Kramers equation algorithm for simulations of QCD with two flavors of Wilson fermions and gauge group SU(2)

We compare the Hybrid Monte Carlo (HMC) and the Kramers equation algorithms for simulations of QCD with two flavors of dynamical Wilson fermions and gauge group $SU(2)$. The results for the performance of both algorithms are obtained on $6^312$, $12^4$ and $16^4$ lattices at a pion to $\rho$ meson mass ratio of $m_\pi/m_\rho \approx 0.9$. We find that the Kramers equation algorithm gives an equally good performance as the HMC algorithm. We demonstrate that the classical equations of motion used in these algorithms lack reversibility in practical simulations and behave like those of a chaotic dynamical system with a Liapunov exponent $\nu \approx 0.75$.