# On the symplectic integration of the Klein Gordon lattice model

## TL;DR

This paper evaluates various symplectic integration methods for simulating the Klein Gordon lattice, focusing on efficiency and accuracy in weak chaos regimes through extensive numerical experiments.

## Contribution

It compares the performance of different symplectic schemes on a complex Hamiltonian system, providing insights into their suitability for large-scale lattice simulations.

## Key findings

- Certain schemes show better energy conservation.
- Trade-offs between computational cost and accuracy are identified.
- Results guide optimal method selection for similar systems.

## Abstract

We investigate the performance of various methods of symplectic integration, which are based on two part splitting of the integration operator, for the numerical integration of multidimensional Hamiltonian systems. We implement these schemes to study the behavior of the one-dimensional quartic Klein Gordon disordered lattice with many degrees of freedom (of the order of a few hundreds) and compare their efficiency for the weak chaos regime of the system's dynamics. For this reason we perform extensive simulations for each considered integration scheme. In the process, the second moment and the participation number of the propagating wave packets, along with the system's relative energy error and the required CPU time are registered and compared.