Since its first observation by John B. Johnson and formulation by Harry Nyquist, Fluctuation-Dissipation Theorem has provided a mechanism for peeking into the behavior of thermodynamic systems as they are perturbed from equilibrium. However, despite the theorem’s widespread usefulness, a great portion of the world around us cannot be reduced to systems which approximate equilibrium closely enough for Fluctuation-Dissipation Theorem to apply. We attempt to help bridge this gap by exploring the statistics of highly tunable non-equilibrium systems. Towards this goal, we return to the Johnson-Nyquist system of electrons scattering around a resistor lattice—by simulating the trajectories of electrons in rapidly fluctuating lattices, we hope to establish the status of Fluctuation-Dissipation Theorem in non-equilibrium systems.
In this project we are interested in studying the ballistic diffusive crossover in a free liquid. In 1827, Robert Brown observed a speck of pollen floating in water moving in diffusive motion. In 1905, Albert Einstein showed that diffusive motion was caused by the pollen being hit by individual water molecules. Fundamental to this theory is that for very short time scales the pollen is moving ballistically. The goal of this experiment is to observe a particle, suspended in a liquid, transition from ballistic to diffusive motion. To observe this behavior we use a homemade holographic microscope in conjunction with a high-speed camera.
This project brings the microscopic world into the laboratory scale. We agitate a container full of water to produce chaotic surface waves which replicate the tumultuous thermal motion of molecules in a gas, but on a centimeter scale rather than angstrom. We’ve shown that these waves have a temperature that is functionally identical that of a thermal gas. This offers us a unique opportunity to study statistical mechanics in a constitutive fashion, exploring directly the dynamics of interparticle interactions, phase transitions, polymer analogs, and many other systems.