A scheme for generating sub-Poisson light in a negative feedback and cascade three-level system is proposed in this paper. By using Langevin quantum theory, it is shown that there is a partial correlation between the ...A scheme for generating sub-Poisson light in a negative feedback and cascade three-level system is proposed in this paper. By using Langevin quantum theory, it is shown that there is a partial correlation between the two output light beams, one of which is fed back to control pump source so that the pump noise may be suppressed. When the pump noise is perfectly suppressed, the photon noise level of the internal field is 50% below the standard quantum limit (SQL), but the reduction of the output photon noise is related with the atomic number N. When N is very large, the output noise level is SQL. When N is very small, the sub-Poisson light can be produced within the cavity bandwidth in the external field, and the fluctuation of output photon flow approaches zero when N approaches 1. The conclusion in this paper is of generality.展开更多
We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] prov...We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0展开更多
In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend t...In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.展开更多
基金the National Natural Science Foundation of China
文摘A scheme for generating sub-Poisson light in a negative feedback and cascade three-level system is proposed in this paper. By using Langevin quantum theory, it is shown that there is a partial correlation between the two output light beams, one of which is fed back to control pump source so that the pump noise may be suppressed. When the pump noise is perfectly suppressed, the photon noise level of the internal field is 50% below the standard quantum limit (SQL), but the reduction of the output photon noise is related with the atomic number N. When N is very large, the output noise level is SQL. When N is very small, the sub-Poisson light can be produced within the cavity bandwidth in the external field, and the fluctuation of output photon flow approaches zero when N approaches 1. The conclusion in this paper is of generality.
基金Supported by NSFC(10631030) and CAS-KJCX3-SYW-S03
文摘We study the following Schrodinger-Poisson system where （Pλ）{-△u＋ V（x）u＋λФ（x）u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф（x） =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 ＋∞, V（x） and Q（x）=1 ,D.Ruiz[19] proved that（Pλ）with p∈ （2, 5） has always a positive radial solution, but （Pλ） with p E （1, 2] has solution only if λ 〉 0 small enough and no any nontrivial solution if λ≥1/4.By using sub-supersolution method,we prove that there exists λ0〉0 such that（Pλ）with p ∈（1＋∞）has alaways a bound state（H^1（R^3）solution for λ∈[0,λ0）and certain functions V（x）and Q（x）in L^∞（R^3）.Moreover,for every λ∈[0,λ0）,the solutions uλ of （Pλ）converges,along a subsequence,to a solution of （P0）in H^1 as λ→0
基金supported by National Natural Science Foundation of China (10901054)
文摘In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.
