# Adaptive Step Size for Hybrid Monte Carlo Algorithm

## TL;DR

This paper introduces an adaptive step size method for the Hybrid Monte Carlo algorithm that maintains reversibility but faces practical efficiency challenges due to overhead costs.

## Contribution

The paper proposes a reversible adaptive step size scheme for Hybrid Monte Carlo based on a symmetric error equation, highlighting its implementation and limitations.

## Key findings

- Adaptive step size maintains reversibility.
- Overhead outweighs benefits in practical scenarios.
- Provides explanation for efficiency issues.

## Abstract

We implement an adaptive step size method for the Hybrid Monte Carlo a lgorithm. The adaptive step size is given by solving a symmetric error equation. An integr ator with such an adaptive step size is reversible. Although we observe appreciable variations of the step size, the overhead of the method exceeds its benefits. We propose an explanation for this phenomenon.