Lattice Model of Brownain Motor

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Addis Ababa University


Nowadays science focuses on small size machine such as Brownian motors due to the need to use energy at small scale. Thus it is important to develop model for studying their working principles. One famous model is Feynman's ratchet and pawl system. We developed a discrete lattice model for this system. The model is Brownian particles moving in a sawtooth potential with or with out external load and trap potential in one dimensional discrete lattice and the lattice is periodically coupled to two (hot and cold) heat reservoirs. We found explicit expressions for current, drift velocity, efficiency and coefficient of performance as a function of the parameters characterizing the model. The parameters are trap potential, ratchet barrier, the strength of noise of the hot reservoir and the external load. From detailed analysis of the expressions we are able to observe that • trap potential affects the current. Current decreases as the strength of trap depth increases. 'D:ap is obstacle for both directions of motion. • the noise and the load are the sources of current and • the ratchet barrier is responsible for rectification of the noise



Brownian motors