Conditional probability calculations for the nonlinear Schrödinger equation with additive noise.

The method for the computation of the conditional probability density function for the nonlinear Schrödinger equation with additive noise is developed. We present in a constructive form the conditional probability density function in the limit of small noise and analytically derive it in a weakly nonlinear case. The general theory results are illustrated using fiber-optic communications as a particular, albeit practically very important, example.

Log-log growth of channel capacity for nondispersive nonlinear optical fiber channel in intermediate power range: Extension of the model.

In our previous paper [Terekhov et al., Phys. Rev. E 95, 062133 (2017)2470-004510.1103/PhysRevE.95.062133] we considered the optical channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. We found per-sample channel capacity for this model. In the present paper we extend the per-sample channel model by introducing the initial signal dependence on time and the output signal detection procedure. The proposed model is a closer approximation of the realistic communications link than the per-sample model where there is no dependence of the initial signal on time. For the proposed model we found the correlators of the output signal both analytically and numerically. Using these correlators we built the conditional probability density function. Then we calculated an entropy of the output signal, a conditional entropy, and the mutual information. Maximizing the mutual information we found the optimal input signal distribution, channel capacity, and their dependence on the shape of the initial signal in the time domain for the intermediate power range.

Publisher Correction: Wave kinetics of random fibre lasers.

This corrects the article DOI: 10.1038/ncomms7214.

Next-to-leading-order corrections to capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region.

We consider the optical fiber channel modeled by the nonlinear Schrödinger equation with zero dispersion and additive Gaussian noise. Using the Feynman path-integral approach for the model, we find corrections to conditional probability density function, output signal distribution, conditional and output signal entropies, and the channel capacity at large signal-to-noise ratio. We demonstrate that the correction to the channel capacity is positive for large signal power. Therefore, this correction increases the earlier calculated capacity for a nondispersive nonlinear optical fiber channel in the intermediate power region.

Log-log growth of channel capacity for nondispersive nonlinear optical fiber channel in intermediate power range.

We consider a model nondispersive nonlinear optical fiber channel with an additive Gaussian noise. Using Feynman path-integral technique, we find the optimal input signal distribution maximizing the channel's per-sample mutual information at large signal-to-noise ratio in the intermediate power range. The optimal input signal distribution allows us to improve previously known estimates for the channel capacity. We calculate the output signal entropy, conditional entropy, and per-sample mutual information for Gaussian, half-Gaussian, and modified Gaussian input signal distributions. We demonstrate that in the intermediate power range the capacity (the per-sample mutual information for the optimal input signal distribution) is greater than the per-sample mutual information for half-Gaussian input signal distribution considered previously as the optimal one. We also show that the capacity grows as loglogP in the intermediate power range, where P is the signal power.

Calculation of mutual information for nonlinear communication channel at large signal-to-noise ratio.

Using the path-integral technique we examine the mutual information for the communication channel modeled by the nonlinear Schrödinger equation with additive Gaussian noise. The nonlinear Schrödinger equation is one of the fundamental models in nonlinear physics, and it has a broad range of applications, including fiber optical communications-the backbone of the internet. At large signal-to-noise ratio we present the mutual information through the path-integral, which is convenient for the perturbative expansion in nonlinearity. In the limit of small noise and small nonlinearity we derive analytically the first nonzero nonlinear correction to the mutual information for the channel.

Wave kinetics of random fibre lasers.

Traditional wave kinetics describes the slow evolution of systems with many degrees of freedom to equilibrium via numerous weak non-linear interactions and fails for very important class of dissipative (active) optical systems with cyclic gain and losses, such as lasers with non-linear intracavity dynamics. Here we introduce a conceptually new class of cyclic wave systems, characterized by non-uniform double-scale dynamics with strong periodic changes of the energy spectrum and slow evolution from cycle to cycle to a statistically steady state. Taking a practically important example-random fibre laser-we show that a model describing such a system is close to integrable non-linear Schrödinger equation and needs a new formalism of wave kinetics, developed here. We derive a non-linear kinetic theory of the laser spectrum, generalizing the seminal linear model of Schawlow and Townes. Experimental results agree with our theory. The work has implications for describing kinetics of cyclical systems beyond photonics.

Bremsstrahlung in alpha decay reexamined.

A high-statistics measurement of bremsstrahlung emitted in the alpha decay of (210)Po has been performed, which allows us to follow the photon spectra up to energies of approximately 500 keV. The measured differential emission probability is in good agreement with our theoretical results obtained within the quasiclassical approximation as well as with the exact quantum mechanical calculation. It is shown that, due to the small effective electric dipole charge of the radiating system, a significant interference between the electric dipole and quadrupole contributions occurs, which is altering substantially the angular correlation between the alpha particle and the emitted photon.

Radiative corrections and parity nonconservation in heavy atoms.

The self-energy and the vertex radiative corrections to the effect of parity nonconservation in heavy atoms are calculated analytically in orders Zalpha2 and Z2alpha3ln((lambda(C)/r(0)), where lambda(C) and r(0) are the Compton wavelength and the nuclear radius, respectively. The sum of the radiative corrections is -0.85% for Cs and -1.41% for Tl. Using these results, we have performed analysis of the experimental data on atomic parity nonconservation. The values obtained for the nuclear weak charge, Q(W)=-72.90(28)exp(35)theor for Cs, and Q(W)=-116.7(1.2)exp(3.4)(theor) for Tl, agree with predictions of the standard model. As an application of our approach, we have also calculated analytically the dependence of the Lamb shift on the finite size of the nucleus.