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Statistical properties of a non-autonomous system. (English) Zbl 1196.37036

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.

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
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