Thermal excitation spectrum from entanglement in an expanding quantum string

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 τ 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_τ=ħ/(2πk_Bτ), even in the absence of any scatterings.