Al-Khayat, Isa A. Statistical properties of a non-autonomous system. (English) Zbl 1196.37036 Int. J. Appl. Math. 22, No. 7, 1113-1125 (2009). The author considers the system \[ {{d}\over{dt}}\langle S_+\rangle = - (\Gamma+\imath\Delta)\langle S_+\rangle - \gamma Me^{2\imath\delta t}\langle S_-\rangle + \epsilon\langle S_z\rangle = {{d}\over{dt}}\langle S_+\rangle^* \]\[ {{d}\over{dt}}\langle S_z\rangle = 2\Gamma\langle S_z\rangle - (1/2)\epsilon\langle S_-\rangle - (1/2)\epsilon^*\langle S_+\rangle \] The solutions are taken as complex Fourier series with \(2\delta\) as basic frequency; the paper shows coefficient determination using continued fractions. Next the Boltzmann-Gibbs entropy is discussed. Reviewer: Vladimir Răsvan (Craiova) MSC: 37B55 Topological dynamics of nonautonomous systems 34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc. 30B70 Continued fractions; complex-analytic aspects 37B40 Topological entropy 42A16 Fourier coefficients, Fourier series of functions with special properties, special Fourier series 81T99 Quantum field theory; related classical field theories Keywords:nonautonomous systems; single 2-level atom; Boltzmann-Gibbs entropy PDFBibTeX XMLCite \textit{I. A. Al-Khayat}, Int. J. Appl. Math. 22, No. 7, 1113--1125 (2009; Zbl 1196.37036)