Abstract
Temporal evolution of a comoving qubit coupled to a scalar field in de Sitter space is studied with an emphasis on reliable extraction of late-time behaviour. The phenomenon of critical slowing down is observed if the effective mass is chosen to be sufficiently close to zero, which narrows the window of parameter space in which the Markovian approximation is valid. The dynamics of the system in this case are solved in a more general setting by accounting for non-Markovian effects in the evolution of the qubit state. Self-interactions for the scalar field are also incorporated, and reveal a breakdown of late-time perturbative predictions due to the presence of secular growth.
Highlights
Temporal evolution of a comoving qubit coupled to a scalar field in de Sitter space is studied with an emphasis on reliable extraction of late-time behaviour
We again identify the relevant master equation for differential qubit evolution once the field is integrated out, and again find that a Markovian approximation works at sufficiently late times, asymptotically approaching a thermal state in much the same manner as in [21]. de Sitter space brings an important complication, : the length of time required for this Markovian limit to apply grows like an inverse power of the scalar mass if this mass is sufficiently small
The Markovian approximation provides a simplistic description of the qubit state when the evolution is constrained to be extremely slow compared to the scales over which the Wightman function varies
Summary
This section reviews for later use some basic properties of de Sitter space, with details of the qubit/field system to be studied. The time evolution to be followed in later sections is along the coordinate direction within the flat slicing of de Sitter space, with line-element ds. Because the Ricci scalar for de Sitter space is constant, from the point of view of the scalar field the nonminimal coupling effectively shifts the scalar field’s mass from m to. Of particular interest for later evaluation of qubit evolution is the scalar field’s Wightman function evaluated in this vacuum, which turns out to be given by [43,44,45,46]. One would perform perturbation theory by expanding in powers of Hint 0 It happens, that at O(g2) the qubit/field interaction shifts the qubit energy splitting so that ω := E↑−E↓ = ω0+g2ω1 for calculable ω1. Not motivated by divergences, this counter-term interaction has an added benefit inasmuch as the quantity ω1 happens to cancel an ultraviolet divergence that arises at second order in g
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