Analogy between electrochemical oscillations and quantum physical processes

• Published in: Journal of physics. Conference series 2014-01, Vol.490 (1), p.12119-4, Article 012119
• Main Authors: Grzanna, J, Lewerenz, H J
• Format: Article
• Language: English
• Subjects: Analogies; Black body radiation; Density; Discretization; Frequency distribution; Green's functions; Integral equations; Kernels; Markov processes; Mathematical models; Oscillations; Oscillators; Physics; Random walk
• ISSN: 1742-6596; 1742-6588; 1742-6596
• DOI: 10.1088/1742-6596/490/1/012119

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.