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Building Langmuir Probes and Emissive Probes for Plasma Potential Measurements in Low Pressure, Low Temperature Plasmas

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Nonlinear Langevin functionals for a driven probe.

Juliana Caspers¹, Matthias Krüger¹

¹Institute for Theoretical Physics, Georg-August-Universität Göttingen, 37073 Göttingen, Germany.

The Journal of Chemical Physics

|September 25, 2024

Summary

This summary is machine-generated.

This study introduces a Volterra series to describe nonlinear forces on particles in fluids. It reveals how these forces depend on driving protocols and non-equilibrium fluid interactions.

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Area of Science:

Statistical Mechanics
Nonlinear Dynamics
Soft Matter Physics

Background:

Probe particles in fluids experience stochastic forces, especially under strong driving.
These forces can exhibit complex nonlinear behaviors dependent on the driving protocol.
Understanding these nonlinearities is crucial for modeling systems like colloids and polymers.

Purpose of the Study:

To develop a theoretical framework for quantifying nonlinear functionals of stochastic forces acting on a probe particle.
To connect these nonlinear functionals to equilibrium correlation functions using nonlinear response theory.
To analyze the non-equilibrium statistics of interaction and trapping forces in driven systems.

Main Methods:

Application of nonlinear response theory within a path integral formalism.
Development of a Volterra series expansion for nonlinear functionals.
Calculation of kernels in terms of connected equilibrium correlation functions.
Simulation of a model system of nonlinearly interacting Brownian particles.

Main Results:

The first cumulant represents the mean force, the second characterizes noise, and higher cumulants capture non-Gaussian fluctuations.
The formalism successfully describes non-equilibrium statistics for prescribed trajectories and moving potentials.
Simulations reveal shear-thinning (third-order response) and oscillating noise covariance (second-order response).

Conclusions:

The Volterra series provides a powerful tool for analyzing nonlinear stochastic forces in driven systems.
The framework links non-equilibrium phenomena to equilibrium properties through correlation functions.
Nonlinear effects like shear-thinning and noise oscillations are observable in driven Brownian systems.