Self-focusing of electromagnetic waves in a degenerate electron-hole plasma

The free carrier nonlinear dielectric constant of a degenerate electron-hole plasma (e.g., Ge) in the presence of a Gaussian electromagnetic beam has been studied by a kinetic treatment. The redistribution of carriers (electrons and holes) is the source of nonlinearity and is effective in causing the self-focusing of the beam. The rise in carrier temperature due to the wave field is almost unaffected by the degeneracy, whereas the nonlinearity is considerably affected by it. The increase of degeneracy (by increasing the equilibrium carrier concentration at the fixed lattice temperature) increases the nonlinear dielectric constant. Hence self-focusing is enhanced by degeneracy. This work was supported by NSF (USA) and CSIR (India).     

PPLN waveguide for quantum communication

We report on energy-time and time-bin entangled photon-pair sources based on a periodically poled lithium niobate (PPLN) waveguide. Degenerate twin photons at 1 314 nm wavelength are created by spontaneous parametric down-conversion and coupled into standard telecom fibers. Our PPLN waveguide features a very high conversion efficiency of about 10^-6, roughly 4 orders of magnitude more than that obtained employing bulk crystals [#!Tanzilli01a!#]. Even if using low power laser diodes, this engenders a significant probability for creating two pairs at a time - an important advantage for some quantum communication protocols. We point out a simple means to characterize the pair creation probability in case of a pulsed pump. To investigate the quality of the entangled states, we perform photon-pair interference experiments, leading to visibilities of 97% for the case of energy-time entanglement and of 84% for the case of time-bin entanglement. Although the last figure must still be improved, these tests demonstrate the high potential of PPLN waveguide based sources to become a key element for future quantum communication schemes. Received 13 July 2001     

有机染料HEASPS在不同波长时的激发态吸收和双光子吸收性质研究

提出了有机染料反式 4 [4′ (N 羟乙基 N 乙基胺基 )苯乙烯基 ] N 甲基吡啶对甲苯磺酸盐 (简称HEASPS)非线性吸收的三态模型。认为在较短波长 (<1 0 0 0nm)时 ,双光子吸收和激发态吸收同时存在。成功地解释了该染料双光子吸收峰相对线性吸收峰的两倍的明显蓝移 ,以及最高上转换效率波长相对最强吸收波长的明显红移。提出了一种新的计算方法 ,利用不同波长的非线性透过率和不同波长的上转换效率 ,求出了该染料的双光子吸收截面和激发态吸收系数。     

双模问题rad~t(-,-)与拟遗传代数

设 Ｂ是 Ｋｒｕｌｌ－ｓｃｈｍｉｄｔ范畴 Ｋ上的一个上三角双模，Ｂｒｕｓｔｌｅ和 Ｈｉｌｌｅ证明了Ｂ的矩阵范畴ｍａｔＢ的投射生成子Ｐ的自同态代数的反代数Ａ是拟遗传代数，而且代数Ａ的△－好模范畴与ｍａｔＢ等价．本文把这些结果推广到由Ｃｒａｗｌｅｙ-Ｂｏｅｖｅｙ给出的具有非零导子的双模上，并在此基础上着重讨论了遗传代数 的投射模范畴Ｐｒｏｊ上的双模ｒａｄｔ（－，－），刻画了它所对应的拟遗传代数的Ｇａｂｒｉｅｌ箭图与关系，以及它们的特征模和Ｒｉｎｇｅｌ对偶．     

五阶变系数模型方程新的Jacobi椭圆函数解

我们给出了一种统一的Jacobi椭圆函数方法来构造非线性偏微分方程精确行波解的新方法．借助于Mathematica，我们获得了五阶变系数模型方程的24种Jacobi椭圆函数解．     

He原子(e,3e)反应中末态波函数的动量相关

在前期工作的基础上,进一步考虑了He原子(e,3e)反应中末态四体的动量相关.用改进后的理论计算了高能电子入射双电离He原子的五重微分截面(FDCS).与前期理论相比,所得结果大大地改善了理论曲线与实验结果的吻合程度.     

关于错排数与Bell数的一些循环公式

In this paper, a further investigation for the number of Derangements and Bell numbers is performed, and some new recursion formulae for the number of Derangements and Bell numbers are established by applying the generating function methods and Padé approximation techniques. Illustrative special cases of the main results are also presented.     

On reducibility of n-ary quasigroups

An n-ary operation Q:Σⁿ→Σ is called an n-ary quasigroup of order |Σ| if in the relation x₀=Q(x₁,…,x_n) knowledge of any n elements of x₀,…,x_n uniquely specifies the remaining one. Q is permutably reducible if Q(x₁,…,x_n)=P(R(x_σ(1),…,x_σ(k)),x_σ(k+1),…,x_σ(n)) where P and R are (n-k+1)-ary and k-ary quasigroups, σ is a permutation, and 1<k<n. An m-ary quasigroup S is called a retract of Q if it can be obtained from Q or one of its inverses by fixing n-me;0 arguments. We prove that if the maximum arity of a permutably irreducible retract of an n-ary quasigroup Q belongs to {3,…,n-3}, then Q is permutably reducible.     

p-Adic Schrödinger-type operator with point interactions

A <em>pem>-adic Schrödinger-type operator <em>Dem><em>αem>+<em>Vem><em>Yem> is studied. <em>Dem><em>αem> (<em>αem>>0) is the operator of fractional differentiation and eight="20" border="0" style="vertical-align:bottom" width="167" alt="View the MathML source" title="View the MathML source" src="http://ars.els-cdn.com/content/image/1-s2.0-S0022247X0700813X-si4.gif">(<em>bem><em>iem><em>jem>∈<em>Cem>) is a singular potential containing the Dirac delta functions <em>δem><em>xem> concentrated on a set of points <em>Yem>={<em>xem>₁,&hellip;,<em>xem><em>nem>} of the field of <em>pem>-adic numbers <em>Qem><em>pem>. It is shown that such a problem is well posed for <em>αem>>1/2 and the singular perturbation <em>Vem><em>Yem> is form-bounded for <em>αem>>1. In the latter case, the spectral analysis of <em>ηem>-self-adjoint operator realizations of <em>Dem><em>αem>+<em>Vem><em>Yem> in <em>Lem>₂(<em>Qem><em>pem>) is carried out.