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Dynamical aspects of macroscopic and quantum transitions due to coherence function and time series events. (English) Zbl 1191.35219
Summary: This study presents the application of dynamical equations able to generate alternating deformations with increasing amplitude and delayed pulses in a certain material medium. It is considered that an external force acts at certain time interval (similar to a time series) upon the material medium in the same area. Using a specific differential equation (considering nonzero initial values and using a function similar to the coherence function between the external force and the deformations inside the material), it results that modulated amplitude oscillations appear inside the material. If the order of the differential dynamical equation is higher, supplementary aspects as different delayed pulses and multiscale behaviour can be noticed. These features are similar to non-Markov aspects of quantum transitions, and for this reason the mathematical model is suitable for describing both quantum phenomena and macroscopic aspects generated by sequence of pulses. An example of a quantum system, namely, the Hydrogen atom, is discussed.
MSC:
35Q40PDEs in connection with quantum mechanics