# Quasi adiabatic dynamics of energy eigenstates for solvable quantum system at finite temperature

## TL;DR

This paper investigates the quasi-adiabatic evolution of energy eigenstates in a solvable quantum system at finite temperature, focusing on a dragged harmonic oscillator interacting with a reservoir, and analyzes deviations from ideal adiabatic behavior.

## Contribution

It provides a rigorous analysis of persistent amplitudes and phase behavior for energy eigenstates in a solvable quantum system under slow potential changes.

## Key findings

- Persistent amplitudes have common phase for ground and excited states
- Deviation from adiabaticity is quantitatively characterized
- The phase of persistent amplitudes remains consistent across states

## Abstract

It is a fundamental problem to characterize the nonequilibrium processes. For a slowly moving one-dimensional potential, we explore the quasi adiabatic dynamics of the initial energy eigenstates for a confined quantum system interacting with a large reservoir. For concreteness, we investigate a dragged harmonic oscillator linearly interacting with an assembly of harmonic oscillators, and explore the deviation from adiabatic processes by rigorously calculating the so-called persistent amplitude. In this way, we also show that the phase of the persistent amplitudes are common both for the ground and excited states.