GENERALIZED OPERATORS AND OPERATOR-VALUED DISTRIBUTIONS IN QUANTUM FIELD THEORY

The relation between generalized operators and operator-valued distributions is discussed so that these two viewpoints can be used alternatively to explain quantum fields.     

量子随机Cable方程的白噪声分析方法

本文讨论了广义算子及其Wick积意义下的非线性量子随机Cable方程.在给出解的存在唯一性定理的基础上,证明了解对初值过程的连续依赖性及其他性质.     

平方协变差和连续半鞅的推广Ito^公式

令X是连续半鞅，f是R上的局部可积函数。本文我们将证明，只要∫0tf(Xs)ds存在，那么平方协变差存在且等于-∫Rf(a)daLta,Lat是X的局部时。因此对具有导数f的绝对连续函数F，有推广的Ito^公式F（Xt)=F(X0) ∫0tf(Xs)dXs 1/2[f(X),X]t。     

Joint nonlinear electrical equalization in coherent optical PDM DFT-spread-OFDM systems

We propose a joint nonlinear electrical equalization approach in coherent optical discrete-Fourier-transform spread orthogonal-frequency-division-multiplexing(DFT-spread-OFDM) systems with polarization division multiplexing(PDM).This method is based on an adaptive Volterra series expansion for nonlinear distortions of two orthogonal polarizations.The nonlinear electrical equalization is validated through numerical simulation of 100-Gb/s quadrature phase shift keying and 200-Gb/s 16 quadrature amplitude modulation PDM DFT-spread-OFDM systems.     

Femtosecond parabolic pulse nonlinear compression with gas-filled hollow-core fiber

We study theoretically the spectral intensity evolutions of the femtosecond Gaussian and parabolic pulses with different initial pulse energies and compare the nonlinear compressions of these pulses based on a meter-long hollow-core fiber filled with neon for different initial pulse durations. The pulses are first coupled into gas-filled hollow-core fiber for spectrum broadening, then compressed by the optimal chirp compensation. The parabolic pulse possesses a shorter pulse duration, larger peak power, and cleaner wings than Gaussian pulse. The properties are useful for compressing the pulses and thus generating the high-energy, short-duration pulses.     

Field-free molecular orientation enhanced by tuning the intensity ratio of a three-color laser field

We theoretically study the field-free molecular orientation induced by a three-color laser field. The three-color laser field with a large asymmetric degree can effectively enhance the molecular orientation. In particular, when the intensity ratio of the three-color laser field is tuned to a proper value of I_3: I_2: I_1= 0.09 : 0.5 : 1, the molecular orientation can be improved by ～ 20% compared with that of the two-color laser field at intensity ratio I_2: I_1= 1 : 1 for the same total laser intensity of 2×10~(13)W/cm~2. Moreover, we investigate the effect of the carrier-envelope phase(CEP) on the molecular orientation and use the asymmetric degree of the laser field to explain the result. We also show the influences of the laser intensity, rotational temperature, and pulse duration on the molecular orientation. These results are meaningful for the theoretical and experimental studies on the molecular orientation.     

随机微分方程终值问题的弱解(英)

设｛Wt．Ft．t∈［0．T］｝为概率空间（Ω，P）上的标准α维Brown运动，为由它生成的自然σ－代数流．本文讨论了如下随机微分方程终值问题弱解的存在性：其中ξ∈L2（Ω，P；Rn），g：［0，T」×Rn×Rnd→Rn为有界可测函数．此外，还讨论了它在金融市场期权定价问题中的应用．     

A MODEL FOR WHITE NOISE ANALYSIS IN P-ADIC NUMBER FIELDS

ＡＭＯＤＥＬＦＯＲＷＨＩＴＥＮＯＩＳＥＡＮＡＬＹＳＩＳＩＮＰ－ＡＤＩＣＮＵＭＢＥＲＦＩＥＬＤＳ（黄志远）￥ＡｎｄｒｅｗＫｈｒｅｎｎｉｋｏｖ（ＭｏｓｃｏｗＩｎｓｔ．ｏｆＥｌｅｃｔｒｏｎｉｃＥｎｇｉｎｅｅｒｉｎｇ，１０３４９８，Ｚｅｌｅｎｏｇｒａｄ，Ｋ－...     

Generation of few-cycle laser pulses:Comparison between atomic and molecular gases in a hollow-core fiber

We numerically study the pulse compression approaches based on atomic or molecular gases in a hollow-core fiber.From the perspective of self-phase modulation(SPM), we give the extensive study of the SPM influence on a probe pulse with molecular phase modulation(MPM) effect. By comparing the two compression methods, we summarize their advantages and drawbacks to obtain the few-cycle pulses with micro- or millijoule energies. It is also shown that the double pump-probe approach can be used as a tunable dual-color source by adjusting the time delay between pump and probe pulses to proper values.     

倒向随机微分方程的理论、发展及其应用

本文全面综述了倒向随机微分方程理论的出现、发展、应用及研究现状，介绍了作者博士论文的主要工作。