  Using the Husimi function, we investigate the phase space signatures of the
excited state quantum phase transitions (ESQPTs) in the Lipkin and coupled top
models. We show that the time evolution of the Husimi function exhibits
distinct behaviors between the different phases of an ESQPT and the presence of
an ESQPT is signaled by the particular dynamics of the Husimi function. We also
evaluate the long time averaged Husimi function and its associated marginal
distributions, and discuss how to identify the signatures of ESQPT from their
properties. Moreover, by exploiting the second moment and Wherl entropy of the
long-time averaged Husimi function, we estimate the critical points of ESQPTs,
demonstrating a good agreement with the analytical results. We thus provide
further evidence that the phase space methods is a valuable tool for the
studies of phase transitions and also open a new way to detect ESQPTs.
