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Phase transitions in nonequilibrium dynamics of many body quantum systems,theso-called dynamical phases transition (DPTs), play an important role forunderstanding various dynamical phenomena observed in different branches ofphysics.In general, there have two types of DPTs, the first one refers to thephase transition that is characterized by distinct evolution behaviors of aphysical observable, while the second one is marked by the nonanalyticities inthe rate function of the initial state survival probability. Here, we focus onsuch DPTs from both quantum and semiclassical perspectives in a spinorBose-Einstein condensate (BEC), an ideal platform to investigate nonequilibriumdynamics.By using the sudden quench process, we demonstrate that the systemexhibits both types of DPTs as the control parameter quenches through thecritical one, referring to as the critical quench. We show analytically how todetermine the critical quenches by means of the semiclassical approach andcarry out a detailed examination on both semiclassical and quantum signaturesof two types of DPTs. Moreover, we further reveal that the occurrence of DPTsis closely connected to the separatrix in the underlying classical system. Ourfindings provide more insights into the properties of DPTs and verify theusefulness of semiclassical analysis for understanding DPTs in quantum systemswith well-defined semiclassical limit.

Characterizing dynamical phase transitions in a spinor Bose-Einstein condensate via quantum and semiclassical analyses