  It was recently discovered that a crystalline many-body state can exist in
the phase space of a closed dynamical system. A phase space crystal can be an
anomalous Chern insulator that supports chiral topological transport without
breaking physical time-reversal symmetry [L. Guo et al., Phys. Rev. B 105,
094301 (2022)]. In this work, we further study the effects of an open
dissipative environment with thermal noise and identify the existence condition
of classical phase space crystals in realistic scenarios. By defining a crystal
order parameter, we plot the phase diagram in the parameter space of
dissipation rate, interaction, and temperature. Our present work paves the way
to realize phase space crystals and explore anomalous chiral transport in
experiments.
