# The Effects of Intrinsic Dynamical Ghost Modes in Discrete-Time Langevin Simulations

## TL;DR

This paper investigates how intrinsic ghost modes in discrete-time Langevin simulations, specifically using the GJF-2GJ thermostat, cause deviations in statistical measures for nonlinear oscillators like the pendulum, independent of time-step size.

## Contribution

It identifies and analyzes discrete-time dynamical ghost modes as the cause of statistical deviations in Langevin simulations, highlighting their inherent nature rather than algorithmic errors.

## Key findings

- Ghost modes cause deviations in statistical data.
- Deviations are due to intrinsic properties of discrete-time dynamics.
- Simulation results align with velocity distribution functions.

## Abstract

Using the recently published GJF-2GJ Langevin thermostat, which can produce time-step-independent statistical measures even for large time steps, we analyze and discuss the causes for abrupt deviations in statistical data as the time step is increased for some simulations of nonlinear oscillators. Exemplified by the pendulum, we identify a couple of discrete-time dynamical modes in the purely damped pendulum equation as the cause of the observed discrepancies in statistics. The existence, stability and kinetics of the modes are consistent with the acquired velocity distribution functions from Langevin simulations, and we conclude that the simulation deviations from physical expectations are not due to normal, systematic algorithmic time-step errors, but instead due to the inherent properties of discrete time in nonlinear dynamics.