In statistical mechanics, linear response is the measure to quantify the average response of a steady state to the small external perturbation of stochastic system. In this talk, we discuss numerical schemes for the linear response computations of invariant measures from fluctuations at equilibrium. The schemes are based on Girsanov's change-of-measure theory and apply reweighting of trajectories by factors derived from a linearization of the Girsanov weights. This approach leads to a class of estimators we call martingale product estimators. We investigate both the discretization error and the finite time approximation error. The designed numerical schemes are shown to be of bounded variance with respect to the integration time, which is a desirable feature for long time simulations. The resulted methodology provides an alternative computational approach to classical linear response methods such as the Green-Kubo approach. (joint work with Gabriel Stoltz and Ting Wang).
Petr Plechac graduated with MSc in theoretical physics and subsequently obtained PhD in numerical analysis at Charles University, Prague (Universita Karlova, Praha). He gained his postdoctoral experience at British universities - Bath, Heriot-Watt and Oxford. Before moving to the US he had been professor at Warwick University. In the US he held joint position between University of Tennessee and Oak Ridge National Laboratory. In last ten years he has been professor at University of Delaware.
His research focuses on problems at the interface of numerical analysis and applied stochastic analysis. Most recently he has been also active in developing numerical multi-scale methods for simulations of quantum systems. His research group has been supported by grants from federal agencies, NSF, DOE etc.