Nonlinear Dynamical Friction from the Doppler-Shifted Equilibrium Memory Kernel

TL;DR

The paper addresses the challenge of computing nonlinear transport coefficients in driven systems by formulating a Doppler-shifted extension of the fluctuation-dissipation theorem within the Generalized Langevin Equation framework. It shows that the non-equilibrium friction experienced by a driven subsystem can be reconstructed from equilibrium bath fluctuations sampled along a Doppler resonance, unifying Stokes-like and Chandrasekhar-type drag regimes. The authors derive an explicit non-Markovian memory kernel for a collisionless plasma and demonstrate that its Markovian limit recovers Chandrasekhar's stopping power, with non-Markovian dynamics capturing transient wake effects. Validation against Particle-in-Cell simulations confirms that the equilibrium memory kernel, when Doppler-shifted, accurately predicts nonlinear drag and wake oscillations, offering a computationally efficient alternative to brute-force non-equilibrium simulations. The methodology has broad implications for predicting transport in dense and strongly coupled plasmas and Warm Dense Matter, where equilibrium fluctuations underpin complex non-equilibrium behavior.

Abstract

We present a statistical mechanics framework for modeling non-equilibrium transport coefficients using the Generalized Langevin Equation (GLE). We show that the kernel, obtained via the Fluctuation-Dissipation Theorem (FDT) from the stochastic force autocorrelation measured in a thermal equilibrium state, is sufficient to model the dynamics of the system in a Non-Equilibrium Steady State (NESS). This approach provides a computationally efficient path to modeling complex transport problems. We apply this framework to the canonical problem of test particle drag in a uniform plasma. The GLE formalism is shown to naturally capture non-Markovian phenomena through the moments of the kernel, including an effective mass renormalization and oscillatory relaxation. We demonstrate that the standard Chandrasekhar stopping power formula arises naturally as the Markovian limit of this equilibrium memory kernel. These theoretical predictions are quantitatively validated by direct Particle-in-Cell simulations, which confirm the predicted oscillatory structure of the memory kernel. This work thus establishes a practical method for predicting non-equilibrium transport properties from first-principles equilibrium simulations.

Figures (1)

• Figure 1: Comparison of the test particle velocity decay. The solid black line represents the high-fidelity PIC result (Set B). The red dashed line represents the GLE prediction using the memory kernel extracted from equilibrium fluctuations (Set A). The agreement at $v_0 = 3.0 v_{th}$ confirms the validity of the Doppler-shifted FDT.