Analysis of the Intensity Fluctuation of Saturation Laser Model in the Real and Imaginary Parts of the Cross-correlation of Quantum Noise;

Under the influence of amplitude modulated signal,we use the linear approximation method to study the output power spectrum and signal-to-noise ratio of the saturation laser model driven by the correlated real and imaginary parts of quantum noise and the pump noise.

Inequalities between the eigenvalues of matrices andits real parts as well as its imaginary parts;

The upper bounds and lower bounds of the matrix eigenvalues,and the inequalities of their real parts and imaginary parts are studied; meantime some new upper bounds and lower bounds of the eigenvalues are also given out in this paper.

Under the Thermofield Dynamics, according to the cutting theorem at finite temperature a set of systematic explicit cutting rules to the Feynman diagrams and the relative Feynman rules are proposed, which can be used as an easy approach to calculate the imaginary parts of the thermal Green functions.