Ordinary chemical reaction process induced by a unidimensional map

Area of Science:

• Chemical Physics
• Nonlinear Dynamics
• Statistical Mechanics

Background:

• A theoretical model proposed that a "non-standard" system, a reactant oscillator interacting with a tent map, could mimic a thermal bath.
• The temperature and friction in this bath were predicted to depend on the map's correlation and response functions.

Purpose of the Study:

• To numerically simulate a standard reaction process using the proposed non-standard system.
• To verify the theoretical prediction of the tent map's equivalence to a thermal bath.
• To test the accuracy of the predicted temperature and friction values by fitting numerical results to an Arrhenius law.

Main Methods:

• Numerical simulation of a reactant oscillator (harmonic oscillator with energy threshold) interacting with a one-dimensional tent map.
• Analysis of the reaction rate by fitting the simulation data to an Arrhenius law.
• Comparison of simulation-derived parameters with theoretically predicted temperature and friction values.

Main Results:

• The numerical simulations confirmed the theoretical prediction that the tent map system acts as a thermal bath.
• The reaction rate data were well-fitted by an Arrhenius law.
• The temperature and friction values derived from the fit matched the predicted values based on the map's properties.

Conclusions:

• The study validates the theoretical framework predicting the equivalence of a specific non-standard system to a thermal bath for reaction dynamics.
• The results demonstrate the applicability of the Arrhenius law with theoretically derived parameters, highlighting the system's sensitivity to statistical details.