Analogy between electrochemical oscillations and quantum physical processes

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Grzanna, J.^1 ; Lewerenz, H.J.^1,2

Helmholtz Zentrum Berlin for Materials and Energy, Hahn-Meitner Platz 1, D-14109 Berlin, Germany^1

Joint Center for Artificial Photosynthesis, California Institute of Technology, 1200 E. California Blvd, Pasadena, CA 91125, United States^2

关键词: Electrochemical oscillations;    Electrochemical process;    Frequency distributions;    Linear integral equations;    Phase-space analysis;    Probability densities;    Sustained oscillations;    Time-dependent oscillators;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012119/pdf
DOI  :  10.1088/1742-6596/490/1/012119

来源: IOP

【 摘 要 】

In (photo) electrochemical oscillations, the discretization of phase oscillators leads to a sequence of time dependent oscillator density functions which describe the passing of the oscillators through their minimum at each cycle. Two consecutive oscillator density functions are connected by a Markov process represented by a linear integral equation of second order which is homogeneous in the case of sustained oscillations. The kernel of the integral equation is a normalized Greens Function and represents the probability density for the periods of the oscillators. Both together, the oscillator density function and the two-dimensional probability density for the periods of the oscillators define a random walk. The relation of the model to the holographic principle is discussed briefly. Further, a detailed analysis of a kernel of the integral equation leads to a frequency distribution g for the period length. Additionally, it is possible to determine the energy E in dependence on the period length from the electrochemical process. The product g E shows qualitatively the same behaviour as the radiation of a black body, indicating that the discretization of phase oscillators, when represented by phase space analysis, show an analogy to quantum processes.