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Seminar: From O.D.E’s to S.D.E’s – an introduction to stochastic processes
October 16 @ 2:00 pm - 3:00 pm
In this tutorial, Tim will introduce basic stochastic processes via the Langevin stochastic differential equation. He will discuss its relation to the Fokker-Planck equation, focusing initially on linear (Ornstein-Ulhenbeck) processes. These are stochastic processes that exhibit linear o.d.e.’s for the time dependence of expectation values of state variables and have a “noise term” that is independent of state-of-the-system and time. Some results for such linear systems will be derived and presented including multivariate systems. In addition, instructive examples will be discussed. Time permitting, Tim will move on to some aspects of state-dependent noise, non-linear systems, and “microscopic” reaction-diffusion systems.
Tim Duty is a professor in the School of Physics at UNSW who leads the Laboratory for Superconducting Quantum Devices. Since completing his PhD at The University of British Columbia in 2000, he has focused on experiments that elucidate quantum behaviour in nanoscale superconducting circuits. These include pioneering development of one of the first superconducting quantum bits, novel methods for single-charge detection, quantum optics of the so-called dynamical Casimir effect, and probing the one-dimensional Bose glass state of disordered Luttinger liquids using long chains of nanostructured superconducting junctions.
In another life (i.e. his PhD studies), he applied tools developed in statistical physics to the study of stochastic reaction-diffusion systems with applications in a number of fields including population genetics. In an even earlier life (his Master’s studies), he used positive muons to experimentally probe the electronic and structural properties of C60 (buckminsterfullerene) solids, in addition to contributing to experiments that provided early evidence for the d-wave pairing symmetry of high-Tc superconductors. Tim received his bachelor’s degree at Virginia Tech in his home state of Virginia in the USA, where he also worked as a research assistant for an experimental particle physics group.