MATHEMATICAL MODELING OF THE HYDROGEN CATALYSIS IN THE BIOLOGICAL SYSTEMS
DOI:
https://doi.org/10.32782/2618-0340/2020.1-3.6Keywords:
hydrogen catalysis, Schrödinger equation, wave function tunneling, mathematical modelingAbstract
The paper is devoted to the presentation of the mathematical model and the numerical calculations results for the tunneling of the wave function in a double-well potential. The biquadratic potential of a double-well form is proposed and used. The aim of the study was to study the phenomenon of tunneling of a quantum mechanical particle in the case when the height of the barrier between the wells significantly exceeds the initial energy of the particle. Based on a mathematical model of the time evolution of the wave function, a numerical algorithm has been developed and a program has been created for solving the Schrödinger equation, which describes the time evolution of the particle's wave function. The physical problem is based on the inclusion in the potential of the time dependency of the stochastic and the sinusoidal form, containing the frequency and modulation index. Thus, the case of a parametric pumping of a quantum system – a particle in a nonstationary potential– is realized. This model can describe the behavior of biological systems in which protons are tunneling between the biologically active sites of complex organic molecules due to the influence of temperature fluctuations, electromagnetic wave irradiation, etc. As a result of numerical experiments, modulation regimes were obtained at which tunneling took place. The absence of tunneling was checked in the regime when sinusoidal modulation was disabled. For various cases of frequency modulation, the results of numerical simulation of the tunneling process are presented. The possibility of adjusting the tunneling efficiency by selecting the modulation frequency is shown. It is also shown that the inclusion in the modulation of the harmonic noise potential of the type of stochastic Ornstein-Uhlenbeck process leads to an increase in the tunneling rate. By the directional change of the modulation parameters, it is possible to control the particle wave function tunneling rate.
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