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

## TL;DR

This paper links non-adiabatic quantum transitions to non-equilibrium statistics in deforming nuclei, revealing universal temperature distributions and fluctuation relations in chaotic many-body quantum systems.

## Contribution

It introduces a novel connection between Landau-Zener transitions and non-equilibrium thermodynamics in finite quantum systems, using the Nilsson model with deformation space random walks.

## Key findings

- Universal distribution of final temperatures observed.
- Fluctuations in free energy and work obey Jarzynski and Bochkov-Kuzovlev equalities.
- Chaotic dynamics lead to non-equilibrium phenomena in quantum nuclei.

## Abstract

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.