Brownian Motion: Langevin Equation in C++

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In this case, we select a particle of interest and find an equation that describes the dynamics of a chosen particle in the presence of the other particles. The classical example of this is the Langevin equation developed in a heuristic way by Paul Langevin to describe the Brownian motion.


The state of the mechanical system considering the classical approach is specified by a set of positions and momenta. This provides an accurate description of the physical state of multibody systems and the system in a fully deterministic way.

The dynamics of such a multibody system are thus typically described by using a coupled set of differential equations, such as Newton’s equations of motion, individual dynamics of each particle in the system.

However, we can apply the alternative approach to describing dynamics, and describe the dynamics by studying, selected particles moving in the presence of the other particles which we regard as a background, whose detailed dynamics are not treated.

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