Time Evolution of Pure Quantum State and Emergence of A Nearly Thermal State

TL;DR

This paper analyzes the evolution of pure quantum states in time-varying harmonic oscillators, revealing how they can exhibit nearly thermal behavior and relate to concepts like the Gibbons-Hawking temperature.

Contribution

It demonstrates that the asymptotic density matrix is determined by particle production, leading to nearly thermal states and providing insights into quantum field behavior in curved spacetime.

Findings

Oscillatory density matrix is determined by produced particles.

Time averaging yields classical or nearly thermal states.

Particle number obeys Planck distribution in a specific limit.

Abstract

Dynamical evolution of the quantum ground state (vacuum) is analyzed for time variant harmonic oscillators characterized by asymptotically constant frequency. The oscillatory density matrix in the asymptotic future is uniquely determined by a constant number of produced particles, independent of other details of transient behavior at intermediate times. Time average over one oscillation period yields a classical, in some cases even an almost thermal behavior. In an analytically soluble model the created particle number obeys the Planck distribution in a parameter limit. This suggests a new way of understanding the Gibbons-Hawking temperature in the de Sitter spacetime.