Universal dynamics of the entropy of work distribution in spinor Bose-Einstein condensates

Abstract

Driving a quantum many-body system across the quantum phase transition (QPT) in the finite time has been concerned in different branches of physics to explore various fundamental questions. Here, we analyze how the underlying QPT affects the work distribution $P(W)$, when the control parameter of a ferromagnetic spinor Bose-Einstein condensates is tuned through the critical point in the finite time. We show that the work distribution undergoes a dramatic change with increasing the driving time $\tau$. To capture the characteristics of the work distribution, we analyze the entropy of $P(W)$ and find three different regions in the evolution of entropy as a function of $\tau$. Specifically, the entropy is insensitive to the driving time in the region of very short $\tau$, while it exhibits a universal power-law decay in the region with intermediate value of $\tau$. In particular, the power-law scaling of the entropy is according with the well-known Kibble-Zurek mechanism. For the region with large $\tau$, the validity of the adiabatic perturbation theory leads to the entropy decay as $\tau^{-2}\ln\tau$. Our results verify the usefulness of the entropy of the work distribution for understanding the critical dynamics and provide an alternative way to experimentally study nonequilibrium properties in quantum many-body systems.