures of the lattice relaxation of excitons in strongly coupled electron-phonon (e-ph) systems using the extended Peierls-Hubbard model, so as to clarify the possible mechanisms of the photoinduced structural phase transition (PISPT) via multi-photon. Focusing on the growth process of relaxed domains that is induced by multi-photoexcitation, we calculate the adiabatic potential energy surfaces relevant to the nonlinear lattice relaxations of excitons in this process. Calculated potentials lead to an essential model of a multi-stepwise potential-crossing (MSPC) system that is composed of many displaced harmonic oscillators as an elementary process of the domain growth in the strongly coupled e-ph systems. We also investigate the dynamical natures in such MSPC systems calculating the time-developments the excited wave packet in this system using the density operator. It is concluded from calculated results that the system possibly develops from the lowest-energy potential state to the higher ones by the effect of the photoexcitations followed by the lattice relaxations.     

Effective Hamiltonian in the extended Krenciglowa-Kuo method

The extended Krenciglowa-Kuo (EKK) method allows us to calculate the effective Hamiltonian in a non-degenerate model space. We show that the EKK method can be implemented numerically in two iterative schemes, which are explained in detail with emphasis on convergence conditions. Using test calculations in a simple model, we clarify how and on what conditions we can calculate the effective Hamiltonian.     

含原子运动非简并双光子JCM的光子统计性质

利用全量子理论,研究了与双模压缩真空场作用的含原子运动非简并双光子JCM中双模光场的光子统计性质着重讨论了不同初始态下原子的运动速度、模场结构和初始光强对光场的光子统计性质的影响,由此得到一些新的结论.     

相应于一类对称自对偶李代数的顶点代数结构

设gsp是给定的对称自对偶李代数,给出了相应于gsp的一个顶点代数结构.     

非简并双光子微脉塞的发射几率

将简并双光子微脉塞的量子理论推广到非简并情形, 给出了原子发射几率的解析表达式并且分析了相应的性质.发现由于在微脉塞中存在两种腔场模式,导致有两个自由度来改变原子在经过腔场时所受到的势场,因此非简并双光子微脉塞的发射几率的行为不同于简并双光子情况下的发射几率.     

New criteria for the simplex algorithm

The standard linear programming problem with a finite optimum value is considered. We derive new criteria which guarantee that(i) a non-basic variable of a basic feasible solution will remain a non-basic variable of an optimal basic solution; (ii) a basic variable of a basic feasible solution will remain a basic variable of an optimal basic solution.     

Modulated amplitude waves with non-trivial phase in quasi-1D inhomogeneous Bose–Einstein condensates

We consider a 1D nonlinear Schrödinger equation (NLSE) which describes the mean field dynamics of an elongated Bose–Einstein condensate and prove the existence of modulated amplitude waves with non-trivial phase and minimal spatial period tending to infinite. The proof combines the theory of local continuation of non-degenerate periodic solutions with a property of the Ermakov–Pinney equation.