Non-adiabatic transitions and non-equilibrium statistics of deforming nuclei

We establish a connection between macroscopic "heating or cooling" of a finite many-body quantum system and the non-adiabatic Landau-Zener-St\"{u}ckelberg transitions between its quantum states. We have considered the well-known Nilsson model for describing the single-particle states of nuclei and subject the system to a random walk in the deformation space. This subsumes modelling of an evolving many-body system where the dynamics is chaotic. We discover a universality in the distribution of final "temperatures", beginning with a canonical equilibrium at some temperature $T$. The quantum system is thrown out of equilibrium where free energy and work undergo fluctuations. These fluctuations are shown to respect Jarzynski inequality, and, the Bochkov-Kuzovlev equalities. We believe that this study will pave the way towards understanding non-equlibrium phenomena in other finite quantum systems like metallic clusters, quantum dots, and others.