Measurement of second-order response without perturbation

Trajectory (left frame) showing equilibrium fluctuations of a 1.32µm radius colloidal particle in an anharmonic potential (right frame) near a wall located at x=0. The inset sketches the particle trapped and pressed against the wall by optical tweezers to tune the potential shape.

The fluctuation dissipation theorem (FDT) is one of the most important relations for systems out of equilibrium: It connects the linear response to fluctuations in equilibrium. Its power is evident from the circumstance that it is used in almost all fields of physics, spanning the whole range from classical to quantum regimes. Despite this fame and influence, the question whether it can be extended to nonlinear responses in an experimentally meaningful and useful manner, remains open in the literature. In this work, we demonstrate that the second order response of a micron-sized colloidal particle, subject to an anharmonic potential, can be obtained from its experimentally measured equilibrium fluctuations. The concept of FDT can thus be extended to nonlinear responses. Compared to the conventional way of measuring responses by application of a perturbation, this approach has the practical advantage that it allows to predict the second-order response to arbitrary perturbation protocols from a single experiment.

Further information

Measurement of second-order response without perturbation
Laurent Helden, Urna Basu, Matthias Krüger, and Clemens Bechinger
EPL 116, 60003 (2016)