Paul Langévin (1872-1946)

Like many physicists of his time, Paul Langévin was involved in unraveling the atomic nature of matter. His work ranged from the structure of ceramic and metallic materials to the origins of magnetism. Among his several contributions to physics was the description of molecular fluctuations in form of a force balance, known as the Langevin equation.

The Langevin Equation

A simple example of a Langevine equation is to write a force balance on a microscopic sphere embedded in a fluid (imagine Robert Brown's pollen in water). The total force is equal to a fluctuating "Brownian" force due to molecular collisions, minus a drag force due to the sphere moving though the fluid
                .
Although simple in form, the Langevin equation must be treated carefully since f_B is a stochastic variable.

In our research we extend the Langevin formalism by considering that the sphere may have "memory" of previous history through the elasticity in the fluid. Thus, we write the so-called generalized Langevin equation as
              .