Instabilities in molecular dynamics integrators used in Hybrid Monte Carlo simulations

We discuss an instability in the leapfrog integration algorithm, widely used in current Hybrid Monte Carlo (HMC) simulations of lattice QCD. We demonstrate the instability in the simple harmonic oscillator (SHO) system where it is manifest. We demonstrate the instability in HMC simulations of lattice QCD with dynamical Wilson-Clover fermions and discuss implications for future simulations of lattice QCD.