Thermal excitation spectrum from entanglement in an expanding quantum string

TL;DR

This paper demonstrates that quantum entanglement in an expanding relativistic string naturally leads to a thermal spectrum of particles, explaining observed thermal properties in high-energy collisions without requiring frequent scatterings.

Contribution

It introduces a quantum entanglement framework for the relativistic string, deriving a thermal reduced density operator at early times in high-energy collisions.

Findings

Entanglement entropy becomes extensive at early proper times.

The reduced density operator is thermal with an entanglement temperature inversely proportional to proper time.

Thermal spectra emerge from quantum entanglement without scatterings.

Abstract

A surprising result in $e^+ e^-$ collisions is that the particle spectra from the string formed between the expanding quark-antiquark pair have thermal properties even though scatterings appear not to be frequent enough to explain this. We address this problem by considering the finite observable interval of a relativistic quantum string in terms of its reduced density operator by tracing over the complement region. We show how quantum entanglement in the presence of a horizon in spacetime for the causal transfer of information leads locally to a reduced mixed-state density operator. For very early proper time $\tau$, we show that the entanglement entropy becomes extensive and scales with the rapidity. At these early times, the reduced density operator is of thermal form, with an entanglement temperature $T_\tau=\hbar/(2\pi k_B \tau)$, even in the absence of any scatterings.