##
**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:

35Q40 | PDEs in connection with quantum mechanics |

PDF
BibTeX
XML
Cite

\textit{E. G. Bakhoum} and \textit{C. Toma}, Math. Probl. Eng. 2010, Article ID 428903, 13 p. (2010; Zbl 1191.35219)

### References:

[1] | A. Toma and C. Morarescu, “Detection of short-step pulses using practical test-functions and resonance aspects,” Mathematical Problems in Engineering, vol. 2008, Article ID 543457, 15 pages, 2008. · Zbl 1162.93385 |

[2] | B. Lazar, A. Sterian, St. Pusca, V. Paun, C. Toma, and C. Morarescu, “Simulating delayed pulses in organic materials,” Computational Science and Its Applications, vol. 3980, pp. 779-784, 2006. · Zbl 05497904 |

[3] | G. Toma and F. Doboga, “Vanishing waves on closed intervals and propagating short-range phenomena,” Mathematical Problems in Engineering, vol. 2008, Article ID 359481, 14 pages, 2008. · Zbl 1177.35022 |

[4] | M. Li, “Fractal time series-a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 157264, 26 pages, 2010. · Zbl 1191.37002 |

[5] | M. Li and W. Zhao, “Representation of a stochastic traffic bound,” IEEE Transactions on Parallel and Distributed Systems, IEEE computer Society Digital Library, IEEE Computer Society, 2009, http://doi.ieeecomputersociety.org/10.1109/TPDS.2009.162. |

[6] | M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584-2594, 2008. |

[7] | D. Griffiths, Introduction to Elementary Particles, John Wiley & Sons, New York, NY, USA, 1987. · Zbl 1162.00012 |

[8] | A. P. French and E. F. Taylor, An Introduction to Quantum Physics, Norton, New York, NY, USA, 1978. |

[9] | E. G. Bakhoum, “Fundamental disagreement of wave mechanics with relativity,” Physics Essays, vol. 15, no. 1, pp. 87-100, 2002. |

[10] | E. G. Bakhoum, “On the equation H=mv2 and the fine structure of the hydrogen atom,” Physics Essays, vol. 15, no. 4, pp. 439-443, 2002. |

[11] | E. G. Bakhoum, “Electrodynamics and the mass-energy equivalence principle,” Physics Essays, vol. 19, no. 3, pp. 305-313, 2006. |

[12] | C. Cattani, “Harmonic wavelets towards the solution of nonlinear PDE,” Computers & Mathematics with Applications, vol. 50, no. 8-9, pp. 1191-1210, 2005. · Zbl 1118.65133 |

[13] | J. J. Rushchitsky, C. Cattani, and E. V. Terletskaya, “Wavelet analysis of the evolution of a solitary wave in a composite material,” International Applied Mechanics, vol. 40, no. 3, pp. 311-318, 2004. · Zbl 1075.74048 |

[14] | C. Cattani, “Multiscale analysis of wave propagation in composite materials,” Mathematical Modelling and Analysis, vol. 8, no. 4, pp. 267-282, 2003. · Zbl 1109.74332 |

[15] | C. Cattani, “Harmonic wavelet analysis of a localized fractal,” International Journal of Engineering and Interdisciplinary Mathematics, vol. 1, no. 1, pp. 35-44, 2009. |

[16] | W.-S. Chen, “Galerkin-shannon of debye/s wavelet method for numerical solutions to the natural integral equations,” International Journal of Engineering and Interdisciplinary Mathematics, vol. 1, no. 1, pp. 63-73, 2009. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.