A parabolic-bistable potential system driven by colored noise is studied. The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived. Furthermore, the m...A parabolic-bistable potential system driven by colored noise is studied. The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived. Furthermore, the mean first-passage time is calculated by the use of two approximate methods, respectively. It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity; (ii) a minimum occurs on the curve of the second-order moment of the system vs. noise intensity at the point ; (iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time , while the conventional steepest descent approximation leads to poor results.展开更多
Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctu-ation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part an...Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctu-ation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part andimaginary part are cross-correlated. We analyzed the valid range for thelinear approximation method by studying theinfluences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities ofthe quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that thevalid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker,the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal hassmaller amplitude and higher frequency.展开更多
According to the fractal characteristics appearing in non-uniform granular system, we found the fractal model to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bri...According to the fractal characteristics appearing in non-uniform granular system, we found the fractal model to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bring forward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granular flow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermal conductivity in the mixed system changes with the fractal parameters such as the solid fraction v, structural character parameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermal conductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental data and the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generality of our prediction on the granular system.展开更多
We present an analytic investigation of the signal-to-noise ratio (SNR) by studying a signal modulated model of a single-mode laser system driven by pump noise and quantum noise with correlated real and imaginary part...We present an analytic investigation of the signal-to-noise ratio (SNR) by studying a signal modulated model of a single-mode laser system driven by pump noise and quantum noise with correlated real and imaginary parts,and find there is a maximum in the curve of the dependence of SNR upon the cross-correlation coefficient λq between the real part and the imaginary part, i.e., stochastic resonance appears in the SNR vs. λq curve. Moreover, when the SNR is at the maximum, the cross-correlation coefficient λq = 0, which is coincidentally at the minimum of the mean normalized intensity fluctuation. The influences on stochastic resonance by the intensities of the pump and the quantum noise, the amplitude of the modulation signal, and the net gain of the laser are also studied. Furthermore, in order to ensure that the results obtained in this paper is reliable, the valid range for the linear approximation method is discussed.展开更多
The. Analytical expressions of eigenstates and eigenenergies are demonstrated using a parameter λ without the assumption of Bethe anstz for two kinds of N-mode mixing models. The parameter is shown to be determined b...The. Analytical expressions of eigenstates and eigenenergies are demonstrated using a parameter λ without the assumption of Bethe anstz for two kinds of N-mode mixing models. The parameter is shown to be determined by the roots of a simple polynomial and is solvable analytically or numerically. In addition, the exact analytical expressions of eigenstates and eigenenergies are illustrated without any unknown parameter.展开更多
By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise...By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. T3.展开更多
Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation ...Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λq between the realand imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Qst(I), the mean (I), and the variance λ2(0) of the laser intensity. It is shown that cross-correlation intensity λq of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠ 0), improving the pump parameters monotonously will make the curves of Qst(I)exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λq and τ when the laser is operated near or below threshold. Especially when τ≠ 0, the heights of the peaks of the curves of λ2(0)-a0 and λ3(0)-a0, (here a0 is the net gain coefficient) go up as λq increases. However the entire curves of λ2(0)-a0 and λ3(0)-a0are abruptly suppressed when λq = 1, in similarity to phase transition of stationary intensity distribution.展开更多
We present the explicit analytical results of all the eigenstates and eigenvalues using a parameter λ without the assumption of Bethe ansatz for three different kinds of six bosonic,modes models. The parameter is det...We present the explicit analytical results of all the eigenstates and eigenvalues using a parameter λ without the assumption of Bethe ansatz for three different kinds of six bosonic,modes models. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.展开更多
文摘A parabolic-bistable potential system driven by colored noise is studied. The exact analytical expressions of the stationary probability distribution (SPD) and the moments of the system are derived. Furthermore, the mean first-passage time is calculated by the use of two approximate methods, respectively. It is found that (i) the double peaks of SPD are rubbed-down into a flat single peak with the increasing of noise intensity; (ii) a minimum occurs on the curve of the second-order moment of the system vs. noise intensity at the point ; (iii) the results obtained by our approximate approach are in good agreement with the numerical calculations for either small or large correlation time , while the conventional steepest descent approximation leads to poor results.
文摘Using the linear approximation method, we calculated the steady-state mean normalized intensity fluctu-ation for a loss-noise model of a single-mode laser driven by a pump noise and a quantum noise, whose real part andimaginary part are cross-correlated. We analyzed the valid range for thelinear approximation method by studying theinfluences on the steady-state mean normalized intensity fluctuation by the cross-correlation coefficient, the intensities ofthe quantum and pump noise, the net gain, and the amplitude and frequency of the input signal, and we found that thevalid range becomes wider when the cross-correlation between the real and imaginary part of quantum noise is weaker,the noise intensities of quantum and pump are weaker, the laser system is far from the threshold and the signal hassmaller amplitude and higher frequency.
文摘According to the fractal characteristics appearing in non-uniform granular system, we found the fractal model to study the effective thermal conductivity in the mixed system. Considering the quasi-equilibrium, we bring forward the fractal velocity probability distribution function. The equipartition of energy is employed to the non-uniform granular system, and the granular temperature is derived. We investigate the thermal conductivity in granular flow due to the movement of the particles, namely the heat transfer induced by the streaming mode only. The thermal conductivity in the mixed system changes with the fractal parameters such as the solid fraction v, structural character parameter η, and fractal dimension D of size distribution. These parameters depict the characteristics of the thermal conductivity in the actual complex granular system. Comparing our conclusion with the correlative experimental data and the theoretical conclusion of binary mixture of granular materials, the results can qualitatively confirm the generality of our prediction on the granular system.
基金国家自然科学基金，the Emphases Item of Education Office of Hubei Province of China under
文摘We present an analytic investigation of the signal-to-noise ratio (SNR) by studying a signal modulated model of a single-mode laser system driven by pump noise and quantum noise with correlated real and imaginary parts,and find there is a maximum in the curve of the dependence of SNR upon the cross-correlation coefficient λq between the real part and the imaginary part, i.e., stochastic resonance appears in the SNR vs. λq curve. Moreover, when the SNR is at the maximum, the cross-correlation coefficient λq = 0, which is coincidentally at the minimum of the mean normalized intensity fluctuation. The influences on stochastic resonance by the intensities of the pump and the quantum noise, the amplitude of the modulation signal, and the net gain of the laser are also studied. Furthermore, in order to ensure that the results obtained in this paper is reliable, the valid range for the linear approximation method is discussed.
文摘The. Analytical expressions of eigenstates and eigenenergies are demonstrated using a parameter λ without the assumption of Bethe anstz for two kinds of N-mode mixing models. The parameter is shown to be determined by the roots of a simple polynomial and is solvable analytically or numerically. In addition, the exact analytical expressions of eigenstates and eigenenergies are illustrated without any unknown parameter.
文摘By using the linear approximation method, the intensity correlation function and the intensity correlation time are calculated in a gain-noise model of a single-mode laser driven by colored cross-correlated pump noise and quantum noise, each of which is colored. We detect that, when the cross-correlation between both noises is negative, the behavior of the intensity correlation function C(t) versus time t, in addition to decreasing monotonously, also exhibits several other cases, such as one maximum, one minimum, and two extrema (one maximum and one minimum), i.e., some parameters of the noises can greatly change the dependence of the intensity correlation function upon time. T3.
文摘Applying the method of the unified colored noise approximation and phase lock, we study in this paper the stationary intensity distribution of the single-mode laser driven by colored pump noise with cross-correlation between the real and imaginary parts of the quantum noise. We present a thorough discussion of how the cross-correlation λq between the realand imaginary parts of the quantum noise and the self-correlation time τ of the pump noise determine the behaviors of the stationary distribution Qst(I), the mean (I), and the variance λ2(0) of the laser intensity. It is shown that cross-correlation intensity λq of the complex quantum noise can induce a first-order-like transition. When the pump noise is colored noise (τ≠ 0), improving the pump parameters monotonously will make the curves of Qst(I)exhibit reentrant phase transition. The fluctuations of laser intensity are strongly influenced by λq and τ when the laser is operated near or below threshold. Especially when τ≠ 0, the heights of the peaks of the curves of λ2(0)-a0 and λ3(0)-a0, (here a0 is the net gain coefficient) go up as λq increases. However the entire curves of λ2(0)-a0 and λ3(0)-a0are abruptly suppressed when λq = 1, in similarity to phase transition of stationary intensity distribution.
文摘We present the explicit analytical results of all the eigenstates and eigenvalues using a parameter λ without the assumption of Bethe ansatz for three different kinds of six bosonic,modes models. The parameter is determined by the roots of a polynomial and is solvable analytically or numerically.
